Solanoa,b0000-0002-2971-8214, D. Soldia,b0000-0001-9059-4831, A.
Staianoa0000-0003-1803-624X, C. Tarriconea,b0000-0001-6233-0513, M.
Tornagoa,b0000-0001-6768-1056, D. Trocinoa0000-0002-2830-5872, G.
Umoreta,b0000-0002-6674-7874, E. Vlasova,b0000-0002-8628-2090

INFN Sezione di Triestea, Università di Triesteb, Trieste, Italy S.
Belfortea0000-0001-8443-4460, V. Candelisea,b0000-0002-3641-5983, M.
Casarsaa0000-0002-1353-8964, F. Cossuttia0000-0001-5672-214X, K. De
Leoa,b0000-0002-8908-409X, G. Della Riccaa,b0000-0003-2831-6982

Kyungpook National University, Daegu, Korea S. Dogra0000-0002-0812-0758, J.
Hong0000-0002-9463-4922, C. Huh0000-0002-8513-2824, B. Kim0000-0002-9539-6815,
D.H. Kim0000-0002-9023-6847, J. Kim, H. Lee, S.W. Lee0000-0002-1028-3468, C.S.
Moon0000-0001-8229-7829, Y.D. Oh0000-0002-7219-9931, S.I.
Pak0000-0002-1447-3533, M.S. Ryu0000-0002-1855-180X, S.
Sekmen0000-0003-1726-5681, Y.C. Yang0000-0003-1009-4621

Chonnam National University, Institute for Universe and Elementary Particles,
Kwangju, Korea G. Bak0000-0002-0095-8185, P. Gwak0009-0009-7347-1480, H.
Kim0000-0001-8019-9387, D.H. Moon0000-0002-5628-9187

Hanyang University, Seoul, Korea E. Asilar0000-0001-5680-599X, D.
Kim0000-0002-8336-9182, T.J. Kim0000-0001-8336-2434, J.A. Merlin, J.
Park0000-0002-4683-6669

Korea University, Seoul, Korea S. Choi0000-0001-6225-9876, S. Han, B.
Hong0000-0002-2259-9929, K. Lee, K.S. Lee0000-0002-3680-7039, J. Park, S.K.
Park, J. Yoo0000-0003-0463-3043

Kyung Hee University, Department of Physics, Seoul, Korea J.
Goh0000-0002-1129-2083

Sejong University, Seoul, Korea H. S. Kim0000-0002-6543-9191, Y. Kim, S. Lee

Seoul National University, Seoul, Korea J. Almond, J.H. Bhyun, J.
Choi0000-0002-2483-5104, S. Jeon0000-0003-1208-6940, W.
Jun0009-0001-5122-4552, J. Kim0000-0001-9876-6642, J.S. Kim, S.
Ko0000-0003-4377-9969, H. Kwon0009-0002-5165-5018, H. Lee0000-0002-1138-3700,
J. Lee0000-0001-6753-3731, J. Lee0000-0002-5351-7201, S. Lee, B.H.
Oh0000-0002-9539-7789, S.B. Oh0000-0003-0710-4956, H. Seo0000-0002-3932-0605,
U.K. Yang, I. Yoon0000-0002-3491-8026

University of Seoul, Seoul, Korea W. Jang0000-0002-1571-9072, D.Y. Kang, Y.
Kang0000-0001-6079-3434, S. Kim0000-0002-8015-7379, B. Ko, J.S.H.
Lee0000-0002-2153-1519, Y. Lee0000-0001-5572-5947, I.C.
Park0000-0003-4510-6776, Y. Roh, I.J. Watson0000-0003-2141-3413, S.
Yang0000-0001-6905-6553

Yonsei University, Department of Physics, Seoul, Korea S.
Ha0000-0003-2538-1551, H.D. Yoo0000-0002-3892-3500

Sungkyunkwan University, Suwon, Korea M. Choi0000-0002-4811-626X, M.R.
Kim0000-0002-2289-2527, H. Lee, Y. Lee0000-0001-6954-9964, I.
Yu0000-0003-1567-5548

College of Engineering and Technology, American University of the Middle East
(AUM), Dasman, Kuwait T. Beyrouthy, Y. Maghrbi0000-0002-4960-7458

Riga Technical University, Riga, Latvia K. Dreimanis0000-0003-0972-5641, A.
Gaile0000-0003-1350-3523, G. Pikurs, A. Potrebko0000-0002-3776-8270, M.
Seidel0000-0003-3550-6151, V. Veckalns550000-0003-3676-9711

University of Latvia (LU), Riga, Latvia N.R. Strautnieks0000-0003-4540-9048

Vilnius University, Vilnius, Lithuania M. Ambrozas0000-0003-2449-0158, A.
Juodagalvis0000-0002-1501-3328, A. Rinkevicius0000-0002-7510-255X, G.
Tamulaitis0000-0002-2913-9634

National Centre for Particle Physics, Universiti Malaya, Kuala Lumpur,
Malaysia N. Bin Norjoharuddeen0000-0002-8818-7476, I.
Yusuff560000-0003-2786-0732, Z. Zolkapli

Universidad de Sonora (UNISON), Hermosillo, Mexico J.F.
Benitez0000-0002-2633-6712, A. Castaneda Hernandez0000-0003-4766-1546, H.A.
Encinas Acosta, L.G. Gallegos Maríñez, M. León Coello0000-0002-3761-911X, J.A.
Murillo Quijada0000-0003-4933-2092, A. Sehrawat0000-0002-6816-7814, L.
Valencia Palomo0000-0002-8736-440X

Centro de Investigacion y de Estudios Avanzados del IPN, Mexico City, Mexico
G. Ayala0000-0002-8294-8692, H. Castilla-Valdez0009-0005-9590-9958, E. De La
Cruz-Burelo0000-0002-7469-6974, I. Heredia-De La Cruz570000-0002-8133-6467, R.
Lopez-Fernandez0000-0002-2389-4831, C.A. Mondragon Herrera, A. Sánchez
Hernández0000-0001-9548-0358

Universidad Iberoamericana, Mexico City, Mexico C. Oropeza
Barrera0000-0001-9724-0016, M. Ramírez García0000-0002-4564-3822

Benemerita Universidad Autonoma de Puebla, Puebla, Mexico I.
Bautista0000-0001-5873-3088, I. Pedraza0000-0002-2669-4659, H.A. Salazar
Ibarguen0000-0003-4556-7302, C. Uribe Estrada0000-0002-2425-7340

University of Montenegro, Podgorica, Montenegro I. Bubanja, N.
Raicevic0000-0002-2386-2290

University of Canterbury, Christchurch, New Zealand P.H.
Butler0000-0001-9878-2140

National Centre for Physics, Quaid-I-Azam University, Islamabad, Pakistan A.
Ahmad0000-0002-4770-1897, M.I. Asghar, A. Awais0000-0003-3563-257X, M.I.M.
Awan, H.R. Hoorani0000-0002-0088-5043, W.A. Khan0000-0003-0488-0941

AGH University of Krakow, Faculty of Computer Science, Electronics and
Telecommunications, Krakow, Poland V. Avati, L. Grzanka0000-0002-3599-854X, M.
Malawski0000-0001-6005-0243

National Centre for Nuclear Research, Swierk, Poland H.
Bialkowska0000-0002-5956-6258, M. Bluj0000-0003-1229-1442, B.
Boimska0000-0002-4200-1541, M. Górski0000-0003-2146-187X, M.
Kazana0000-0002-7821-3036, M. Szleper0000-0002-1697-004X, P.
Zalewski0000-0003-4429-2888

Institute of Experimental Physics, Faculty of Physics, University of Warsaw,
Warsaw, Poland K. Bunkowski0000-0001-6371-9336, K. Doroba0000-0002-7818-2364,
A. Kalinowski0000-0002-1280-5493, M. Konecki0000-0001-9482-4841, J.
Krolikowski0000-0002-3055-0236, A. Muhammad0000-0002-7535-7149

Laboratório de Instrumentação e Física Experimental de Partículas, Lisboa,
Portugal M. Araujo0000-0002-8152-3756, D. Bastos0000-0002-7032-2481, C. Beirão
Da Cruz E Silva0000-0002-1231-3819, A. Boletti0000-0003-3288-7737, M.
Bozzo0000-0002-1715-0457, P. Faccioli0000-0003-1849-6692, M.
Gallinaro0000-0003-1261-2277, J. Hollar0000-0002-8664-0134, N.
Leonardo0000-0002-9746-4594, T. Niknejad0000-0003-3276-9482, A.
Petrilli0000-0003-0887-1882, M. Pisano0000-0002-0264-7217, J.
Seixas0000-0002-7531-0842, J. Varela0000-0003-2613-3146

Faculty of Physics, University of Belgrade, Belgrade, Serbia P.
Adzic0000-0002-5862-7397, P. Milenovic0000-0001-7132-3550

VINCA Institute of Nuclear Sciences, University of Belgrade, Belgrade, Serbia
M. Dordevic0000-0002-8407-3236, J. Milosevic0000-0001-8486-4604, V. Rekovic

Centro de Investigaciones Energéticas Medioambientales y Tecnológicas
(CIEMAT), Madrid, Spain M. Aguilar-Benitez, J. Alcaraz
Maestre0000-0003-0914-7474, M. Barrio Luna, Cristina F.
Bedoya0000-0001-8057-9152, M. Cepeda0000-0002-6076-4083, M.
Cerrada0000-0003-0112-1691, N. Colino0000-0002-3656-0259, B. De La
Cruz0000-0001-9057-5614, A. Delgado Peris0000-0002-8511-7958, D. Fernández Del
Val0000-0003-2346-1590, J.P. Fernández Ramos0000-0002-0122-313X, J.
Flix0000-0003-2688-8047, M.C. Fouz0000-0003-2950-976X, O. Gonzalez
Lopez0000-0002-4532-6464, S. Goy Lopez0000-0001-6508-5090, J.M.
Hernandez0000-0001-6436-7547, M.I. Josa0000-0002-4985-6964, J. León
Holgado0000-0002-4156-6460, D. Moran0000-0002-1941-9333, C. M. Morcillo
Perez0000-0001-9634-848X, Á. Navarro Tobar0000-0003-3606-1780, C. Perez
Dengra0000-0003-2821-4249, A. Pérez-Calero Yzquierdo0000-0003-3036-7965, J.
Puerta Pelayo0000-0001-7390-1457, I. Redondo0000-0003-3737-4121, D.D. Redondo
Ferrero0000-0002-3463-0559, L. Romero, S. Sánchez Navas0000-0001-6129-9059, L.
Urda Gómez0000-0002-7865-5010, J. Vazquez Escobar0000-0002-7533-2283, C.
Willmott

Universidad Autónoma de Madrid, Madrid, Spain J.F. de
Trocóniz0000-0002-0798-9806

Universidad de Oviedo, Instituto Universitario de Ciencias y Tecnologías
Espaciales de Asturias (ICTEA), Oviedo, Spain B. Alvarez
Gonzalez0000-0001-7767-4810, J. Cuevas0000-0001-5080-0821, J. Fernandez
Menendez0000-0002-5213-3708, S. Folgueras0000-0001-7191-1125, I. Gonzalez
Caballero0000-0002-8087-3199, J.R. González Fernández0000-0002-4825-8188, E.
Palencia Cortezon0000-0001-8264-0287, C. Ramón Álvarez0000-0003-1175-0002, V.
Rodríguez Bouza0000-0002-7225-7310, A. Soto Rodríguez0000-0002-2993-8663, A.
Trapote0000-0002-4030-2551, C. Vico Villalba0000-0002-1905-1874, P.
Vischia0000-0002-7088-8557

Instituto de Física de Cantabria (IFCA), CSIC-Universidad de Cantabria,
Santander, Spain S. Bhowmik0000-0003-1260-973X, S. Blanco
Fernández0000-0001-7301-0670, J.A. Brochero Cifuentes0000-0003-2093-7856, I.J.
Cabrillo0000-0002-0367-4022, A. Calderon0000-0002-7205-2040, J. Duarte
Campderros0000-0003-0687-5214, M. Fernandez0000-0002-4824-1087, C. Fernandez
Madrazo0000-0001-9748-4336, G. Gomez0000-0002-1077-6553, C. Lasaosa
García0000-0003-2726-7111, C. Martinez Rivero0000-0002-3224-956X, P. Martinez
Ruiz del Arbol0000-0002-7737-5121, F. Matorras0000-0003-4295-5668, P. Matorras
Cuevas0000-0001-7481-7273, E. Navarrete Ramos0000-0002-5180-4020, J. Piedra
Gomez0000-0002-9157-1700, C. Prieels, L. Scodellaro0000-0002-4974-8330, I.
Vila0000-0002-6797-7209, J.M. Vizan Garcia0000-0002-6823-8854

University of Colombo, Colombo, Sri Lanka M.K. Jayananda0000-0002-7577-310X,
B. Kailasapathy580000-0003-2424-1303, D.U.J. Sonnadara0000-0001-7862-2537,
D.D.C. Wickramarathna0000-0002-6941-8478

University of Ruhuna, Department of Physics, Matara, Sri Lanka W.G.D.
Dharmaratna0000-0002-6366-837X, K. Liyanage0000-0002-3792-7665, N.
Perera0000-0002-4747-9106, N. Wickramage0000-0001-7760-3537

