Abstract
Fault tolerance is a prerequisite for scalable quantum computing. Architectures based on 2D topological codes are effective for near-term implementations of fault tolerance. To obtain high performance with these architectures, we require a decoder which can adapt to the wide variety of error models present in experiments. The typical approach to the problem of decoding the surface code is to reduce it to minimum-weight perfect matching in a way that provides a suboptimal threshold error rate, and is specialized to correct a specific error model. Recently, optimal threshold error rates for a variety of error models have been obtained by methods which do not use minimum-weight perfect matching, showing that such thresholds can be achieved in polynomial time. It is an open question whether these results can also be achieved by minimum-weight perfect matching. In this work, we use belief propagation and a novel algorithm for producing edge weights to increase the utility of minimum-weight perfect matching for decoding surface codes. This allows us to correct depolarizing errors using the rotated surface code, obtaining a threshold of 17.76±0.02%. This is larger than the threshold achieved by previous matching-based decoders (14.88±0.02%), though still below the known upper bound of ∼18.9%.
Highlights
Quantum information processing (QIP) provides a means of implementing certain algorithms with far lower memory and processing requirements than is possible in classical computing [1, 2]
The analog nature of quantum operations suggests that devices which perform QIP will have to function correctly in the presence of small deviations between ideal operations and those that are implemented, a property called fault tolerance [3, 4]
Many external sources of error exist in current QIP devices, making fault tolerance a practical necessity as well as a theoretical one
Summary
Quantum information processing (QIP) provides a means of implementing certain algorithms with far lower memory and processing requirements than is possible in classical computing [1, 2]. In order to design fault-tolerant QIP protocols, we first require a set of quantum states for which the effect of small deviations can be reversed, called a quantum error-correcting code [5], analogous to classical error-correcting codes [6]. A large set of quantum error-correcting codes, called stabiliser codes [3], allow the measurement of multi-qubit operators which yield results depending only on which error has occurred, and not on the code state itself. In order to correct these Pauli errors, it is necessary to derive an error which reproduces the given syndrome, and is unlikely to alter the intended logical state if performed on the system This process, called decoding, is non-trivial, since a code with n physical qubits will typically contain O(n) stabilisers, so the number of possible syndromes scales as 2n, prohibiting the use of a simple lookup table.
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