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Bulletin of the American Physical Society

Diagnosing Errors in Qubit Gates Using Continuous Measurements (Theory)

John Steinmetz, Debmalya Das, Gerwin Koolstra, Noah Stevenson, Karthik Siva, William P. Livingston, Ravi Naik, David Santiago, Irfan A. Siddiqi, Andrew N. Jordan

Published Mar 15, 2021• 0 citations
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Canonical discrete quantum error correction (DQEC) schemes use projective von Neumann measurements on stabilizers to discretize the error syndromes into a finite set, and fast unitary gates are applied to recover the corrupted information. Quantum error correction (QEC) based on continuous measurement, known as continuous quantum error correction (CQEC), in principle, can be executed faster than DQEC and can also be resource efficient. However, CQEC requires meticulous filtering of noisy continuous measurement data to reliably extract error syndromes on the basis of which errors could be detected. In this paper, we show that by constructing a measurement-based estimator (MBE) of the logical qubit to be protected, which is driven by the noisy continuous measurement currents of the stabilizers, it is possible to accurately track the errors occurring on the physical qubits in real time. We use this MBE to develop a continuous quantum error correction (MBE-CQEC) scheme that can protect the logical qubit to a high degree, surpassing the performance of DQEC, and also allows QEC to be conducted either immediately or in delayed time with instantaneous feedbacks.
Faults are stochastic by nature while most man-made systems, and especially computers, work deterministically. This necessitates the linking of probability theory with mathematical logics, automata, and switching circuit theory. This paper provides such a connecting via quantum information theory which is an intuitive approach as quantum physics obeys probability laws. In this paper we provide a novel approach for computing diagnosis of switching circuits with gate-based quantum computers. The approach is based on the idea of putting the qubits representing faults in superposition and compute all, often exponentially many, diagnoses simultaneously. We empirically compare the quantum algorithm for diagnostics to an approach based on SAT and model-counting. For a benchmark of combinational circuits we establish an error of less than one percent in estimating the true probability of faults.