Quantum Simulations of Hadron Dynamics in the Schwinger Model using 112
  Qubits
Hadron wavepackets are prepared and time evolved in the Schwinger model using
112 qubits of IBM's 133-qubit Heron quantum computer ibm_torino. The
initialization of the hadron wavepacket is performed in two steps. First, the
vacuum is prepared across the whole lattice using the recently developed
SC-ADAPT-VQE algorithm and workflow. SC-ADAPT-VQE is then extended to the
preparation of localized states, and used to establish a hadron wavepacket on
top of the vacuum. This is done by adaptively constructing low-depth circuits
that maximize the overlap with an adiabatically prepared hadron wavepacket. Due
to the localized nature of the wavepacket, these circuits can be determined on
a sequence of small lattices using classical computers, and then robustly
scaled to prepare wavepackets on large lattices for simulations using quantum
computers. Time evolution is implemented with a second-order Trotterization. To
reduce both the required qubit connectivity and circuit depth, an approximate
quasi-local interaction is introduced. This approximation is made possible by
the emergence of confinement at long distances, and converges exponentially
with increasing distance of the interactions. Using multiple error-mitigation
strategies, up to 14 Trotter steps of time evolution are performed, employing
13,858 two-qubit gates (with a CNOT depth of 370). The propagation of hadrons
is clearly identified, with results that compare favorably with Matrix Product
State simulations. Prospects for a near-term quantum advantage in simulations
of hadron scattering are discussed.
Roland C. Farrell Marc Illa Anthony N. Ciavarella Martin J. Savage