Abstract
A fault-tolerant quantum computation requires an efficient means to detect and correct errors that accumulate in encoded quantum information. In the context of machine learning, neural networks are a promising new approach to quantum error correction. Here we show that a recurrent neural network can be trained, using only experimentally accessible data, to detect errors in a widely used topological code, the surface code, with a performance above that of the established minimum-weight perfect matching (or blossom) decoder. The performance gain is achieved because the neural network decoder can detect correlations between bit-flip (X) and phase-flip (Z) errors. The machine learning algorithm adapts to the physical system, hence no noise model is needed. The long short-term memory layers of the recurrent neural network maintain their performance over a large number of quantum error correction cycles, making it a practical decoder for forthcoming experimental realizations of the surface code.
Highlights
A quantum computer needs the help of a powerful classical computer to overcome the inherent fragility of entangled qubits
Topological codes such as the surface code, which store a logical qubit in the topology of an array of physical qubits, are attractive because they combine a favorable performance on small circuits with scalability to larger circuits [4–9]
A test on a topological code (Kitaev’s toric code [14]) revealed a performance for phase-flip errors that was comparable to decoders based on the minimum-weight perfect matching (MWPM or “blossom”) algorithm of Edmonds [15–17]
Summary
A quantum computer needs the help of a powerful classical computer to overcome the inherent fragility of entangled qubits. In this work we design a recurrent neural network decoder that has both these features, and demonstrate a performance improvement over a blossom decoder in a realistic simulation of a forthcoming error correction experiment. Our decoder achieves this improvement through its ability to detect bit-flip (X) and phase-flip (Z) errors separately as well as correlations (Y). Right: Since direct four-fold parity measurements are impractical, the measurements are instead performed by entanglement with an ancilla qubit, followed by a measurement of the ancilla in the computational basis Both data qubits and ancilla qubits accumulate errors during idle periods (labeled I) and during gate operations (Hadamard H and cnot), which must be accounted for by a decoder.
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