Abstract
Laboratory hardware is rapidly progressing towards a state where quantum error-correcting codes can be realised. As such, we must learn how to deal with the complex nature of the noise that may occur in real physical systems. Single qubit Pauli errors are commonly used to study the behaviour of error-correcting codes, but in general we might expect the environment to introduce correlated errors to a system. Given some knowledge of structures that errors commonly take, it may be possible to adapt the error-correction procedure to compensate for this noise, but performing full state tomography on a physical system to analyse this structure quickly becomes impossible as the size increases beyond a few qubits. Here we develop and test new methods to analyse blue a particular class of spatially correlated errors by making use of parametrised families of decoding algorithms. We demonstrate our method numerically using a diffusive noise model. We show that information can be learnt about the parameters of the noise model, and additionally that the logical error rates can be improved. We conclude by discussing how our method could be utilised in a practical setting blue and propose extensions of our work to study more general error models.
Highlights
The success of scalable quantum computation depends on our ability to diagnose and repair errors incident to the underlying physical qubits [1, 2, 3, 4, 5, 6, 7] of the system
We show that information can be learnt about the parameters of the noise model, and that the logical error rates can be improved
We have developed diagnostic tools to analyse an unknown parameter of a correlated error model acting on the toric code
Summary
The success of scalable quantum computation depends on our ability to diagnose and repair errors incident to the underlying physical qubits [1, 2, 3, 4, 5, 6, 7] of the system. Correlated errors occur when considering syndrome measurements under the circuit-based noise model [40, 41, 42, 43, 44], and while applying transversal logical gates to quantum error-correcting codes that are not in their code space [45]. [54] that recently became available These works make use of local syndrome data to determine different parameters in the error model. We make use of a decoding algorithm that uses global syndrome data to distinguish more generic correlated error models where error events may correlate over a large number of adjacent qubits.
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