CERN, European Organization for Nuclear Research, Geneva, Switzerland D.
Abbaneo0000-0001-9416-1742, C. Amendola0000-0002-4359-836X, E.
Auffray0000-0001-8540-1097, G. Auzinger0000-0001-7077-8262, J. Baechler, D.
Barney0000-0002-4927-4921, A. Bermúdez Martínez0000-0001-8822-4727, M.
Bianco0000-0002-8336-3282, B. Bilin0000-0003-1439-7128, A.A. Bin
Anuar0000-0002-2988-9830, A. Bocci0000-0002-6515-5666, E.
Brondolin0000-0001-5420-586X, C. Caillol0000-0002-5642-3040, T.
Camporesi0000-0001-5066-1876, G. Cerminara0000-0002-2897-5753, N.
Chernyavskaya0000-0002-2264-2229, D. d’Enterria0000-0002-5754-4303, A.
Dabrowski0000-0003-2570-9676, A. David0000-0001-5854-7699, A. De
Roeck0000-0002-9228-5271, M.M. Defranchis0000-0001-9573-3714, M.
Deile0000-0001-5085-7270, M. Dobson0009-0007-5021-3230, F. Fallavollita59, L.
Forthomme0000-0002-3302-336X, G. Franzoni0000-0001-9179-4253, W.
Funk0000-0003-0422-6739, S. Giani, D. Gigi, K. Gill0009-0001-9331-5145, F.
Glege0000-0002-4526-2149, L. Gouskos0000-0002-9547-7471, M.
Haranko0000-0002-9376-9235, J. Hegeman0000-0002-2938-2263, V.
Innocente0000-0003-3209-2088, T. James0000-0002-3727-0202, P.
Janot0000-0001-7339-4272, J. Kieseler0000-0003-1644-7678, S.
Laurila0000-0001-7507-8636, P. Lecoq0000-0002-3198-0115, E.
Leutgeb0000-0003-4838-3306, C. Lourenço0000-0003-0885-6711, B.
Maier0000-0001-5270-7540, L. Malgeri0000-0002-0113-7389, M.
Mannelli0000-0003-3748-8946, A.C. Marini0000-0003-2351-0487, F.
Meijers0000-0002-6530-3657, S. Mersi0000-0003-2155-6692, E.
Meschi0000-0003-4502-6151, V. Milosevic0000-0002-1173-0696, F.
Moortgat0000-0001-7199-0046, M. Mulders0000-0001-7432-6634, S. Orfanelli, F.
Pantaleo0000-0003-3266-4357, M. Peruzzi0000-0002-0416-696X, G.
Petrucciani0000-0003-0889-4726, A. Pfeiffer0000-0001-5328-448X, M.
Pierini0000-0003-1939-4268, D. Piparo0009-0006-6958-3111, H.
Qu0000-0002-0250-8655, D. Rabady0000-0001-9239-0605, G. Reales Gutiérrez, M.
Rovere0000-0001-8048-1622, H. Sakulin0000-0003-2181-7258, S.
Scarfi0009-0006-8689-3576, M. Selvaggi0000-0002-5144-9655, A.
Sharma0000-0002-9860-1650, K. Shchelina0000-0003-3742-0693, P.
Silva0000-0002-5725-041X, P. Sphicas600000-0002-5456-5977, A.G. Stahl
Leiton0000-0002-5397-252X, A. Steen0009-0006-4366-3463, S.
Summers0000-0003-4244-2061, D. Treille0009-0005-5952-9843, P.
Tropea0000-0003-1899-2266, A. Tsirou, D. Walter0000-0001-8584-9705, J.
Wanczyk610000-0002-8562-1863, K.A. Wozniak620000-0002-4395-1581, P.
Zehetner0009-0002-0555-4697, P. Zejdl0000-0001-9554-7815, W.D. Zeuner

Paul Scherrer Institut, Villigen, Switzerland T.
Bevilacqua630000-0001-9791-2353, L. Caminada630000-0001-5677-6033, A.
Ebrahimi0000-0003-4472-867X, W. Erdmann0000-0001-9964-249X, R.
Horisberger0000-0002-5594-1321, Q. Ingram0000-0002-9576-055X, H.C.
Kaestli0000-0003-1979-7331, D. Kotlinski0000-0001-5333-4918, C.
Lange0000-0002-3632-3157, M. Missiroli630000-0002-1780-1344, L.
Noehte630000-0001-6125-7203, T. Rohe0009-0005-6188-7754

ETH Zurich - Institute for Particle Physics and Astrophysics (IPA), Zurich,
Switzerland T.K. Aarrestad0000-0002-7671-243X, K.
Androsov610000-0003-2694-6542, M. Backhaus0000-0002-5888-2304, A.
Calandri0000-0001-7774-0099, C. Cazzaniga0000-0003-0001-7657, K.
Datta0000-0002-6674-0015, A. De Cosa0000-0003-2533-2856, G.
Dissertori0000-0002-4549-2569, M. Dittmar, M. Donegà0000-0001-9830-0412, F.
Eble0009-0002-0638-3447, M. Galli0000-0002-9408-4756, K.
Gedia0009-0006-0914-7684, F. Glessgen0000-0001-5309-1960, C.
Grab0000-0002-6182-3380, D. Hits0000-0002-3135-6427, W.
Lustermann0000-0003-4970-2217, A.-M. Lyon0009-0004-1393-6577, R.A.
Manzoni0000-0002-7584-5038, M. Marchegiani0000-0002-0389-8640, L.
Marchese0000-0001-6627-8716, C. Martin Perez0000-0003-1581-6152, A.
Mascellani610000-0001-6362-5356, F. Nessi-Tedaldi0000-0002-4721-7966, F.
Pauss0000-0002-3752-4639, V. Perovic0009-0002-8559-0531, S.
Pigazzini0000-0002-8046-4344, M.G. Ratti0000-0003-1777-7855, M.
Reichmann0000-0002-6220-5496, C. Reissel0000-0001-7080-1119, T.
Reitenspiess0000-0002-2249-0835, B. Ristic0000-0002-8610-1130, F.
Riti0000-0002-1466-9077, D. Ruini, D.A. Sanz Becerra0000-0002-6610-4019, R.
Seidita0000-0002-3533-6191, J. Steggemann610000-0003-4420-5510, D.
Valsecchi0000-0001-8587-8266, R. Wallny0000-0001-8038-1613

Universität Zürich, Zurich, Switzerland C. Amsler640000-0002-7695-501X, P.
Bärtschi0000-0002-8842-6027, C. Botta0000-0002-8072-795X, D. Brzhechko, M.F.
Canelli0000-0001-6361-2117, K. Cormier0000-0001-7873-3579, R. Del Burgo, J.K.
Heikkilä0000-0002-0538-1469, M. Huwiler0000-0002-9806-5907, W.
Jin0009-0009-8976-7702, A. Jofrehei0000-0002-8992-5426, B.
Kilminster0000-0002-6657-0407, S. Leontsinis0000-0002-7561-6091, S.P.
Liechti0000-0002-1192-1628, A. Macchiolo0000-0003-0199-6957, P.
Meiring0009-0001-9480-4039, V.M. Mikuni0000-0002-1579-2421, U.
Molinatti0000-0002-9235-3406, I. Neutelings0009-0002-6473-1403, A.
Reimers0000-0002-9438-2059, P. Robmann, S. Sanchez Cruz0000-0002-9991-195X, K.
Schweiger0000-0002-5846-3919, M. Senger0000-0002-1992-5711, Y.
Takahashi0000-0001-5184-2265

National Central University, Chung-Li, Taiwan C. Adloff65, C.M. Kuo, W. Lin,
P.K. Rout0000-0001-8149-6180, P.C. Tiwari390000-0002-3667-3843, S.S.
Yu0000-0002-6011-8516

National Taiwan University (NTU), Taipei, Taiwan L. Ceard, Y.
Chao0000-0002-5976-318X, K.F. Chen0000-0003-1304-3782, P.s. Chen, Z.g. Chen,
W.-S. Hou0000-0002-4260-5118, T.h. Hsu, Y.w. Kao, R. Khurana, G.
Kole0000-0002-3285-1497, Y.y. Li0000-0003-3598-556X, R.-S.
Lu0000-0001-6828-1695, E. Paganis0000-0002-1950-8993, A. Psallidas, X.f. Su,
J. Thomas-Wilsker0000-0003-1293-4153, H.y. Wu, E. Yazgan0000-0001-5732-7950

High Energy Physics Research Unit, Department of Physics, Faculty of Science,
Chulalongkorn University, Bangkok, Thailand C.
Asawatangtrakuldee0000-0003-2234-7219, N. Srimanobhas0000-0003-3563-2959, V.
Wachirapusitanand0000-0001-8251-5160

Çukurova University, Physics Department, Science and Art Faculty, Adana,
Turkey D. Agyel0000-0002-1797-8844, F. Boran0000-0002-3611-390X, Z.S.
Demiroglu0000-0001-7977-7127, F. Dolek0000-0001-7092-5517, I.
Dumanoglu660000-0002-0039-5503, E. Eskut0000-0001-8328-3314, Y.
Guler670000-0001-7598-5252, E. Gurpinar Guler670000-0002-6172-0285, C.
Isik0000-0002-7977-0811, O. Kara, A. Kayis Topaksu0000-0002-3169-4573, U.
Kiminsu0000-0001-6940-7800, G. Onengut0000-0002-6274-4254, K.
Ozdemir680000-0002-0103-1488, A. Polatoz0000-0001-9516-0821, B.
Tali690000-0002-7447-5602, U.G. Tok0000-0002-3039-021X, S.
Turkcapar0000-0003-2608-0494, E. Uslan0000-0002-2472-0526, I.S.
Zorbakir0000-0002-5962-2221

Middle East Technical University, Physics Department, Ankara, Turkey K.
Ocalan700000-0002-8419-1400, M. Yalvac710000-0003-4915-9162

Bogazici University, Istanbul, Turkey B. Akgun0000-0001-8888-3562, I.O.
Atakisi0000-0002-9231-7464, E. Gülmez0000-0002-6353-518X, M.
Kaya720000-0003-2890-4493, O. Kaya730000-0002-8485-3822, S.
Tekten740000-0002-9624-5525

Istanbul Technical University, Istanbul, Turkey A. Cakir0000-0002-8627-7689,
K. Cankocak660000-0002-3829-3481, Y. Komurcu0000-0002-7084-030X, S.
Sen750000-0001-7325-1087

Istanbul University, Istanbul, Turkey O. Aydilek0000-0002-2567-6766, S.
Cerci690000-0002-8702-6152, V. Epshteyn0000-0002-8863-6374, B.
Hacisahinoglu0000-0002-2646-1230, I. Hos760000-0002-7678-1101, B.
Isildak770000-0002-0283-5234, B. Kaynak0000-0003-3857-2496, S.
Ozkorucuklu0000-0001-5153-9266, O. Potok0009-0005-1141-6401, H.
Sert0000-0003-0716-6727, C. Simsek0000-0002-7359-8635, D. Sunar
Cerci690000-0002-5412-4688, C. Zorbilmez0000-0002-5199-061X

Institute for Scintillation Materials of National Academy of Science of
Ukraine, Kharkiv, Ukraine A. Boyaryntsev0000-0001-9252-0430, B.
Grynyov0000-0003-1700-0173

National Science Centre, Kharkiv Institute of Physics and Technology, Kharkiv,
Ukraine L. Levchuk0000-0001-5889-7410

University of Bristol, Bristol, United Kingdom D. Anthony0000-0002-5016-8886,
J.J. Brooke0000-0003-2529-0684, A. Bundock0000-0002-2916-6456, F.
Bury0000-0002-3077-2090, E. Clement0000-0003-3412-4004, D.
Cussans0000-0001-8192-0826, H. Flacher0000-0002-5371-941X, M. Glowacki, J.
Goldstein0000-0003-1591-6014, H.F. Heath0000-0001-6576-9740, L.
Kreczko0000-0003-2341-8330, B. Krikler0000-0001-9712-0030, S.
Paramesvaran0000-0003-4748-8296, S. Seif El Nasr-Storey, V.J.
Smith0000-0003-4543-2547, N. Stylianou780000-0002-0113-6829, K. Walkingshaw
Pass, R. White0000-0001-5793-526X

Rutherford Appleton Laboratory, Didcot, United Kingdom A.H. Ball, K.W.
Bell0000-0002-2294-5860, A. Belyaev790000-0002-1733-4408, C.
Brew0000-0001-6595-8365, R.M. Brown0000-0002-6728-0153, D.J.A.
Cockerill0000-0003-2427-5765, C. Cooke0000-0003-3730-4895, K.V. Ellis, K.
Harder0000-0002-2965-6973, S. Harper0000-0001-5637-2653, M.-L.
Holmberg800000-0002-9473-5985, Sh. Jain0000-0003-1770-5309, J.
Linacre0000-0001-7555-652X, K. Manolopoulos, D.M. Newbold0000-0002-9015-9634,
E. Olaiya, D. Petyt0000-0002-2369-4469, T. Reis0000-0003-3703-6624, G.
Salvi0000-0002-2787-1063, T. Schuh, C.H. Shepherd-
Themistocleous0000-0003-0551-6949, I.R. Tomalin0000-0003-2419-4439, T.
Williams0000-0002-8724-4678

Imperial College, London, United Kingdom R. Bainbridge0000-0001-9157-4832, P.
Bloch0000-0001-6716-979X, C.E. Brown0000-0002-7766-6615, O. Buchmuller, V.
Cacchio, C.A. Carrillo Montoya0000-0002-6245-6535, G.S.
Chahal810000-0003-0320-4407, D. Colling0000-0001-9959-4977, J.S. Dancu, P.
Dauncey0000-0001-6839-9466, G. Davies0000-0001-8668-5001, J. Davies, M. Della
Negra0000-0001-6497-8081, S. Fayer, G. Fedi0000-0001-9101-2573, G.
Hall0000-0002-6299-8385, M.H. Hassanshahi0000-0001-6634-4517, A. Howard, G.
Iles0000-0002-1219-5859, M. Knight0009-0008-1167-4816, J.
Langford0000-0002-3931-4379, L. Lyons0000-0001-7945-9188, A.-M.
Magnan0000-0002-4266-1646, S. Malik, A. Martelli0000-0003-3530-2255, M.
Mieskolainen0000-0001-8893-7401, J. Nash820000-0003-0607-6519, M. Pesaresi,
B.C. Radburn-Smith0000-0003-1488-9675, A. Richards, A.
Rose0000-0002-9773-550X, C. Seez0000-0002-1637-5494, R.
Shukla0000-0001-5670-5497, A. Tapper0000-0003-4543-864X, K.
Uchida0000-0003-0742-2276, G.P. Uttley0009-0002-6248-6467, L.H. Vage, T.
Virdee280000-0001-7429-2198, M. Vojinovic0000-0001-8665-2808, N.
Wardle0000-0003-1344-3356, D. Winterbottom0000-0003-4582-150X

Brunel University, Uxbridge, United Kingdom K. Coldham, J.E.
Cole0000-0001-5638-7599, A. Khan, P. Kyberd0000-0002-7353-7090, I.D.
Reid0000-0002-9235-779X

