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Paper 1

Non-Exponential Behaviour in Logical Randomized Benchmarking

Athena Ceasura, Pavithran Iyer, Joel J. Wallman, Hakop Pashayan

Year

2022

Journal

arXiv preprint

DOI

arXiv:2212.05488

arXiv

2212.05488

We construct a gate and time-independent noise model that results in the output of a logical randomized benchmarking protocol oscillating rather than decaying exponentially. To illustrate our idea, we first construct an example in standard randomized benchmarking where we assume the existence of ``hidden'' qubits, permitting a choice of representation of the Clifford group that contains multiplicities. We use the multiplicities to, with each gate application, update a hidden memory of the gate history that we use to circumvent theorems which guarantee the output decays exponentially. In our focal setting of logical randomized benchmarking, we show that the presence of machinery associated with the implementation of quantum error correction can facilitate non-exponential decay. Since, in logical randomized benchmarking, the role of the hidden qubits is assigned to the syndrome qubits used in error correction and these are strongly coupled to the logical qubits via a decoder.

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Paper 2

Estimating and decoding coherent errors of QEC experiments with detector error models

Evangelia Takou, Kenneth R. Brown

Year

2025

Journal

arXiv preprint

DOI

arXiv:2510.23797

arXiv

2510.23797

Decoders of quantum error correction (QEC) experiments make decisions based on detected errors and the expected rates of error events, which together comprise a detector error model. Here we show that the syndrome history of QEC experiments is sufficient to detect and estimate coherent errors, removing the need for prior device benchmarking experiments. Importantly, our method shows that experimentally determined detector error models work equally well for both stochastic and coherent noise regimes. We model fully-coherent or fully-stochastic noise for repetition and surface codes and for various phenomenological and circuit-level noise scenarios, by employing Majorana and Monte Carlo simulators. We capture the interference of coherent errors, which appears as enhanced or suppressed physical error rates compared to the stochastic case, and also observe hyperedges that do not appear in the corresponding Pauli-twirled models. Finally, we decode the detector error models undergoing coherent noise and find different thresholds compared to detector error models built based on the stochastic noise assumption.

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