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Improving the speed of variational quantum algorithms for quantum error correction

Author(s)
Zoratti, Fabio; De Palma, Giacomo; Kiani, Bobak; Nguyen, Quynh T.; Marvian, Milad; Lloyd, Seth; Giovannetti, Vittorio; ... Show more Show less
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Abstract
We consider the problem of devising suitable quantum error correction (QEC) procedures for a generic quantum noise acting on a quantum circuit. In general, there is no analytic universal procedure to obtain the encoding and correction unitary gates, and the problem is even harder if the noise is unknown and has to be reconstructed. The existing procedures rely on variational quantum algorithms (VQAs) and are very difficult to train since the size of the gradient of the cost function decays exponentially with the number of qubits. We address this problem using a cost function based on the quantum Wasserstein distance of order 1 (QW1). At variance with other quantum distances typically adopted in quantum information processing, QW1 lacks the unitary invariance property which makes it a suitable tool to avoid getting trapped in local minima. Focusing on a simple noise model for which an exact QEC solution is known and can be used as a theoretical benchmark, we run a series of numerical tests that show how, guiding the VQA search through the QW1, can indeed significantly increase both the probability of a successful training and the fidelity of the recovered state, with respect to the results one obtains when using conventional approaches.
Date issued
2023-08-18
URI
https://hdl.handle.net/1721.1/153922
Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science; Massachusetts Institute of Technology. Department of Mechanical Engineering
Journal
Physical Review A
Publisher
American Physical Society
Citation
Zoratti, Fabio, De Palma, Giacomo, Kiani, Bobak, Nguyen, Quynh T., Marvian, Milad et al. 2023. "Improving the speed of variational quantum algorithms for quantum error correction." Physical Review A, 108 (2).
Version: Final published version
ISSN
2469-9926
2469-9934

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