Baylor University, Waco, Texas, USA S. Abdullin0000-0003-4885-6935, A.
Brinkerhoff0000-0002-4819-7995, B. Caraway0000-0002-6088-2020, J.
Dittmann0000-0002-1911-3158, K. Hatakeyama0000-0002-6012-2451, J.
Hiltbrand0000-0003-1691-5937, A.R. Kanuganti0000-0002-0789-1200, B.
McMaster0000-0002-4494-0446, M. Saunders0000-0003-1572-9075, S.
Sawant0000-0002-1981-7753, C. Sutantawibul0000-0003-0600-0151, M.
Toms830000-0002-7703-3973, J. Wilson0000-0002-5672-7394

Catholic University of America, Washington, DC, USA R.
Bartek0000-0002-1686-2882, A. Dominguez0000-0002-7420-5493, C. Huerta
Escamilla, A.E. Simsek0000-0002-9074-2256, R. Uniyal0000-0001-7345-6293, A.M.
Vargas Hernandez0000-0002-8911-7197

The University of Alabama, Tuscaloosa, Alabama, USA R.
Chudasama0009-0007-8848-6146, S.I. Cooper0000-0002-4618-0313, S.V.
Gleyzer0000-0002-6222-8102, C.U. Perez0000-0002-6861-2674, P.
Rumerio840000-0002-1702-5541, E. Usai0000-0001-9323-2107, C.
West0000-0003-4460-2241, R. Yi0000-0001-5818-1682

Boston University, Boston, Massachusetts, USA A. Akpinar0000-0001-7510-6617,
A. Albert0000-0003-2369-9507, D. Arcaro0000-0001-9457-8302, C.
Cosby0000-0003-0352-6561, Z. Demiragli0000-0001-8521-737X, C.
Erice0000-0002-6469-3200, E. Fontanesi0000-0002-0662-5904, D.
Gastler0009-0000-7307-6311, J. Rohlf0000-0001-6423-9799, K.
Salyer0000-0002-6957-1077, D. Sperka0000-0002-4624-2019, D.
Spitzbart0000-0003-2025-2742, I. Suarez0000-0002-5374-6995, A.
Tsatsos0000-0001-8310-8911, S. Yuan0000-0002-2029-024X

Brown University, Providence, Rhode Island, USA G. Benelli0000-0003-4461-8905,
X. Coubez23, D. Cutts0000-0003-1041-7099, M. Hadley0000-0002-7068-4327, U.
Heintz0000-0002-7590-3058, J.M. Hogan850000-0002-8604-3452, T.
Kwon0000-0001-9594-6277, G. Landsberg0000-0002-4184-9380, K.T.
Lau0000-0003-1371-8575, D. Li0000-0003-0890-8948, J. Luo0000-0002-4108-8681,
S. Mondal0000-0003-0153-7590, M.
Narain${}^{\textrm{\textdagger}}$0000-0002-7857-7403, N.
Pervan0000-0002-8153-8464, S. Sagir860000-0002-2614-5860, F.
Simpson0000-0001-8944-9629, M. Stamenkovic0000-0003-2251-0610, W.Y. Wong, X.
Yan0000-0002-6426-0560, W. Zhang

University of California, Davis, Davis, California, USA S.
Abbott0000-0002-7791-894X, J. Bonilla0000-0002-6982-6121, C.
Brainerd0000-0002-9552-1006, R. Breedon0000-0001-5314-7581, M. Calderon De La
Barca Sanchez0000-0001-9835-4349, M. Chertok0000-0002-2729-6273, M.
Citron0000-0001-6250-8465, J. Conway0000-0003-2719-5779, P.T.
Cox0000-0003-1218-2828, R. Erbacher0000-0001-7170-8944, G.
Haza0009-0001-1326-3956, F. Jensen0000-0003-3769-9081, O.
Kukral0009-0007-3858-6659, G. Mocellin0000-0002-1531-3478, M.
Mulhearn0000-0003-1145-6436, D. Pellett0009-0000-0389-8571, B.
Regnery0000-0003-1539-923X, W. Wei0000-0003-4221-1802, Y.
Yao0000-0002-5990-4245, F. Zhang0000-0002-6158-2468

University of California, Los Angeles, California, USA M.
Bachtis0000-0003-3110-0701, R. Cousins0000-0002-5963-0467, A.
Datta0000-0003-2695-7719, J. Hauser0000-0002-9781-4873, M.
Ignatenko0000-0001-8258-5863, M.A. Iqbal0000-0001-8664-1949, T.
Lam0000-0002-0862-7348, E. Manca0000-0001-8946-655X, W.A.
Nash0009-0004-3633-8967, D. Saltzberg0000-0003-0658-9146, B.
Stone0000-0002-9397-5231, V. Valuev0000-0002-0783-6703

University of California, Riverside, Riverside, California, USA R.
Clare0000-0003-3293-5305, M. Gordon, G. Hanson0000-0002-7273-4009, W.
Si0000-0002-5879-6326, S.
Wimpenny${}^{\textrm{\textdagger}}$0000-0003-0505-4908

University of California, San Diego, La Jolla, California, USA J.G.
Branson0009-0009-5683-4614, S. Cittolin0000-0002-0922-9587, S.
Cooperstein0000-0003-0262-3132, D. Diaz0000-0001-6834-1176, J.
Duarte0000-0002-5076-7096, R. Gerosa0000-0001-8359-3734, L.
Giannini0000-0002-5621-7706, J. Guiang0000-0002-2155-8260, R.
Kansal0000-0003-2445-1060, V. Krutelyov0000-0002-1386-0232, R.
Lee0009-0000-4634-0797, J. Letts0000-0002-0156-1251, M.
Masciovecchio0000-0002-8200-9425, F. Mokhtar0000-0003-2533-3402, M.
Pieri0000-0003-3303-6301, M. Quinnan0000-0003-2902-5597, B.V. Sathia
Narayanan0000-0003-2076-5126, V. Sharma0000-0003-1736-8795, M.
Tadel0000-0001-8800-0045, E. Vourliotis0000-0002-2270-0492, F.
Würthwein0000-0001-5912-6124, Y. Xiang0000-0003-4112-7457, A.
Yagil0000-0002-6108-4004

University of California, Santa Barbara - Department of Physics, Santa
Barbara, California, USA A. Barzdukas0000-0002-0518-3286, L.
Brennan0000-0003-0636-1846, C. Campagnari0000-0002-8978-8177, G.
Collura0000-0002-4160-1844, A. Dorsett0000-0001-5349-3011, J.
Incandela0000-0001-9850-2030, M. Kilpatrick0000-0002-2602-0566, J.
Kim0000-0002-2072-6082, A.J. Li0000-0002-3895-717X, P.
Masterson0000-0002-6890-7624, H. Mei0000-0002-9838-8327, M.
Oshiro0000-0002-2200-7516, J. Richman0000-0002-5189-146X, U.
Sarica0000-0002-1557-4424, R. Schmitz0000-0003-2328-677X, F.
Setti0000-0001-9800-7822, J. Sheplock0000-0002-8752-1946, D.
Stuart0000-0002-4965-0747, S. Wang0000-0001-7887-1728

California Institute of Technology, Pasadena, California, USA A.
Bornheim0000-0002-0128-0871, O. Cerri, A. Latorre, J.M.
Lawhorn0000-0002-8597-9259, J. Mao0009-0002-8988-9987, H.B.
Newman0000-0003-0964-1480, T. Q. Nguyen0000-0003-3954-5131, M.
Spiropulu0000-0001-8172-7081, J.R. Vlimant0000-0002-9705-101X, C.
Wang0000-0002-0117-7196, S. Xie0000-0003-2509-5731, R.Y.
Zhu0000-0003-3091-7461

Carnegie Mellon University, Pittsburgh, Pennsylvania, USA J.
Alison0000-0003-0843-1641, S. An0000-0002-9740-1622, M.B.
Andrews0000-0001-5537-4518, P. Bryant0000-0001-8145-6322, V.
Dutta0000-0001-5958-829X, T. Ferguson0000-0001-5822-3731, A.
Harilal0000-0001-9625-1987, C. Liu0000-0002-3100-7294, T.
Mudholkar0000-0002-9352-8140, S. Murthy0000-0002-1277-9168, M.
Paulini0000-0002-6714-5787, A. Roberts0000-0002-5139-0550, A.
Sanchez0000-0002-5431-6989, W. Terrill0000-0002-2078-8419

University of Colorado Boulder, Boulder, Colorado, USA J.P.
Cumalat0000-0002-6032-5857, W.T. Ford0000-0001-8703-6943, A.
Hassani0009-0008-4322-7682, G. Karathanasis0000-0001-5115-5828, E. MacDonald,
N. Manganelli0000-0002-3398-4531, F. Marini0000-0002-2374-6433, A.
Perloff0000-0001-5230-0396, C. Savard0009-0000-7507-0570, N.
Schonbeck0009-0008-3430-7269, K. Stenson0000-0003-4888-205X, K.A.
Ulmer0000-0001-6875-9177, S.R. Wagner0000-0002-9269-5772, N.
Zipper0000-0002-4805-8020

Cornell University, Ithaca, New York, USA J. Alexander0000-0002-2046-342X, S.
Bright-Thonney0000-0003-1889-7824, X. Chen0000-0002-8157-1328, D.J.
Cranshaw0000-0002-7498-2129, J. Fan0009-0003-3728-9960, X.
Fan0000-0003-2067-0127, D. Gadkari0000-0002-6625-8085, S.
Hogan0000-0003-3657-2281, J. Monroy0000-0002-7394-4710, J.R.
Patterson0000-0002-3815-3649, J. Reichert0000-0003-2110-8021, M.
Reid0000-0001-7706-1416, A. Ryd0000-0001-5849-1912, J.
Thom0000-0002-4870-8468, P. Wittich0000-0002-7401-2181, R.
Zou0000-0002-0542-1264

Fermi National Accelerator Laboratory, Batavia, Illinois, USA M.
Albrow0000-0001-7329-4925, M. Alyari0000-0001-9268-3360, O.
Amram0000-0002-3765-3123, G. Apollinari0000-0002-5212-5396, A.
Apresyan0000-0002-6186-0130, L.A.T. Bauerdick0000-0002-7170-9012, D.
Berry0000-0002-5383-8320, J. Berryhill0000-0002-8124-3033, P.C.
Bhat0000-0003-3370-9246, K. Burkett0000-0002-2284-4744, J.N.
Butler0000-0002-0745-8618, A. Canepa0000-0003-4045-3998, G.B.
Cerati0000-0003-3548-0262, H.W.K. Cheung0000-0001-6389-9357, F.
Chlebana0000-0002-8762-8559, G. Cummings0000-0002-8045-7806, J.
Dickinson0000-0001-5450-5328, I. Dutta0000-0003-0953-4503, V.D.
Elvira0000-0003-4446-4395, Y. Feng0000-0003-2812-338X, J.
Freeman0000-0002-3415-5671, A. Gandrakota0000-0003-4860-3233, Z.
Gecse0009-0009-6561-3418, L. Gray0000-0002-6408-4288, D. Green, S.
Grünendahl0000-0002-4857-0294, D. Guerrero0000-0001-5552-5400, O.
Gutsche0000-0002-8015-9622, R.M. Harris0000-0003-1461-3425, R.
Heller0000-0002-7368-6723, T.C. Herwig0000-0002-4280-6382, J.
Hirschauer0000-0002-8244-0805, L. Horyn0000-0002-9512-4932, B.
Jayatilaka0000-0001-7912-5612, S. Jindariani0009-0000-7046-6533, M.
Johnson0000-0001-7757-8458, U. Joshi0000-0001-8375-0760, T.
Klijnsma0000-0003-1675-6040, B. Klima0000-0002-3691-7625, K.H.M.
Kwok0000-0002-8693-6146, S. Lammel0000-0003-0027-635X, D.
Lincoln0000-0002-0599-7407, R. Lipton0000-0002-6665-7289, T.
Liu0009-0007-6522-5605, C. Madrid0000-0003-3301-2246, K.
Maeshima0009-0000-2822-897X, C. Mantilla0000-0002-0177-5903, D.
Mason0000-0002-0074-5390, P. McBride0000-0001-6159-7750, P.
Merkel0000-0003-4727-5442, S. Mrenna0000-0001-8731-160X, S.
Nahn0000-0002-8949-0178, J. Ngadiuba0000-0002-0055-2935, D.
Noonan0000-0002-3932-3769, V. Papadimitriou0000-0002-0690-7186, N.
Pastika0009-0006-0993-6245, K. Pedro0000-0003-2260-9151, C.
Pena870000-0002-4500-7930, F. Ravera0000-0003-3632-0287, A. Reinsvold
Hall880000-0003-1653-8553, L. Ristori0000-0003-1950-2492, E. Sexton-
Kennedy0000-0001-9171-1980, N. Smith0000-0002-0324-3054, A.
Soha0000-0002-5968-1192, L. Spiegel0000-0001-9672-1328, S.
Stoynev0000-0003-4563-7702, J. Strait0000-0002-7233-8348, L.
Taylor0000-0002-6584-2538, S. Tkaczyk0000-0001-7642-5185, N.V.
Tran0000-0002-8440-6854, L. Uplegger0000-0002-9202-803X, E.W.
Vaandering0000-0003-3207-6950, I. Zoi0000-0002-5738-9446

University of Florida, Gainesville, Florida, USA C. Aruta0000-0001-9524-3264,
P. Avery0000-0003-0609-627X, D. Bourilkov0000-0003-0260-4935, L.
Cadamuro0000-0001-8789-610X, P. Chang0000-0002-2095-6320, V.
Cherepanov0000-0002-6748-4850, R.D. Field, E. Koenig0000-0002-0884-7922, M.
Kolosova0000-0002-5838-2158, J. Konigsberg0000-0001-6850-8765, A.
Korytov0000-0001-9239-3398, K.H. Lo, K. Matchev0000-0003-4182-9096, N.
Menendez0000-0002-3295-3194, G. Mitselmakher0000-0001-5745-3658, A.
Muthirakalayil Madhu0000-0003-1209-3032, N. Rawal0000-0002-7734-3170, D.
Rosenzweig0000-0002-3687-5189, S. Rosenzweig0000-0002-5613-1507, K.
Shi0000-0002-2475-0055, J. Wang0000-0003-3879-4873

