A promising strategy to protect quantum information from noise-induced errors
is to encode it into the low-energy states of a topological quantum memory
device. However, readout errors from such memory under realistic settings is
less understood. We study the problem of decoding quantum information encoded
in the groundspaces of topological stabilizer Hamiltonians in the presence of
generic perturbations, such as quenched disorder. We first prove that the
standard stabilizer-based error correction and decoding schemes work adequately
well in such perturbed quantum codes by showing that the decoding error
diminishes exponentially in the distance of the underlying unperturbed code. We
then prove that Quantum Neural Network (QNN) decoders provide an almost
quadratic improvement on the readout error. Thus, we demonstrate provable
advantage of using QNNs for decoding realistic quantum error-correcting codes,
and our result enables the exploration of a wider range of non-stabilizer codes
in the near-term laboratory settings.

一种保护量子信息免受噪音诱导错误的有前途的策略是将其编码到拓扑量子存储设备的低能态中。在现实情况下，对于这种存储器的读出错误却不为人所熟知。我们研究在存在诸如淬灭性紊乱等通用扰动的情况下，解码编码在拓扑稳定子哈密顿量的基态中的量子信息的问题。首先，我们通过证明在这种扰动的量子码中，基于稳定子的纠错和解码方案能够适当地发挥作用，从而使得解码误差按照基础未扰动码的距离呈指数下降。然后，我们证明了量子神经网络（QNN）编码器可以几乎使读出错误有二次改善。因此，我们证明了在解码现实量子纠错码时使用 QNN 的有利，这一结果使得在近期实验室环境中可以探索更广泛的非稳定子码范围。

量子神经网络作为量子信息解码器的优势

Advantage of Quantum Neural Networks as Quantum Information Decoders

In the current era of noisy intermediate-scale quantum (NISQ) computers,
noisy qubits can result in biased results for early quantum algorithm
applications. This is a significant challenge for interpreting results from
quantum computer simulations for quantum chemistry, nuclear physics, high
energy physics, and other emerging scientific applications. An important class
of qubit errors are readout errors. The most basic method to correct readout
errors is matrix inversion, using a response matrix built from simple
operations to probe the rate of transitions from known initial quantum states
to readout outcomes. One challenge with inverting matrices with large
off-diagonal components is that the results are sensitive to statistical
fluctuations. This challenge is familiar to high energy physics, where
prior-independent regularized matrix inversion techniques (`unfolding') have
been developed for years to correct for acceptance and detector effects when
performing differential cross section measurements. We study various unfolding
methods in the context of universal gate-based quantum computers with the goal
of connecting the fields of quantum information science and high energy physics
and providing a reference for future work. The method known as iterative
Bayesian unfolding is shown to avoid pathologies from commonly used matrix
inversion and least squares methods.

本文探讨如何纠正嘈杂中间尺度量子计算机的传输误差，并研究了一种名为迭代贝叶斯展开的方法，在量子信息科学和高能物理领域之间建立桥梁，并为未来的研究提供参考。