arXiv subjects

Sam J. Griffiths

Publications and source records attributed to Sam J. Griffiths.

3 recordsLinked to original sources

arXiv2026

The limits of erasure-based postselection for quantum error mitigation

In both classical and quantum error correction, heralded erasures are known to be easier to tolerate than unheralded general stochastic errors. Whilst an established benefit of loss-dominant quantum architectures such as photonic qubits, this fact has received renewed interest, with a pivot towards reconstructing other architectures to be erasure-dominant, such as dual-rail transmons. This work investigates exploiting these 'erasure qubits' in the near term by using postselection as a technique for error mitigation, wherein circuit shots detecting any erased qubits are discarded from the computational ensemble and repeated. Firstly, we outline a numerical framework for representing circuit-level erasure noise and present 'erado', an open-source library capable of simulating erasure noise and postselection. Secondly, we investigate the effects of both erasure noise and noise in the erasure checks themselves on the quantum Fourier transform (QFT), in the additional presence of gate depolarising noise. A worked example is provided of postselection fully mitigating against the erasure channel for erasure check error rates less than 3.0%. We also show how a postselected dual-rail system can surpass a fundamental noise floor at the kiloquop scale where a comparable single-rail system cannot, justifying this approach in the NISQ regime before (and, perhaps, combined with) the practical arrival of QEC.

quant-ph↗

arXiv2025

Online Gaussian elimination for quantum LDPC decoding

Decoders for quantum LDPC codes generally rely on solving a parity-check equation with Gaussian elimination, with the generalised union-find decoder performing this repeatedly on growing clusters. We present an online variant of the Gaussian elimination algorithm which maintains an LUP decomposition in order to process only new rows and columns as they are added to a system of equations. This is equivalent to performing Gaussian elimination once on the final system of equations, in contrast to the multiple rounds of Gaussian elimination employed by the generalised union-find decoder. It thus significantly reduces the number of operations performed by the decoder. We consider the generalised union-find decoder as an example use case and present a complexity analysis demonstrating that both variants take time cubic in the number of qubits in the general case, but that the number of operations performed by the online variant is lower by an amount which itself scales cubically. This analysis is also extended to the regime of 'well-behaved' codes in which the number of growth iterations required is bounded logarithmically in error weight. Finally, we show empirically that our online variant outperforms the original offline decoder in average-case time complexity on codes with sparser parity-check matrices or greater covering radius.

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arXiv2023

Union-find quantum decoding without union-find

The union-find decoder is a leading algorithmic approach to the correction of quantum errors on the surface code, achieving code thresholds comparable to minimum-weight perfect matching (MWPM) with amortised computational time scaling near-linearly in the number of physical qubits. This complexity is achieved via optimisations provided by the disjoint-set data structure. We demonstrate, however, that the behaviour of the decoder at scale underutilises this data structure for twofold analytic and algorithmic reasons, and that improvements and simplifications can be made to architectural designs to reduce resource overhead in practice. To reinforce this, we model the behaviour of erasure clusters formed by the decoder and show that there does not exist a percolation threshold within the data structure for any mode of operation. This yields a linear-time worst-case complexity for the decoder at scale, even with a naive implementation omitting popular optimisations.

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