Florida State University, Tallahassee, Florida, USA T.
Adams0000-0001-8049-5143, A. Al Kadhim0000-0003-3490-8407, A.
Askew0000-0002-7172-1396, N. Bower0000-0001-8775-0696, R.
Habibullah0000-0002-3161-8300, V. Hagopian0000-0002-3791-1989, R.
Hashmi0000-0002-5439-8224, R.S. Kim0000-0002-8645-186X, S.
Kim0000-0003-2381-5117, T. Kolberg0000-0002-0211-6109, G. Martinez, H.
Prosper0000-0002-4077-2713, P.R. Prova, O. Viazlo0000-0002-2957-0301, M.
Wulansatiti0000-0001-6794-3079, R. Yohay0000-0002-0124-9065, J. Zhang

Florida Institute of Technology, Melbourne, Florida, USA B. Alsufyani, M.M.
Baarmand0000-0002-9792-8619, S. Butalla0000-0003-3423-9581, T.
Elkafrawy530000-0001-9930-6445, M. Hohlmann0000-0003-4578-9319, R. Kumar
Verma0000-0002-8264-156X, M. Rahmani

University of Illinois Chicago, Chicago, USA, Chicago, USA M.R.
Adams0000-0001-8493-3737, C. Bennett, R. Cavanaugh0000-0001-7169-3420, S.
Dittmer0000-0002-5359-9614, R. Escobar Franco0000-0003-2090-5010, O.
Evdokimov0000-0002-1250-8931, C.E. Gerber0000-0002-8116-9021, D.J.
Hofman0000-0002-2449-3845, J.h. Lee0000-0002-5574-4192, D. S.
Lemos0000-0003-1982-8978, A.H. Merrit0000-0003-3922-6464, C.
Mills0000-0001-8035-4818, S. Nanda0000-0003-0550-4083, G.
Oh0000-0003-0744-1063, B. Ozek0009-0000-2570-1100, D.
Pilipovic0000-0002-4210-2780, T. Roy0000-0001-7299-7653, S.
Rudrabhatla0000-0002-7366-4225, M.B. Tonjes0000-0002-2617-9315, N.
Varelas0000-0002-9397-5514, X. Wang0000-0003-2792-8493, Z.
Ye0000-0001-6091-6772, J. Yoo0000-0002-3826-1332

The University of Iowa, Iowa City, Iowa, USA M. Alhusseini0000-0002-9239-470X,
D. Blend, K. Dilsiz890000-0003-0138-3368, L. Emediato0000-0002-3021-5032, G.
Karaman0000-0001-8739-9648, O.K. Köseyan0000-0001-9040-3468, J.-P. Merlo, A.
Mestvirishvili900000-0002-8591-5247, J. Nachtman0000-0003-3951-3420, O. Neogi,
H. Ogul910000-0002-5121-2893, Y. Onel0000-0002-8141-7769, A.
Penzo0000-0003-3436-047X, C. Snyder, E. Tiras920000-0002-5628-7464

Johns Hopkins University, Baltimore, Maryland, USA B.
Blumenfeld0000-0003-1150-1735, L. Corcodilos0000-0001-6751-3108, J.
Davis0000-0001-6488-6195, A.V. Gritsan0000-0002-3545-7970, L.
Kang0000-0002-0941-4512, S. Kyriacou0000-0002-9254-4368, P.
Maksimovic0000-0002-2358-2168, M. Roguljic0000-0001-5311-3007, J.
Roskes0000-0001-8761-0490, S. Sekhar0000-0002-8307-7518, M.
Swartz0000-0002-0286-5070, T.Á. Vámi0000-0002-0959-9211

The University of Kansas, Lawrence, Kansas, USA A. Abreu0000-0002-9000-2215,
L.F. Alcerro Alcerro0000-0001-5770-5077, J. Anguiano0000-0002-7349-350X, P.
Baringer0000-0002-3691-8388, A. Bean0000-0001-5967-8674, Z.
Flowers0000-0001-8314-2052, D. Grove, J. King0000-0001-9652-9854, G.
Krintiras0000-0002-0380-7577, M. Lazarovits0000-0002-5565-3119, C. Le
Mahieu0000-0001-5924-1130, C. Lindsey, J. Marquez0000-0003-3887-4048, N.
Minafra0000-0003-4002-1888, M. Murray0000-0001-7219-4818, M.
Nickel0000-0003-0419-1329, M. Pitt0000-0003-2461-5985, S.
Popescu930000-0002-0345-2171, C. Rogan0000-0002-4166-4503, C.
Royon0000-0002-7672-9709, R. Salvatico0000-0002-2751-0567, S.
Sanders0000-0002-9491-6022, C. Smith0000-0003-0505-0528, Q.
Wang0000-0003-3804-3244, G. Wilson0000-0003-0917-4763

Kansas State University, Manhattan, Kansas, USA B. Allmond0000-0002-5593-7736,
A. Ivanov0000-0002-9270-5643, K. Kaadze0000-0003-0571-163X, A.
Kalogeropoulos0000-0003-3444-0314, D. Kim, Y. Maravin0000-0002-9449-0666, K.
Nam, J. Natoli0000-0001-6675-3564, D. Roy0000-0002-8659-7762, G.
Sorrentino0000-0002-2253-819X

Lawrence Livermore National Laboratory, Livermore, California, USA F.
Rebassoo0000-0001-8934-9329, D. Wright0000-0002-3586-3354

University of Maryland, College Park, Maryland, USA E.
Adams0000-0003-2809-2683, A. Baden0000-0002-6159-3861, O. Baron, A.
Belloni0000-0002-1727-656X, A. Bethani0000-0002-8150-7043, Y.M.
Chen0000-0002-5795-4783, S.C. Eno0000-0003-4282-2515, N.J.
Hadley0000-0002-1209-6471, S. Jabeen0000-0002-0155-7383, R.G.
Kellogg0000-0001-9235-521X, T. Koeth0000-0002-0082-0514, Y.
Lai0000-0002-7795-8693, S. Lascio0000-0001-8579-5874, A.C.
Mignerey0000-0001-5164-6969, S. Nabili0000-0002-6893-1018, C.
Palmer0000-0002-5801-5737, C. Papageorgakis0000-0003-4548-0346, M.M. Paranjpe,
L. Wang0000-0003-3443-0626, K. Wong0000-0002-9698-1354

Massachusetts Institute of Technology, Cambridge, Massachusetts, USA J.
Bendavid0000-0002-7907-1789, W. Busza0000-0002-3831-9071, I.A.
Cali0000-0002-2822-3375, Y. Chen0000-0003-2582-6469, M.
D’Alfonso0000-0002-7409-7904, J. Eysermans0000-0001-6483-7123, C.
Freer0000-0002-7967-4635, G. Gomez-Ceballos0000-0003-1683-9460, M. Goncharov,
P. Harris, D. Hoang, D. Kovalskyi0000-0002-6923-293X, J.
Krupa0000-0003-0785-7552, L. Lavezzo0000-0002-1364-9920, Y.-J.
Lee0000-0003-2593-7767, K. Long0000-0003-0664-1653, C.
Mironov0000-0002-8599-2437, C. Paus0000-0002-6047-4211, D.
Rankin0000-0001-8411-9620, C. Roland0000-0002-7312-5854, G.
Roland0000-0001-8983-2169, S. Rothman0000-0002-1377-9119, Z.
Shi0000-0001-5498-8825, G.S.F. Stephans0000-0003-3106-4894, J. Wang, Z.
Wang0000-0002-3074-3767, B. Wyslouch0000-0003-3681-0649, T. J.
Yang0000-0003-4317-4660

University of Minnesota, Minneapolis, Minnesota, USA B.
Crossman0000-0002-2700-5085, B.M. Joshi0000-0002-4723-0968, C.
Kapsiak0009-0008-7743-5316, M. Krohn0000-0002-1711-2506, D.
Mahon0000-0002-2640-5941, J. Mans0000-0003-2840-1087, B.
Marzocchi0000-0001-6687-6214, S. Pandey0000-0003-0440-6019, M.
Revering0000-0001-5051-0293, R. Rusack0000-0002-7633-749X, R.
Saradhy0000-0001-8720-293X, N. Schroeder0000-0002-8336-6141, N.
Strobbe0000-0001-8835-8282, M.A. Wadud0000-0002-0653-0761

University of Mississippi, Oxford, Mississippi, USA L.M.
Cremaldi0000-0001-5550-7827

University of Nebraska-Lincoln, Lincoln, Nebraska, USA K.
Bloom0000-0002-4272-8900, M. Bryson, D.R. Claes0000-0003-4198-8919, C.
Fangmeier0000-0002-5998-8047, F. Golf0000-0003-3567-9351, J.
Hossain0000-0001-5144-7919, C. Joo0000-0002-5661-4330, I.
Kravchenko0000-0003-0068-0395, I. Reed0000-0002-1823-8856, J.E.
Siado0000-0002-9757-470X, G.R. Snow${}^{\textrm{\textdagger}}$, W.
Tabb0000-0002-9542-4847, A. Vagnerini0000-0001-8730-5031, A.
Wightman0000-0001-6651-5320, F. Yan0000-0002-4042-0785, D.
Yu0000-0001-5921-5231, A.G. Zecchinelli0000-0001-8986-278X

State University of New York at Buffalo, Buffalo, New York, USA G.
Agarwal0000-0002-2593-5297, H. Bandyopadhyay0000-0001-9726-4915, L.
Hay0000-0002-7086-7641, I. Iashvili0000-0003-1948-5901, A.
Kharchilava0000-0002-3913-0326, C. McLean0000-0002-7450-4805, M.
Morris0000-0002-2830-6488, D. Nguyen0000-0002-5185-8504, J.
Pekkanen0000-0002-6681-7668, S. Rappoccio0000-0002-5449-2560, H. Rejeb Sfar,
A. Williams0000-0003-4055-6532

Northeastern University, Boston, Massachusetts, USA G.
Alverson0000-0001-6651-1178, E. Barberis0000-0002-6417-5913, Y.
Haddad0000-0003-4916-7752, Y. Han0000-0002-3510-6505, A.
Krishna0000-0002-4319-818X, J. Li0000-0001-5245-2074, M.
Lu0000-0002-6999-3931, G. Madigan0000-0001-8796-5865, D.M.
Morse0000-0003-3163-2169, V. Nguyen0000-0003-1278-9208, T.
Orimoto0000-0002-8388-3341, A. Parker0000-0002-9421-3335, L.
Skinnari0000-0002-2019-6755, A. Tishelman-Charny0000-0002-7332-5098, B.
Wang0000-0003-0796-2475, D. Wood0000-0002-6477-801X

Northwestern University, Evanston, Illinois, USA S.
Bhattacharya0000-0002-0526-6161, J. Bueghly, Z. Chen0000-0003-4521-6086, K.A.
Hahn0000-0001-7892-1676, Y. Liu0000-0002-5588-1760, Y.
Miao0000-0002-2023-2082, D.G. Monk0000-0002-8377-1999, M.H.
Schmitt0000-0003-0814-3578, A. Taliercio0000-0002-5119-6280, M. Velasco

University of Notre Dame, Notre Dame, Indiana, USA R. Band0000-0003-4873-0523,
R. Bucci, S. Castells0000-0003-2618-3856, M. Cremonesi, A.
Das0000-0001-9115-9698, R. Goldouzian0000-0002-0295-249X, M.
Hildreth0000-0002-4454-3934, K.W. Ho0000-0003-2229-7223, K. Hurtado
Anampa0000-0002-9779-3566, C. Jessop0000-0002-6885-3611, K.
Lannon0000-0002-9706-0098, J. Lawrence0000-0001-6326-7210, N.
Loukas0000-0003-0049-6918, L. Lutton0000-0002-3212-4505, J. Mariano, N.
Marinelli, I. Mcalister, T. McCauley0000-0001-6589-8286, C.
Mcgrady0000-0002-8821-2045, K. Mohrman0009-0007-2940-0496, C.
Moore0000-0002-8140-4183, Y. Musienko130009-0006-3545-1938, H.
Nelson0000-0001-5592-0785, M. Osherson0000-0002-9760-9976, R.
Ruchti0000-0002-3151-1386, A. Townsend0000-0002-3696-689X, M.
Wayne0000-0001-8204-6157, H. Yockey, M. Zarucki0000-0003-1510-5772, L.
Zygala0000-0001-9665-7282

The Ohio State University, Columbus, Ohio, USA A. Basnet0000-0001-8460-0019,
B. Bylsma, M. Carrigan0000-0003-0538-5854, L.S. Durkin0000-0002-0477-1051, C.
Hill0000-0003-0059-0779, M. Joyce0000-0003-1112-5880, A.
Lesauvage0000-0003-3437-7845, M. Nunez Ornelas0000-0003-2663-7379, K. Wei,
B.L. Winer0000-0001-9980-4698, B. R. Yates0000-0001-7366-1318

Princeton University, Princeton, New Jersey, USA F.M.
Addesa0000-0003-0484-5804, H. Bouchamaoui0000-0002-9776-1935, P.
Das0000-0002-9770-1377, G. Dezoort0000-0002-5890-0445, P.
Elmer0000-0001-6830-3356, A. Frankenthal0000-0002-2583-5982, B.
Greenberg0000-0002-4922-1934, N. Haubrich0000-0002-7625-8169, S.
Higginbotham0000-0002-4436-5461, G. Kopp0000-0001-8160-0208, S.
Kwan0000-0002-5308-7707, D. Lange0000-0002-9086-5184, A.
Loeliger0000-0002-5017-1487, D. Marlow0000-0002-6395-1079, I.
Ojalvo0000-0003-1455-6272, J. Olsen0000-0002-9361-5762, D.
Stickland0000-0003-4702-8820, C. Tully0000-0001-6771-2174

University of Puerto Rico, Mayaguez, Puerto Rico, USA S.
Malik0000-0002-6356-2655

