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Recovery map quantum error correction4/30/2023 Recently, the development of error correcting codes tailored to particular physical noise models has helped relax these requirements. Our work sheds new light on the understanding of QECC in general, which may also help to enhance near-term device performance with channel-adaptive error-correcting codes.Įxecuting quantum algorithms on error-corrected logical qubits is a critical step for scalable quantum computing, but the requisite numbers of qubits and physical error rates are demanding for current experimental hardware. Furthermore, we found many new channel-adaptive codes for error models involving nearest-neighbor correlated errors. We also found new ( ( 6, 2, 3 ) ) 2 and ( ( 7, 2, 3 ) ) 2 codes that are not equivalent to any stabilizer code, and extensive numerical evidence with VarQEC suggests that a ( ( 7, 3, 3 ) ) 2 code does not exist. We have verified its effectiveness by (re)discovering some symmetric and asymmetric codes, e.g., ( ( n, 2 n − 6, 3 ) ) 2 for n from 7 to 14. In principle, VarQEC can find quantum codes for any error model, whether additive or non-additive, degenerate or non-degenerate, pure or impure. Given the target noise channel (or the target code parameters) and the hardware connectivity graph, we optimize a shallow variational quantum circuit to prepare the basis states of an eligible code. The cost functions are inspired by the most general and fundamental requirements of a QECC, the Knill-Laflamme conditions. Here we present VarQEC, a noise-resilient variational quantum algorithm to search for quantum codes with a hardware-efficient encoding circuit. However, the majority of these codes are not suitable for near-term quantum devices. In the past two decades, various constructions of quantum error-correcting codes (QECCs) have been developed, leading to many good code families. Quantum error correction is believed to be a necessity for large-scale fault-tolerant quantum computation. Moreover, we find that, even in the presence of moderate noise in the quantum autoencoders themselves, they may still be successfully used to perform beneficial quantum error correction and thereby extend the lifetime of a logical qubit. We also show that quantum neural networks can be used to discover new logical encodings that are optimally adapted to the underlying noise. We highlight that the denoising capabilities of quantum autoencoders are not limited to the protection of specific states but extend to the entire logical codespace. Specifically, we demonstrate how quantum neural networks, in the form of quantum autoencoders, can be trained to learn optimal strategies for active detection and correction of errors, including spatially correlated computational errors as well as qubit losses. In this paper we investigate the potential of quantum machine learning for quantum error correction in a quantum memory. Active quantum error correction is a central ingredient to achieve robust quantum processors.
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