A zero-entropy classical shadow reconstruction of density state
  operators
Classical shadow (CS) has opened the door to predicting the characteristics
of quantum systems using very few measurements. As quantum systems grow in
size, new ways to characterize them are needed to show the quality of their
qubits, gates, and how noise affects them. In this work, we explore the
capabilities of CS for reconstructing density state operators of sections of
quantum devices to make a diagnostic of their qubits quality. We introduce
zero-entropy classical shadow (ZECS), a methodology that focuses on
reconstructing a positive semidefinite and unit trace density state operator
using the CS information. This procedure makes a reliable reconstruction of the
density state operator removing partially the errors associated with a limited
sampling and quantum device noise. It gives a threshold of the maximum coherent
information that qubits on a quantum device have. We test ZECS on ibm_lagos and
ibm_brisbane using up to 10,000 shots. We show that with only 6,000 shots, we
can make a diagnostic of the properties of groups of 2, 3, and 4 qubits on the
127-qubits ibm_brisbane device. We show two applications of ZECS: as a routing
technique and as a detector for non-local noisy correlations. In the routing
technique, an optimal set of 20 ibm_brisbane qubits is selected based on the
ZECS procedure and used for a quantum optimization application. This method
improves the solution quality by 10% and extends the quantum algorithm's
lifetime by 33% when compared to the qubits chosen by the best transpilation
procedure in Qiskit. Additionally, with the detector of non-local correlations,
we identify regions of ibm\_brisbane that are not directly connected but have a
strong correlation that maintains in time, suggesting some non-local crosstalk
that can come, for example, at the multiplexing readout stage.
J. A. Montañez-Barrera G. P. Beretta Kristel Michielsen Michael R. von Spakovsky