Purdue University, West Lafayette, Indiana, USA A.S.
Bakshi0000-0002-2857-6883, V.E. Barnes0000-0001-6939-3445, S.
Chandra0009-0000-7412-4071, R. Chawla0000-0003-4802-6819, S.
Das0000-0001-6701-9265, A. Gu0000-0002-6230-1138, L. Gutay, M.
Jones0000-0002-9951-4583, A.W. Jung0000-0003-3068-3212, D.
Kondratyev0000-0002-7874-2480, A.M. Koshy, M. Liu0000-0001-9012-395X, G.
Negro0000-0002-1418-2154, N. Neumeister0000-0003-2356-1700, G.
Paspalaki0000-0001-6815-1065, S. Piperov0000-0002-9266-7819, A.
Purohit0000-0003-0881-612X, J.F. Schulte0000-0003-4421-680X, M.
Stojanovic0000-0002-1542-0855, J. Thieman0000-0001-7684-6588, A. K.
Virdi0000-0002-0866-8932, F. Wang0000-0002-8313-0809, W.
Xie0000-0003-1430-9191

Purdue University Northwest, Hammond, Indiana, USA J.
Dolen0000-0003-1141-3823, N. Parashar0009-0009-1717-0413, A.
Pathak0000-0001-9861-2942

Rice University, Houston, Texas, USA D. Acosta0000-0001-5367-1738, A.
Baty0000-0001-5310-3466, T. Carnahan0000-0001-7492-3201, S.
Dildick0000-0003-0554-4755, K.M. Ecklund0000-0002-6976-4637, P.J. Fernández
Manteca0000-0003-2566-7496, S. Freed, P. Gardner, F.J.M.
Geurts0000-0003-2856-9090, A. Kumar0000-0002-5180-6595, W.
Li0000-0003-4136-3409, O. Miguel Colin0000-0001-6612-432X, B.P.
Padley0000-0002-3572-5701, R. Redjimi, J. Rotter0009-0009-4040-7407, E.
Yigitbasi0000-0002-9595-2623, Y. Zhang0000-0002-6812-761X

University of Rochester, Rochester, New York, USA A. Bodek0000-0003-0409-0341,
P. de Barbaro0000-0002-5508-1827, R. Demina0000-0002-7852-167X, J.L.
Dulemba0000-0002-9842-7015, C. Fallon, A. Garcia-Bellido0000-0002-1407-1972,
O. Hindrichs0000-0001-7640-5264, A. Khukhunaishvili0000-0002-3834-1316, P.
Parygin830000-0001-6743-3781, E. Popova830000-0001-7556-8969, R.
Taus0000-0002-5168-2932, G.P. Van Onsem0000-0002-1664-2337

The Rockefeller University, New York, New York, USA K.
Goulianos0000-0002-6230-9535

Rutgers, The State University of New Jersey, Piscataway, New Jersey, USA B.
Chiarito, J.P. Chou0000-0001-6315-905X, Y. Gershtein0000-0002-4871-5449, E.
Halkiadakis0000-0002-3584-7856, A. Hart0000-0003-2349-6582, M.
Heindl0000-0002-2831-463X, D. Jaroslawski0000-0003-2497-1242, O.
Karacheban260000-0002-2785-3762, I. Laflotte0000-0002-7366-8090, A.
Lath0000-0003-0228-9760, R. Montalvo, K. Nash, H. Routray0000-0002-9694-4625,
S. Salur0000-0002-4995-9285, S. Schnetzer, S. Somalwar0000-0002-8856-7401, R.
Stone0000-0001-6229-695X, S.A. Thayil0000-0002-1469-0335, S. Thomas, J.
Vora0000-0001-9325-2175, H. Wang0000-0002-3027-0752

University of Tennessee, Knoxville, Tennessee, USA H. Acharya, D.
Ally0000-0001-6304-5861, A.G. Delannoy0000-0003-1252-6213, S.
Fiorendi0000-0003-3273-9419, T. Holmes0000-0002-3959-5174, N.
Karunarathna0000-0002-3412-0508, L. Lee0000-0002-5590-335X, E.
Nibigira0000-0001-5821-291X, S. Spanier0000-0002-7049-4646

Texas A&M University, College Station, Texas, USA D. Aebi0000-0001-7124-6911,
M. Ahmad0000-0001-9933-995X, O. Bouhali940000-0001-7139-7322, M.
Dalchenko0000-0002-0137-136X, R. Eusebi0000-0003-3322-6287, J.
Gilmore0000-0001-9911-0143, T. Huang0000-0002-0793-5664, T.
Kamon950000-0001-5565-7868, H. Kim0000-0003-4986-1728, S.
Luo0000-0003-3122-4245, S. Malhotra, R. Mueller0000-0002-6723-6689, D.
Overton0009-0009-0648-8151, D. Rathjens0000-0002-8420-1488, A.
Safonov0000-0001-9497-5471

Texas Tech University, Lubbock, Texas, USA N. Akchurin0000-0002-6127-4350, J.
Damgov0000-0003-3863-2567, V. Hegde0000-0003-4952-2873, A.
Hussain0000-0001-6216-9002, Y. Kazhykarim, K. Lamichhane0000-0003-0152-7683,
S.W. Lee0000-0002-3388-8339, A. Mankel0000-0002-2124-6312, T. Mengke, S.
Muthumuni0000-0003-0432-6895, T. Peltola0000-0002-4732-4008, I.
Volobouev0000-0002-2087-6128, A. Whitbeck0000-0003-4224-5164

Vanderbilt University, Nashville, Tennessee, USA E. Appelt0000-0003-3389-4584,
S. Greene, A. Gurrola0000-0002-2793-4052, W. Johns0000-0001-5291-8903, R.
Kunnawalkam Elayavalli0000-0002-9202-1516, A. Melo0000-0003-3473-8858, F.
Romeo0000-0002-1297-6065, P. Sheldon0000-0003-1550-5223, S.
Tuo0000-0001-6142-0429, J. Velkovska0000-0003-1423-5241, J.
Viinikainen0000-0003-2530-4265

University of Virginia, Charlottesville, Virginia, USA B.
Cardwell0000-0001-5553-0891, B. Cox0000-0003-3752-4759, J.
Hakala0000-0001-9586-3316, R. Hirosky0000-0003-0304-6330, A.
Ledovskoy0000-0003-4861-0943, A. Li0000-0002-4547-116X, C.
Neu0000-0003-3644-8627, C.E. Perez Lara0000-0003-0199-8864

Wayne State University, Detroit, Michigan, USA P.E. Karchin0000-0003-1284-3470

University of Wisconsin - Madison, Madison, Wisconsin, USA A. Aravind, S.
Banerjee0000-0001-7880-922X, K. Black0000-0001-7320-5080, T.
Bose0000-0001-8026-5380, S. Dasu0000-0001-5993-9045, I. De
Bruyn0000-0003-1704-4360, P. Everaerts0000-0003-3848-324X, C. Galloni, H.
He0009-0008-3906-2037, M. Herndon0000-0003-3043-1090, A.
Herve0000-0002-1959-2363, C.K. Koraka0000-0002-4548-9992, A. Lanaro, R.
Loveless0000-0002-2562-4405, J. Madhusudanan Sreekala0000-0003-2590-763X, A.
Mallampalli0000-0002-3793-8516, A. Mohammadi0000-0001-8152-927X, S. Mondal, G.
Parida0000-0001-9665-4575, D. Pinna, A. Savin, V. Shang0000-0002-1436-6092, V.
Sharma0000-0003-1287-1471, W.H. Smith0000-0003-3195-0909, D. Teague, H.F.
Tsoi0000-0002-2550-2184, W. Vetens0000-0003-1058-1163, A.
Warden0000-0001-7463-7360

Authors affiliated with an institute or an international laboratory covered by
a cooperation agreement with CERN S. Afanasiev0009-0006-8766-226X, V.
Andreev0000-0002-5492-6920, Yu. Andreev0000-0002-7397-9665, T.
Aushev0000-0002-6347-7055, M. Azarkin0000-0002-7448-1447, A.
Babaev0000-0001-8876-3886, A. Belyaev0000-0003-1692-1173, V. Blinov96, E.
Boos0000-0002-0193-5073, V. Borshch0000-0002-5479-1982, D.
Budkouski0000-0002-2029-1007, V. Bunichev0000-0003-4418-2072, M.
Chadeeva960000-0003-1814-1218, V. Chekhovsky, M. Danilov960000-0001-9227-5164,
A. Dermenev0000-0001-5619-376X, T. Dimova960000-0002-9560-0660, D.
Druzhkin970000-0001-7520-3329, M. Dubinin870000-0002-7766-7175, L.
Dudko0000-0002-4462-3192, G. Gavrilov0000-0001-9689-7999, V.
Gavrilov0000-0002-9617-2928, S. Gninenko0000-0001-6495-7619, V.
Golovtcov0000-0002-0595-0297, N. Golubev0000-0002-9504-7754, I.
Golutvin0009-0007-6508-0215, I. Gorbunov0000-0003-3777-6606, Y.
Ivanov0000-0001-5163-7632, V. Kachanov0000-0002-3062-010X, L.
Kardapoltsev960009-0000-3501-9607, V. Karjavine0000-0002-5326-3854, A.
Karneyeu0000-0001-9983-1004, V. Kim960000-0001-7161-2133, M. Kirakosyan, D.
Kirpichnikov0000-0002-7177-077X, M. Kirsanov0000-0002-8879-6538, V.
Klyukhin0000-0002-8577-6531, O. Kodolova980000-0003-1342-4251, D.
Konstantinov0000-0001-6673-7273, V. Korenkov0000-0002-2342-7862, A.
Kozyrev960000-0003-0684-9235, N. Krasnikov0000-0002-8717-6492, A.
Lanev0000-0001-8244-7321, P. Levchenko990000-0003-4913-0538, O.
Lukina0000-0003-1534-4490, N. Lychkovskaya0000-0001-5084-9019, V.
Makarenko0000-0002-8406-8605, A. Malakhov0000-0001-8569-8409, V.
Matveev960000-0002-2745-5908, V. Murzin0000-0002-0554-4627, A.
Nikitenko100,980000-0002-1933-5383, S. Obraztsov0009-0001-1152-2758, V.
Oreshkin0000-0003-4749-4995, A. Oskin, V. Palichik0009-0008-0356-1061, V.
Perelygin0009-0005-5039-4874, S. Petrushanko0000-0003-0210-9061, V. Popov, O.
Radchenko960000-0001-7116-9469, V. Rusinov, M. Savina0000-0002-9020-7384, V.
Savrin0009-0000-3973-2485, V. Shalaev0000-0002-2893-6922, S.
Shmatov0000-0001-5354-8350, S. Shulha0000-0002-4265-928X, Y.
Skovpen960000-0002-3316-0604, S. Slabospitskii0000-0001-8178-2494, V.
Smirnov0000-0002-9049-9196, A. Snigirev0000-0003-2952-6156, D.
Sosnov0000-0002-7452-8380, V. Sulimov0009-0009-8645-6685, E.
Tcherniaev0000-0002-3685-0635, A. Terkulov0000-0003-4985-3226, O.
Teryaev0000-0001-7002-9093, I. Tlisova0000-0003-1552-2015, A.
Toropin0000-0002-2106-4041, L. Uvarov0000-0002-7602-2527, A.
Uzunian0000-0002-7007-9020, A. Vorobyev${}^{\textrm{\textdagger}}$, N.
Voytishin0000-0001-6590-6266, B.S. Yuldashev101, A.
Zarubin0000-0002-1964-6106, I. Zhizhin0000-0001-6171-9682, A.
Zhokin0000-0001-7178-5907

†: Deceased
1Also at Yerevan State University, Yerevan, Armenia
2Also at TU Wien, Vienna, Austria
3Also at Institute of Basic and Applied Sciences, Faculty of Engineering, Arab
Academy for Science, Technology and Maritime Transport, Alexandria, Egypt
4Also at Ghent University, Ghent, Belgium
5Also at Universidade Estadual de Campinas, Campinas, Brazil
6Also at Federal University of Rio Grande do Sul, Porto Alegre, Brazil
7Also at UFMS, Nova Andradina, Brazil
8Also at Nanjing Normal University, Nanjing, China
9Now at The University of Iowa, Iowa City, Iowa, USA
10Also at University of Chinese Academy of Sciences, Beijing, China
11Also at University of Chinese Academy of Sciences, Beijing, China
12Also at Université Libre de Bruxelles, Bruxelles, Belgium
13Also at an institute or an international laboratory covered by a cooperation
agreement with CERN
14Also at Suez University, Suez, Egypt
15Now at British University in Egypt, Cairo, Egypt
16Also at Birla Institute of Technology, Mesra, Mesra, India
17Also at Purdue University, West Lafayette, Indiana, USA
18Also at Université de Haute Alsace, Mulhouse, France
19Also at Department of Physics, Tsinghua University, Beijing, China
20Also at The University of the State of Amazonas, Manaus, Brazil
21Also at Erzincan Binali Yildirim University, Erzincan, Turkey
22Also at University of Hamburg, Hamburg, Germany
23Also at RWTH Aachen University, III. Physikalisches Institut A, Aachen,
Germany
24Also at Isfahan University of Technology, Isfahan, Iran
25Also at Bergische University Wuppertal (BUW), Wuppertal, Germany
26Also at Brandenburg University of Technology, Cottbus, Germany
27Also at Forschungszentrum Jülich, Juelich, Germany
28Also at CERN, European Organization for Nuclear Research, Geneva,
Switzerland
29Also at Physics Department, Faculty of Science, Assiut University, Assiut,
Egypt
30Also at Wigner Research Centre for Physics, Budapest, Hungary
31Also at Institute of Physics, University of Debrecen, Debrecen, Hungary
32Also at Institute of Nuclear Research ATOMKI, Debrecen, Hungary
33Now at Universitatea Babes-Bolyai - Facultatea de Fizica, Cluj-Napoca,
Romania
34Also at Faculty of Informatics, University of Debrecen, Debrecen, Hungary
35Also at Punjab Agricultural University, Ludhiana, India
36Also at UPES - University of Petroleum and Energy Studies, Dehradun, India
37Also at University of Visva-Bharati, Santiniketan, India
38Also at University of Hyderabad, Hyderabad, India
39Also at Indian Institute of Science (IISc), Bangalore, India
40Also at IIT Bhubaneswar, Bhubaneswar, India
41Also at Institute of Physics, Bhubaneswar, India
42Also at Deutsches Elektronen-Synchrotron, Hamburg, Germany
43Also at Department of Physics, Isfahan University of Technology, Isfahan,
Iran
44Also at Sharif University of Technology, Tehran, Iran
45Also at Department of Physics, University of Science and Technology of
Mazandaran, Behshahr, Iran
46Also at Helwan University, Cairo, Egypt
47Also at Italian National Agency for New Technologies, Energy and Sustainable
Economic Development, Bologna, Italy
48Also at Centro Siciliano di Fisica Nucleare e di Struttura Della Materia,
Catania, Italy
49Also at Università degli Studi Guglielmo Marconi, Roma, Italy
50Also at Scuola Superiore Meridionale, Università di Napoli ’Federico II’,
Napoli, Italy
51Also at Fermi National Accelerator Laboratory, Batavia, Illinois, USA
52Also at Università di Napoli ’Federico II’, Napoli, Italy
53Also at Ain Shams University, Cairo, Egypt
54Also at Consiglio Nazionale delle Ricerche - Istituto Officina dei
Materiali, Perugia, Italy
55Also at Riga Technical University, Riga, Latvia
56Also at Department of Applied Physics, Faculty of Science and Technology,
Universiti Kebangsaan Malaysia, Bangi, Malaysia
57Also at Consejo Nacional de Ciencia y Tecnología, Mexico City, Mexico
58Also at Trincomalee Campus, Eastern University, Sri Lanka, Nilaveli, Sri
Lanka
59Also at INFN Sezione di Pavia, Università di Pavia, Pavia, Italy
60Also at National and Kapodistrian University of Athens, Athens, Greece
61Also at Ecole Polytechnique Fédérale Lausanne, Lausanne, Switzerland
62Also at University of Vienna Faculty of Computer Science, Vienna, Austria
63Also at Universität Zürich, Zurich, Switzerland
64Also at Stefan Meyer Institute for Subatomic Physics, Vienna, Austria
65Also at Laboratoire d’Annecy-le-Vieux de Physique des Particules,
IN2P3-CNRS, Annecy-le-Vieux, France
66Also at Near East University, Research Center of Experimental Health
Science, Mersin, Turkey
67Also at Konya Technical University, Konya, Turkey
68Also at Izmir Bakircay University, Izmir, Turkey
69Also at Adiyaman University, Adiyaman, Turkey
70Also at Necmettin Erbakan University, Konya, Turkey
71Also at Bozok Universitetesi Rektörlügü, Yozgat, Turkey
72Also at Marmara University, Istanbul, Turkey
73Also at Milli Savunma University, Istanbul, Turkey
74Also at Kafkas University, Kars, Turkey
75Also at Hacettepe University, Ankara, Turkey
76Also at Istanbul University - Cerrahpasa, Faculty of Engineering, Istanbul,
Turkey
77Also at Yildiz Technical University, Istanbul, Turkey
78Also at Vrije Universiteit Brussel, Brussel, Belgium
79Also at School of Physics and Astronomy, University of Southampton,
Southampton, United Kingdom
80Also at University of Bristol, Bristol, United Kingdom
81Also at IPPP Durham University, Durham, United Kingdom
82Also at Monash University, Faculty of Science, Clayton, Australia
83Now at an institute or an international laboratory covered by a cooperation
agreement with CERN
84Also at Università di Torino, Torino, Italy
85Also at Bethel University, St. Paul, Minnesota, USA
86Also at Karamanoğlu Mehmetbey University, Karaman, Turkey
87Also at California Institute of Technology, Pasadena, California, USA
88Also at United States Naval Academy, Annapolis, Maryland, USA
89Also at Bingol University, Bingol, Turkey
90Also at Georgian Technical University, Tbilisi, Georgia
91Also at Sinop University, Sinop, Turkey
92Also at Erciyes University, Kayseri, Turkey
93Also at Horia Hulubei National Institute of Physics and Nuclear Engineering
(IFIN-HH), Bucharest, Romania
94Also at Texas A&M University at Qatar, Doha, Qatar
95Also at Kyungpook National University, Daegu, Korea
96Also at another institute or international laboratory covered by a
cooperation agreement with CERN
97Also at Universiteit Antwerpen, Antwerpen, Belgium
98Also at Yerevan Physics Institute, Yerevan, Armenia
99Also at Northeastern University, Boston, Massachusetts, USA
100Also at Imperial College, London, United Kingdom
101Also at Institute of Nuclear Physics of the Uzbekistan Academy of Sciences,
Tashkent, Uzbekistan


††thanks: This manuscript has been authored by UT-Battelle, LLC, under
Contract No. DE-AC0500OR22725 with the U.S. Department of Energy. The United
States Government retains and the publisher, by accepting the article for
publication, acknowledges that the United States Government retains a non-
exclusive, paid-up, irrevocable, world-wide license to publish or reproduce
the published form of this manuscript, or allow others to do so, for the
United States Government purposes. The Department of Energy will provide
public access to these results of federally sponsored research in accordance
with the DOE Public Access Plan.

# Re-QGAN: an optimized adversarial quantum circuit learning framework

Sandra Nguemto  Department of Mathematics, University of Tennessee, Knoxville,
TN 37996, USA  Vicente Leyton-Ortega<EMAIL_ADDRESS>Computational
Sciences and Engineering Division, Oak Ridge National Laboratory, Oak Ridge,
TN 37831, USA

###### Abstract

Adversarial learning represents a powerful technique for generating data
statistics. Its successful implementation in quantum computational platforms
is not straightforward due to limitations in connectivity, quantum operation
fidelity, and limited access to the quantum processor for statistically
relevant results. Constraining the number of quantum operations and providing
a design with a low compilation cost, we propose a quantum generative
adversarial network design that uses real Hilbert spaces as the framework for
the generative model and a novel strategy to encode classical information into
the quantum framework. We consider quantum generator and discriminator
architectures based on a variational quantum circuit. We encode classical
information by the stereographic projection, which allows us to use the entire
classical domain without normalization procedures. For low-depth ansätze
designs, we consider the real Hilbert space as the working space for the
quantum adversarial game. This architecture improves state-of-the-art quantum
generative adversarial performance while maintaining a shallow-depth quantum
circuit and a reduced parameter set. We tested our design in a low resource
regime, generating handwritten digits with the MNIST as the reference dataset.
We could generate undetected data (digits) with just 15 epochs working in the
real Hilbert space of 2, 3, and 4 qubits. Our design uses native quantum
operations established in superconducting-based quantum processors and is
compatible with ion-trapped-based architectures.

Quantum computation, Quantum machine learning, Adversarial learning,
Optimization, Benchmarking

##

Quantum Machine Learning [1, 2] has been concerned with applying concepts and
tools from quantum computation and quantum information to enhance the
treatment and processing of classical machine learning tasks. Several
approaches demonstrate a level of advantage when the quantum processor (QPU)
is used in classical-quantum hybrid architectures, from the implementation of
generative tasks using the QPU as a parameterized sample generator [3] until
classification procedures exploiting an entangled measurement scheme in the
QPU to enhance the discrimination efficiency [4]. One case is the adversarial
networks framework upgrading, known as quantum generative adversarial neural
networks (qGANs). This quantum framework uses the QPU to build discriminative
and generative models based on parameterized quantum circuits (PQC), where the
data is encoded into a quantum state and processed by quantum operations. The
adversarial game structure (quantum or classical) requires a classical
database known as the real-data, a generative model (generator) that can
produce data known as fake-data, and a discriminative model (discriminator)
that can measure the difference between real and fake. The generator and
discriminator compete; from one side, the generator tends to produce fake-data
that can be treated as real-data by the discriminator. On the other side, the
discriminator improves the way of distinguishing real- from fake-data.

qGANs were introduced in 2018 in two companion papers [5, 6], presenting a
roadmap to build their architecture and sketch their operational structure and
advantages over their classical counterpart. Since then, several works have
proposed different qGANs architectures in several paradigms and for other
applications. In addition, these works have tackled the various problems
linked to implementing and training qGANs. For instance, quantum conditional
GANs [7] that outperformed their classical counterpart, quantum style-based
GAN (style-qGAN) [8], where the quantum generator model is optimized to
generate Monte-Carlo events for high-energy physics applications, quantum
dissipative GAN [9] based on dissipative neural networks, entanglement qGAN
(EQ-GAN) [10] that entangles target and generated states to achieve the Nash
equilibrium in the adversarial game, and qGANs to model classical continuous
distributions [11].

Other works treat implementation matters, like strategies using shallow
quantum circuits and post-measurement procedures to discriminate the
generator’s output [12], studies on the convergence of qGANs and score
functions to enhance the convergence time [13], and encoding protocols to
efficiently load random distributions into $n$-qubit quantum states [14]. Most
of the proposed qGANs schemes require a non-trivial compilation for their
implementation into commercial QPUs, and a resetting according to quantum
hardware limitations in connectivity and quantum circuits executions.

One crucial aspect not present in the classical framework is the classical
information encoding into quantum information. The adversarial game works in
unison with the encoding procedure. Some efforts on this matter cover the
effects of data encoding on the expressivity of quantum models [15], and the
impact of the encoding on binary quantum classifiers [16], where they evaluate
decision boundaries for different encoding strategies under noise influence. A
typical procedure is to shrink the classical information into the Hilbert
space and return the processed quantum information to the classical world. If
the encoding is not one-to-one, we can incur loss and tergiversation. In this
work, we address the question of how to design simple qGAN that suit the
quantum hardware limitation and at the same time leverage its capabilities,
and how we can encode classical information in a quantum state without
incurring transformations that yield imprecise information in the de-encoding
process.

We contribute to this rich body of work by proposing a novel classical-quantum
encoding based on the stereographic projection and a real quantum state qGAN
(re-qGAN) that, in general, requires an optimal value of parameters, according
to the size of the classical data, and only single-qubit rotations and CXs to
be achieved. This design produces less computationally complex quantum neural
networks compared to previous architectures. The real amplitude quantum state
preparation, in turn, improves training time and feasibility on near-term
quantum devices.

##  I Results

### Quantum Adversarial Game

We propose a generative adversarial quantum circuit learning for an
unsupervised learning task. In this work, we test the strategy in image
generation using a supervised loss for an unsupervised learning task. We
consider the standard structure for quantum generative adversarial algorithms,
a real-data agent that encodes the sample of classical information (training
sample) into quantum information, a generator that prepares quantum states
that eventually will be decoded into classical data, and a discriminator that
measures how qualitatively different is the generator’s output is from the
training dataset. We describe the input data and present the quantum
adversarial model in the following.

Quantum adversarial game

Input:

  * •

$\cal C$: dataset $\\{\vec{u}_{0},\cdots,\vec{u}_{N}\\}$, with
$\vec{u}_{k}=(u_{1},\cdots,u_{M})$

  * •

EPOCHS: Number of learning cycles

Initialization:

  * •

SI encoding ${\cal C}\rightarrow{\cal C}_{Q}$ (Eq. II.1)

  * •

$n=\lceil\log_{2}(M)\rceil$, number of qubits

  * •

set $\vec{\theta_{D}}\in[-\pi,\pi)^{2^{n+1}-1}$ arbitrarily

  * •

set $\\{\vec{\theta}_{G}^{\,k}\in[-\pi,\pi)^{2^{n}-1}$ } arbitrarily,
$k=1,\cdots,N$

  * •

build ${\cal D}^{n}$ and ${\cal G}^{n}$ (Fig. 2(c) and (d))

for $i=1$ to EPOCHS do (Fig. 2(b))

${\cal D}^{n}$ training: $\vec{\theta}_{D}\leftarrow{\rm
arg\,min}_{\theta_{D}}{\cal L}_{D}$ (Eq. I)

${\cal G}^{n}$ training: $\\{\vec{\theta}_{G}^{\,k}\\}\leftarrow{\rm
arg\,min}_{\\{\vec{\theta}_{G}^{\,k}\\}}{\cal L}_{G}$ (Eq. I)

end for  • prepare ${\cal Q}_{Q}=\\{|q_{0}\rangle,\cdots,|q_{N}\rangle\\}$
from $\\{\vec{\theta}_{G}^{\,k}\\}$ (Eq. II.2) • SI de-encoding ${\cal
Q}_{Q}\rightarrow{\cal Q}$ (Eq. 5)

Output:

  * •

${\cal Q}$: artificial dataset $\\{\vec{q}_{0},\cdots,\vec{q}_{N}\\}$

We consider as input data a collection of images ${\cal
C}=\\{\vec{u}_{1},\cdots,\vec{u}_{N}\\}$, that follow an equivalence relation.
For simplicity, we convert the images into grayscale. Thus, the input data can
be easily formatted into arrays. The vectorized images are compressed by a
principal component analysis (PCA) to be projected into the $n$-qubit real
Hilbert (a hypersphere) by the inverse stereographic projection. The
stereographic projection allows the use of the projected information, from the
real plane where the input data lies to the hypersphere, to define the set of
quantum state ${\cal C}_{Q}=\\{|u_{1}\rangle,\cdots,|u_{N}\rangle\\}$ that
will represent the classical data. With the state amplitude representation of
the classical data, the discriminator’s goal is to differentiate this set from
any output produced by the generator.

The generator and discriminator agents are designed using parameterized
quantum circuits ${\cal G}(\mathbf{\theta})$ and ${\cal D}(\mathbf{\theta})$,
respectively, that prepare arbitrary quantum states with real amplitudes. The
generator follows a special design that minimizes the number of parameters to
the optimal point $2^{n}-1$ for full expressivity, given $n$ the number of
qubits. On the other hand, the discriminator entangles any pair of quantum
states with real amplitudes and uses an ancillary qubit whose measurement
decides whether an input state is equivalent to the training sample.

The discriminator is calibrated with $C_{Q}$ tuning the parameters
$\vec{\theta}_{D}$ in ${\cal D}$ such that the quantity

$\sigma(|s\rangle,\vec{\theta})=\langle\psi_{D}^{s}(\vec{\theta})|I\cdots
I\cdot Z|\psi_{D}^{s}(\vec{\theta})\rangle$ (1)

becomes $1$ for each $|\psi_{D}^{s}(\vec{\theta})\rangle={\cal
D}(\vec{\theta})|s\rangle\otimes|0\rangle_{ancilla}$ with $|s\rangle\in{\cal
C}_{Q}$, and -1 for every other state $|s\rangle\not\in{\cal C}_{Q}$. In
concurrency, the generator is updated to prepare quantum states more
equivalent to the sampling training set with the goal of being undetected by
the discriminator, this procedure defines a set of parameters $\theta_{D}$. We
prepare a sample of fake-data produced by ${\cal G}$ defining the set of
parameters $\\{\vec{\theta}^{\,1}_{G},\cdots,\vec{\theta}^{\,N}_{G}\\}$; for a
short notation $\\{\vec{\theta}^{\,k}_{G}\\}_{N}$. As a first step, the fake
sample is compared with the training dataset to calibrate the discriminator.
To capture the generator-discriminator adversarial dynamics, we define the
cost functions for the discriminator and generator training as

$\displaystyle{\cal L}_{D}(\vec{\theta}_{D};\\{\vec{\theta}^{\,k}_{G}\\}_{N})$
$\displaystyle=$
$\displaystyle\frac{1}{2N}\sum_{l=1}^{N}\left(\left[1-\sigma(|u_{l}\rangle,\vec{\theta}_{D})\right]^{2}\right.$
$\displaystyle+\left.\left[1+\sigma(|\psi_{G}(\vec{\theta}_{G}^{\,l})\rangle,\vec{\theta}_{D})\right]^{2}\right),$
$\displaystyle{\cal L}_{G}(\\{\vec{\theta}^{\,k}_{G}\\}_{N};\vec{\theta_{D}})$
$\displaystyle=$
$\displaystyle\frac{1}{N}\sum_{l=1}^{N}\left[1-\sigma(|\psi_{G}(\vec{\theta}_{G}^{\,l})\rangle,\vec{\theta}_{D})\right]^{2},$

respectively, with $|\psi_{G}(\vec{\theta}_{l})\rangle={\cal
G}(\vec{\theta}_{l})|0\cdots 0\rangle$ as the $l$th state prepared by the
generator. The minimization of the discriminator cost function, ${\cal
L}_{D}$, sets a configuration where the elements of ${\cal C}_{Q}$ and the
artificial data from ${\cal G}$ are recognized with $\sigma=1$ and
$\sigma=-1$, respectively. The minimization of ${\cal L}_{G}$ gives the
parameter configuration for the generator ${\cal G}$ that produces $\sigma=1$.
In every epoch cycle, the discriminator is optimized to detect the generator’s
output, and the generator is optimized to fool the discriminator. Once a stop
criterion is reached, either a maximum number of iterations or convergence,
the set $\\{\vec{\theta}^{\,k}_{G}\\}_{N}$ will generate new data
indistinguishable to ${\cal C}$ after a SI de-encoding procedure. In Algorithm
I we present the pseudo-code for the quantum adversarial game. This procedure
considers the compressed information when the PCA is applied as to the input
information. In the next section, we shall provide more details about the
Discriminator’s and Generator’s training.

### Generating MNIST handwritten digits

Figure 1: MNIST benchmark generation problem. In this Figure, we present the
re-qGAN generated digits using a subset of the MNIST as the reference dataset.
In a) we present the generated digits for each qubit configuration, we
compress the reference dataset according to the number of qubits; see Table 1
for the level of compression $n_{PCA}$ and re-qGANs characteristics used. In
panel b), the learning for the discriminator and generator at various epochs
(Epoch 1, 15, and 25), for four qubits, learning the digit ‘8’. Each epoch
represents one learning cycle, with 500 CMA-ES iterations. In the top row of
this panel, we have the evolution concerning the number of CMA-ES iterations
of the discriminator and generator’s loss functions, $\mathcal{L}_{D}$ and
$\mathcal{L}_{G}$, respectively. In the bottom row, we have the evolution of
the variances of $\mathcal{L}_{D}$ and $\mathcal{L}_{G}$ throughout the
optimization process. In panel c), we present representative elements of the
generated samples by re-qGAN for the digits ‘3’, ‘5’ and ‘8’ using four qubits
and 50 training samples per digit at different epochs, namely, epochs 1, 15,
and 25. Here, the cumulative explained variance for the PCA transformation is
$\sim 75\%$.

Generating handwritten digits using the MNIST dataset constitutes a vast
common recognition task and a vital benchmark problem in machine learning. In
this case, we considered a subset of the MNIST as the training dataset for our
re-qGAN model. We compress the MNIST subset to fit the amount of information
we can encode for a given number of qubits, so we test the performance of the
qGAN in generating low-resolution images. In this experiment, we consider 25
epochs and a subset of 20 images from the MNIST to generate a new digit. In
all the numerical experiments, we consider a reduced number of qubits (from 2
to 4) and low resolution ($28\times 28$) black and white images in the
training dataset compressed by the principal component analysis (PCA) at a
degree of explained variance that depends on the number of qubits used, i.e.,
for $n$ qubits the number of components $n_{\rm PCA}$ must be less than or
equal to $2^{n}-1$. On the other hand, the maximal number of components
depends on the training dataset size. In Table 1, we show relevant details of
the numerical experiments. In Figure 1(a), we present the numerical experiment
results and generated images for different sizes in the quantum
representation.

In this experiment, the re-qGAN could generate undetectably (from the
discriminator viewpoint) samples at the 15th epoch cycle (top row in Fig.
1(b)), where we observe a good trade-off between the optimal values of ${\cal
L}_{D}$ and ${\cal L}_{G}$. In Figure 1(b) we show the variance of ${\cal
L}_{D}$ and ${\cal L}_{G}$, and according to the CMA-ES search mechanism, the
generator output is closer to a converged value that the discriminator, a
favorable scenario in the adversarial game. The fewer epochs for good quality
outputs represent an improvement compared to the results in recent proposals,
which generally require around 100 epochs to generate undetectable samples
[12]. From this observation, we can infer the ability of re-qGAN to learn from
a reference database and its potential implementation on limited access
quantum devices.

In addition, where we consider a subset of the MNIST as a reference dataset,
the generated digit’s resolution and quality do not scale with the number of
qubits (Fig. 1(a) and (c)), which is related to the size of the subset chosen
for the learning task. In this case, we found an attractive characteristic to
explore, how the subset size works in unison with the number of qubits to
generate undetectable data. Looking at the samples generated by re-qGAN for
four qubits (Fig. 1(c)), we observe a diverse selection of outputs, which
indicates that the qGAN is effectively learning the original distribution
instead of simply producing random outcomes. We also deal with lower
resolution training samples than in Figure 1(a) when increasing the training
dataset size because of the decreased cumulative explained variance (CEV) in
the PCA process. Better resolution outputs would likely require finding a good
trade-off between sample size and CEV.

| ${\cal G}^{n}$ | ${\cal D}^{n}$ | PCA
---|---|---|---
$n$ |  $Y_{\theta}$s | CXs |  $Y_{\theta}$s | CXs | $n_{\rm PCA}$ | CEV
2 | 3 | 1 | 9 | 4 | 3 | 51 %
3 | 7 | 4 | 18 | 11 | 7 | 76 %
4 | 15 | 11 | 35 | 26 | 15 | 96 %
Table 1: List of parameters used in the numerical experiments. We present the
number of parameters ($Y_{\theta}$s) and entangling gates (CXs) used in every
case. In addition, we present the number of components used and the cumulative
explained variance (CEV). The training dataset is a subset of 20 images from
MNIST.

##  II methods

###  II.1 Classical dataset encoding

A standard classical-quantum encoding procedure requires mapping an element of
the classical data as quantum state amplitude, i.e., we can associate
$\vec{u}\in{\cal C}$ with an element
$\vec{v}=(v_{1}(\vec{u}),\cdots,v_{N}(\vec{u}))$, whose components define the
amplitudes of a quantum state, therefore
$||\vec{v}||\stackrel{{\scriptstyle!}}{{=}}1$. For instance, in the standard
amplitude encoding $v_{j}=u_{j}/||\vec{u}||$, every single element in the set
$\\{\alpha\vec{u}:\alpha\in\mathbb{R}\\}$ will have the same representation
$\vec{v}$, losing information and creating a non one-to-one map between the
classical and quantum information. We employed the inverse of the
stereographic projection (IS map) to dodge this.

The IS map associates vectors $\vec{u}$ in the real plane
$\mathbb{R}^{2^{n}-1}$ with vectors $\vec{v}$ in
$\mathbb{S}^{(2^{n}-1)}-\\{{\rm N}\\}$ (see Fig. 2(b)), using the relationship

$\displaystyle v_{i}$ $\displaystyle=$
$\displaystyle\frac{2u_{i}}{||\vec{u}||^{2}+1},\ {\rm for}\
i=1,\cdots,2^{n}-1$ $\displaystyle v_{2^{n}}$ $\displaystyle=$
$\displaystyle\frac{||\vec{u}||^{2}-1}{||\vec{u}||^{2}+1}.$ (4)

With this, we can define a unique quantum state

$|v\rangle=v_{0}|0\cdots 00\rangle+v_{1}|0\cdots
01\rangle+\cdots+v_{2^{n}-1}|1\cdots 11\rangle\ .$

The stereographic encoding can accurately represent any vector in the real
plane, meaning that encoding is one-to-one. Nevertheless, any variation in the
real plane scales with the inverse $||\vec{u}||^{-2}$, i.e., the area is not
conserved; we can see this from the relation: $dA_{\rm sphere}\propto dA_{\rm
plane}/(1+||\vec{u}||^{2})$ with $dA_{\rm sphere}$ and $dA_{\rm plane}$ are
the area elements of the sphere and the plane, respectively. This feature
could make it hard to distinguish the quantum state representation of large
vectors, $||\vec{u}||>>1$. Without loss of generative power, we scale the
training dataset to be close, in magnitude, to a unitary value, keeping
$||\vec{u}||\sim 1$, where $dA_{\rm sphere}\sim dA_{\rm plane}$ [17]. In the
IS map, we need to establish one scaling factor for all elements in the
classical dataset. Once we process the information in the Hilbert space, the
answer can be de-encoded back to the real plane by

$u_{i}=v_{i}/(1-v_{2^{n}}),\ {\rm for}\ i=1,\cdots,2^{n}-1\ .$ (5)

Figure 2: Sketch of the quantum adversarial game elements. In a), we present
an illustration of the SI encoding of a subset of the MNIST. We compress the
images using the principal component analysis (PCA) and project them onto a
hypersphere to define the representative quantum state amplitudes. On-hardware
implementation requires the preparation of every element of the set ${\cal
C}_{Q}$ by using the PQC used for the generator. b) Once we get the real-data
set, ${\cal C}_{Q}$, we proceed to the sequential discriminator and generator
training. Inside, OPT is the classical optimization algorithm that updates the
discriminator or generator parameters. The stop criteria depend on the
optimizer choice. In c) we present the generator quantum circuit, the ansatz
prepares a 2-qubit state and entangles it with the third qubit through a
uniformly controlled rotation (UCR). This PQC can be extended to more qubits
by applying a cascade of UCRs. For the 4-qubit case, we need to add the UCR
$U_{3}$ growing the PQC parameter set in $2^{3}$ more elements. At the bottom,
the relation between $U_{3}^{0,1,2}$ and $U_{3}^{1,2}$. The recurrence can be
used for higher levels of UCRs (see text for more details). d) Three-qubit
discriminator ansatz, ${\cal G}^{3}$. The ansatz transforms the generated
quantum state or ${\cal C}_{Q}$ to a quantum state in a higher dimensional
Hilbert space. The measurement in the ancillary qubit serves as a metric to
establish the nature of the input.

###  II.2 Quantum state generator and discriminator

We have established the quantum representation of the classical dataset; now,
we shall proceed to introduce a parameterized quantum circuit (PQC) able to
prepare the elements in $C_{Q}$ and new quantum states that the discriminator
will test.

For the quantum state generator and discriminator, we consider the real
amplitude version of the PQC introduced by Möttönen _et al._ [18, 19]. The
generator is designed to prepare an $n$-qubit arbitrary quantum state with the
optimal number of parameters, $2^{n}-1$. Figure 2(b) presents the 3-qubit PQC
based on $Y_{\theta}$ rotations and CX gates. The first part of the ansatz
prepares an arbitrary two-qubit quantum state. This design was studied in [20]
as an optimal preparation. The second part introduces a two-fold uniformly
controlled rotation (UCR) $U_{2}^{0,1}$. In general, the $m$-fold UCR
$U_{q_{m}}^{q_{0},\cdots,q_{m-1}}(\theta_{1},\cdots,\theta_{2^{m}})$ plays a
vital role the state preparation. This operator applies the rotation
$Y_{\theta_{l}}$ on the target qubit state $|q_{m}\rangle$ when $|q_{0}\cdots
q_{m-1}\rangle=|l^{*}\rangle$ with $l^{*}$ as the $m$-bit representation of
$l$, for $l=1,\cdots,2^{m}$. The $m$-fold UCR is built recursively following

$\displaystyle
U_{q_{m}}^{q_{0},\cdots,q_{m-1}}(\theta_{1},\cdots,\theta_{2^{m}})$
$\displaystyle=$ $\displaystyle
U_{q_{m}}^{q_{1},\cdots,q_{m-1}}(\theta_{1},\cdots,\theta_{2^{m-1}})$
$\displaystyle\cdot$ $\displaystyle CX_{q_{0},q_{m}}$ $\displaystyle\cdot$
$\displaystyle
U_{q_{m}}^{q_{1},\cdots,q_{m-1}}(\theta_{2^{m-1}+1},\cdots,\theta_{2^{m}}),$

for $m>1$, where
$U_{q_{1}}^{q_{0}}(\theta_{1},\theta_{2})=[IY]_{\theta_{1}}CX_{q_{0}q_{1}}[IY]_{\theta_{2}}$.
The bottom in Figure 2(c) shows how to generate $U_{3}^{0,1,2}$ from
$U_{2}^{0,1}$. The $n$-qubit generator is built with the application of UCRs
at different levels,

$\displaystyle{\cal G}^{n}(\theta_{1},\cdots,\theta_{2^{n}-1})$
$\displaystyle=$ $\displaystyle[YI\cdots I]_{\theta_{1}}$ $\displaystyle\cdot$
$\displaystyle U_{q_{1}}^{q_{0}}(\theta_{2},\theta_{3})$ $\displaystyle\cdot$
$\displaystyle U_{q_{2}}^{q_{0},q_{1}}(\theta_{4},\cdots,\theta_{7})$
$\displaystyle\vdots$ $\displaystyle\cdot$ $\displaystyle
U_{q_{n-1}}^{q_{0},\cdots,q_{n-2}}(\theta_{2^{n}-2^{n-2}},\cdots,\theta_{2^{n}-1}).$

The number of parameters scale as $2^{n}-1$ and the number of $CX$ gates as
$2^{n}-n-1$. The relationship between the quantum state amplitudes generated
by ${\cal G}^{n}$ with the parameters $\vec{\theta}_{G}$ defines a
parameterization of $\mathbb{S}^{2^{n}-1}$. For more details, see Appendix A.

Figure 3: The expressive power of the 2-qubit discriminator. We represent the
discrimination power by its projection on the characteristic plane for each
discriminator parameter. In a) the quantum circuit for the two-qubit
discriminator, b) the SI encoding model for a single-qubit, and c) heat plots
showing how the discriminator can separate data classes, identified by the
values of $\langle Z\rangle=\pm 1$.

For the discriminator’s ${\cal D}(\theta_{D})$ structure, we consider an
ancillary qubit whose measurement decides whether an input state belongs or
not to the quantum dataset ${\cal C}_{Q}$. In Figure 2(d), we present the
four-qubit PQC design, three qubits for the input to discriminate and a fourth
qubit to measure. The discriminator aims to project an arbitrary quantum state
in $\mathbb{S}^{(2^{n}-1)}$ into a Hilbert space $\mathbb{S}^{(2^{n+1}-1)}$.
For that, we consider the same structure used for the generator with extra
local rotations in the last layer. This makes the number of parameters scale
as $2^{n+1}+n-1$ and the number of CX gates as $2^{n+1}-n-2$. To illustrate
the discrimination mechanism behind ${\cal D}^{n}$, consider the single-qubit
quantum state discrimination. We consider a two-qubit discriminator and
classical data domain in the real line, from 0 to 10 (see Figure 3). Following
the SI encoding, see Fig. 3(b), we show in Fig. 3(c) the different decision
boundaries the discriminator defines when one of its parameters is active,
i.e., $\neq 0$. The decision boundary is defined by $\langle Z\rangle=0$ (see
dotted green lines in Fig. 3(c)).

###  II.3 Interaction and optimization

The discriminator’s interaction with ${\cal C}_{Q}$ and the generator’s output
is as follows. Initially, we calibrate the discriminator by minimizing ${\cal
L}_{D}(\vec{\theta}_{D};\\{\vec{\theta}^{\,k}_{G}\\}_{N})$ with respect to
$\vec{\theta}_{D}$. Once we calibrate the discriminator, we use the optimal
parameter values $\theta_{D}^{*}$ in the generator optimization, i.e.
$\vec{\theta}_{D}\leftarrow\vec{\theta}_{D}^{*}$. In this step, the algorithm
minimizes ${\cal
L}_{G}(\\{\vec{\theta}^{\,k}_{G}\\}_{N};\vec{\theta}_{D}^{*})$, obtaining the
optimal configuration $\\{\vec{\theta}^{\,k}_{G}\\}^{*}_{N}$ that will be used
to update $\\{\vec{\theta}^{\,k}_{G}\\}_{N}$ in the next epoch, i.e.
$\\{\vec{\theta}^{\,k}_{G}\\}_{N}\leftarrow\\{\vec{\theta}^{\,k}_{G}\\}^{*}_{N}$.
In both training processes, discriminator and generator, the algorithm
iterates for a fixed number of steps or quantum circuit executions or until
the learning reach a local minimum and the costs, ${\cal L}_{G}$ and ${\cal
L}_{D}$, do not decrease.

We consider the Covariance Matrix Adaptation Evolution Strategy (CMA-ES), a
gradient-free optimization algorithm, to update the generator and
discriminator parameters in each learning process. This optimization algorithm
uses the principle of biological evolution, where the repeated interplay of
variation and selection yields a global minimum. The evolution strategy starts
with an initial population of
$\Theta=\\{\vec{\theta}_{1},\cdots\vec{\theta}_{P}\\}$, with $P=4+\lfloor
2\log M\rfloor$ and $\vec{\theta}_{k}=(\theta_{1},\cdots,\theta_{M})$. In our
case, $M$ is the number of PQC parameters. In each generation (execution of
$P$ quantum circuits), a new population $\Theta^{\prime}$ is generated by
variation (according to a multivariate normal distribution) of the current
parental population $\Theta$. Then, some individuals in $\Theta^{\prime}$ are
selected to become the next generation parents based on their ${\cal L}_{D/G}$
value. Over the generation sequence, sets of parameters with better and better
${\cal L}_{D/G}$ values are generated. If the population has enough
information to estimate the covariance matrix reliably, the optimizer updates
the covariance matrix that helps compute the new mean value for the
distribution presented in $\Theta^{\prime}$. For a deeper discussion about
stochastic research algorithms, see Ref. [21]. In the numerical experiments,
we use the CMA-ES python implementation [22].

##  III Discussion

We addressed the question of building a quantum adversarial model per the
limitations of commercial quantum processors. We proposed re-qGAN, a re-
imagined and optimized architecture for quantum generative adversarial
networks, using low-budget resources regarding quantum circuit depth and
executions. To avoid any possible loss of information in the classical
encoding, we proposed a novel strategy based on stereographic projection. The
SI encoding offers a one-to-one map to encode classical data into a real
Hilbert space. We can extend this encoding to complex values by embedding the
$n$-qubit Bloch sphere in a $\mathbb{R}^{2^{n+1}-1}$, defining a
$\mathbb{S}^{2^{n+1}-1}$, and associating the points of this hyper-sphere with
points in the real plane $\mathbb{R}^{2^{n+1}-2}$. In doing so, we increase
the size of the real-data dimension we can encode per qubit and simultaneously
the number of CXs and local operations in the quantum state preparation. To
keep the depth of the quantum circuit at a low level and to avoid an
unnecessary boost of quantum imperfection in an eventual on-hardware
implementation, we stick with the real amplitude constraint even though it
needs more qubits to encode the classical information.

Additionally, as illustrated in figure 3, the more affluent input class
enabled by the stereographic encoding positively affects the discriminator’s
classification ability. However, since the inverse stereographic projection is
a conformal map, i.e., it does not preserve distances, fluctuations around the
north pole can be amplified in the real plane bringing error in the de-
encoding process. We can consider a re-scaling factor for the classical input
to keep the projection onto the hyper-sphere away from the north pole.

In the quantum adversarial game, The generator is designed for real amplitude
quantum state preparation. We require fewer parameters but more qubits than we
would if we considered complex amplitude quantum states to encode classical
information. This approach is motivated by the limited set of native gates
available in physical devices and, on the other hand, to minimize the noise
effects related to the quantum circuits’ depth. The relationship between the
generator’s parameters and the quantum amplitudes defines a hyper-sphere
parameterization as illustrated in the 2 and 3 qubit cases in Appendix A. By
constructing a generator that covers the entire real Hilbert space, we get a
good trade-off between expressive power and computational resource
requirements for the adversarial model.

Agents trained in an adversarial game, both in classical or quantum machine
learning [23], do not always converge to Nash equilibrium with gradient
descent [24]. Therefore, by building an architecture using fewer parameters,
we can update the generator and discriminator by gradient-free optimization
procedures without error propagation in consecutive evaluations present in
gradient-based optimizations. The classical optimization performance depends
on the choice of the loss function [25]. In this case, we consider a least-
square-based loss function (Eqs. I and I), with $\pm 1$ as target values. The
configuration of the loss functions pushes the discriminator to converge to a
local minimum, under adversarial training, that yields the desired outcome of
not being able to classify generated samples as fake data.

In the discriminator’s design, we considered the projection of the input
quantum state into a higher dimensional Hilbert space. In Figure 3, we observe
an excellent nonlinear behavior in the way the discriminator can separate data
classes, where the mean value $\langle Z\rangle$ determines the data class in
the ancillary qubit.

We tested our qGAN architecture in the learning task of generating images of
handwritten digits, using a subset of the MNIST dataset as our reference
database. We successfully generated handwritten digit images using 2,3 and 4
qubits. We use a genetic algorithm (CMA-ES) to update the generator’s and
discriminator’s parameters due to the reduced number of parameters in our
model. the re-qGAN algorithm convergences after a fewer number of epochs, in
comparison to state-of-the-art qGAN models, such as [12], while using fewer
resources in general. Its ability to learn distributions in a few epochs,
using a reduced number of parameters and a small training data set, points to
its feasibility on real quantum hardware, with potential advantages such as
quantum error robustness, from using fewer operations and qubits.
Additionally, the re-qGAN structure uses native quantum operations in most of
the superconducting quantum platforms [26], with a small compilation effort in
trapped ions platforms [27]. This further points to its feasibility on
commercial devices.

Counter-intuitively, the re-qGAN’s output resolution does not improve with the
number of qubits. We can explore this feature by studying the non-trivial
correlation between the size of the reference dataset and the number of
qubits. Furthermore, even though re-qGAN’s architecture theoretically provides
flexibility to add more qubits and thus train it on more complex data, scaling
it on quantum hardware will require a good trade-off between computational
resources and algorithmic efficiency. More importantly, re-qGAN can be easily
implemented on a real quantum machine, such as trapped-ion-based quantum
processors, to test its real-world efficiency and benchmark the hardware
capabilities.

## Data availability

All data needed to evaluate the conclusions are available from the
corresponding author upon request.

###### Acknowledgements.

This work was performed at Oak Ridge National Laboratory, operated by UT-
Battelle, LLC under contract DE-AC05-00OR22725 for the US Department of Energy
(DOE). Support for the work came from the DOE Advanced Scientific Computing
Research (ASCR) Accelerated Research in Quantum Computing (ARQC) Program under
field work proposal ERKJ354. S.N. was supported in part by the U.S. Department
of Energy, Office of Science, Office of Workforce Development for Teachers and
Scientists (WDTS) under the Science Graduate Laboratory Internship program.

## Author contributions

S.N. and V.L.-O designed the qGAN workflow and the adversarial algorithm.
V.L.-O. designed the stereographic encoding. S.N. and V.L.-O wrote the code
for the analysis and figures, analyzed the experimental results, and
contributed to the final version of the manuscript.

## Competing interests

The authors declare that there are no competing interests.

##  Appendix A preparation of an arbitrary two-qubit quantum state with real
amplitudes

To clarify the relationship between the parameters $\vec{\theta}$ and the real
amplitudes $x_{1},....,x_{2^{n}}$, we consider the two and three-qubit cases.
The two-qubit case is straightforward and was studied in [20]. There, the
amplitudes follow

$\displaystyle x_{1}$ $\displaystyle=$ $\displaystyle
c_{\theta_{1}}c_{\theta^{\prime}_{1}},\
x_{2}=c_{\theta_{1}}s_{\theta^{\prime}_{1}}$ $\displaystyle x_{3}$
$\displaystyle=$ $\displaystyle s_{\theta_{1}}c_{\theta^{\prime}_{2}},\
x_{4}=s_{\theta_{1}}s_{\theta^{\prime}_{2}}$ (8)

with
$H_{2}(\theta_{2},\theta_{3})^{T}=(\theta^{\prime}_{1},\theta^{\prime}_{2})$.
Where, $H_{k}$ stands for the Hadamard matrix of order $k$,
$c_{\theta}=\cos(\theta/2)$, and $s_{\theta}=\sin(\theta/2)$. The
transformation (8) defines a parameterization for $\mathbb{S}^{3}$, for more
details see Ref. [20]. For the three-qubit case, the amplitudes follow a
pattern

$\displaystyle x_{1}$ $\displaystyle=$ $\displaystyle
c_{\theta_{1}}c_{\theta^{\prime}_{1}}c_{\theta^{\prime\prime}_{1}},\
x_{2}=c_{\theta_{1}}c_{\theta^{\prime}_{1}}s_{\theta^{\prime\prime}_{1}},$
$\displaystyle x_{3}$ $\displaystyle=$ $\displaystyle
c_{\theta_{1}}s_{\theta^{\prime}_{1}}c_{\theta^{\prime\prime}_{4}},\
x_{4}=c_{\theta_{1}}s_{\theta^{\prime}_{1}}s_{\theta^{\prime\prime}_{4}},$
$\displaystyle x_{5}$ $\displaystyle=$ $\displaystyle
s_{\theta_{1}}s_{\theta^{\prime}_{2}}s_{\theta^{\prime\prime}_{2}},\
x_{6}=s_{\theta_{1}}s_{\theta^{\prime}_{2}}c_{\theta^{\prime\prime}_{2}},$
$\displaystyle x_{7}$ $\displaystyle=$ $\displaystyle
s_{\theta_{1}}c_{\theta^{\prime}_{2}}s_{\theta^{\prime\prime}_{3}},\
x_{8}=s_{\theta_{1}}c_{\theta^{\prime}_{2}}c_{\theta^{\prime\prime}_{3}},$ (9)

where,
$H_{2}(\theta_{2},\theta_{3})^{T}=(\theta^{\prime}_{1},\theta^{\prime}_{2})$,
and
$H_{4}(\theta_{4},\cdots,\theta_{7})^{T}=(\theta^{\prime\prime}_{1},\cdots,\theta^{\prime\prime}_{4})^{T}$.
Defining a parameterization for ${\mathbb{S}^{7}}$, therefore, for three (two)
qubits ${\cal G}^{3(2)}$ covers the entire real Hilbert space. By induction,
we can establish that ${\cal G}^{n}$ can prepare an arbitrary quantum state.

An arbitrary real amplitude quantum state
$|\psi\rangle=x_{1}|00\rangle+x_{2}|01\rangle+x_{3}|10\rangle+x_{4}|11\rangle$
in the 2-qubit Hilbert space is prepared following 8. This map between the
parameter space and the hypersphere is one-to-one. It is also surjective,
since we can find for every $\vec{x}\in\mathbb{S}^{3}$, a vector
$\vec{\theta}$ in the parameter space, such that
$\vec{\theta}\rightarrow\vec{x}$ [20]. Since this is true for
$\mathbb{S}^{3}$, an induction argument will show that this is the case for
the n-qubit Hilbert space.

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