Neural networks have shown their effectiveness in various tasks in the realm
of quantum computing. However, their application in quantum error mitigation, a
crucial step towards realizing practical quantum advancements, has been
restricted by reliance on noise-free statistics. To tackle this critical
challenge, we propose a data augmentation empowered neural model for error
mitigation (DAEM). Our model does not require any prior knowledge about the
specific noise type and measurement settings and can estimate noise-free
statistics solely from the noisy measurement results of the target quantum
process, rendering it highly suitable for practical implementation. In
numerical experiments, we show the model's superior performance in mitigating
various types of noise, including Markovian noise and Non-Markovian noise,
compared with previous error mitigation methods. We further demonstrate its
versatility by employing the model to mitigate errors in diverse types of
quantum processes, including those involving large-scale quantum systems and
continuous-variable quantum states. This powerful data augmentation-empowered
neural model for error mitigation establishes a solid foundation for realizing
more reliable and robust quantum technologies in practical applications.

我们提出了一种数据增强的神经模型来进行错误缓解，可以从目标量子过程的噪声测量结果中估计无噪声的统计数据，相比之前的错误缓解方法，在缓解各种类型的噪声方面具有卓越的性能。

具有数据增强的柔性量子进程误差修正的神经模型

Flexible Error Mitigation of Quantum Processes with Data Augmentation  Empowered Neural Model

Quantum computers are actively competing to surpass classical supercomputers,
but quantum errors remain their chief obstacle. The key to overcoming these on
near-term devices has emerged through the field of quantum error mitigation,
enabling improved accuracy at the cost of additional runtime. In practice,
however, the success of mitigation is limited by a generally exponential
overhead. Can classical machine learning address this challenge on today's
quantum computers? Here, through both simulations and experiments on
state-of-the-art quantum computers using up to 100 qubits, we demonstrate that
machine learning for quantum error mitigation (ML-QEM) can drastically reduce
overheads, maintain or even surpass the accuracy of conventional methods, and
yield near noise-free results for quantum algorithms. We benchmark a variety of
machine learning models -- linear regression, random forests, multi-layer
perceptrons, and graph neural networks -- on diverse classes of quantum
circuits, over increasingly complex device-noise profiles, under interpolation
and extrapolation, and for small and large quantum circuits. These tests employ
the popular digital zero-noise extrapolation method as an added reference. We
further show how to scale ML-QEM to classically intractable quantum circuits by
mimicking the results of traditional mitigation results, while significantly
reducing overhead. Our results highlight the potential of classical machine
learning for practical quantum computation.

今天的量子计算机是否能通过传统方法的量子错误纠正来解决量子计算机的潜在困难是一个挑战，但机器学习为量子错误纠正提供了潜在解决方案，通过模拟和实验，机器学习在 100 量子位的量子计算机上得到了许多正面结果，并且展现了在各种量子电路和设备噪声情况下的潜力。

实用量子误差缓解的机器学习

Machine Learning for Practical Quantum Error Mitigation

Quantum computers can exploit a Hilbert space whose dimension increases
exponentially with the number of qubits. In experiment, quantum supremacy has
recently been achieved by the Google team by using a noisy intermediate-scale
quantum (NISQ) device with over 50 qubits. However, the question of what can be
implemented on NISQ devices is still not fully explored, and discovering useful
tasks for such devices is a topic of considerable interest. Hybrid
quantum-classical algorithms are regarded as well-suited for execution on NISQ
devices by combining quantum computers with classical computers, and are
expected to be the first useful applications for quantum computing. Meanwhile,
mitigation of errors on quantum processors is also crucial to obtain reliable
results. In this article, we review the basic results for hybrid
quantum-classical algorithms and quantum error mitigation techniques. Since
quantum computing with NISQ devices is an actively developing field, we expect
this review to be a useful basis for future studies.

本文回顾了混合量子 - 经典算法和量子误差缓解技术的基本结果，提出了评估使用嘈杂中尺度量子（NISQ）设备的有用性的方法。

混合量子 - 经典算法与量子误差纠正

Hybrid quantum-classical algorithms and quantum error mitigation

Noise in quantum hardware remains the biggest roadblock for the
implementation of quantum computers. To fight the noise in the practical
application of near-term quantum computers, instead of relying on quantum error
correction which requires large qubit overhead, we turn to quantum error
mitigation, in which we make use of extra measurements. Error extrapolation is
an error mitigation technique that has been successfully implemented
experimentally. Numerical simulation and heuristic arguments have indicated
that exponential curves are effective for extrapolation in the large circuit
limit with an expected circuit error count around unity. In this article, we
extend this to multi-exponential error extrapolation and provide more rigorous
proof for its effectiveness under Pauli noise. This is further validated via
our numerical simulations, showing orders of magnitude improvements in the
estimation accuracy over single-exponential extrapolation. Moreover, we develop
methods to combine error extrapolation with two other error mitigation
techniques: quasi-probability and symmetry verification, through exploiting
features of these individual techniques. As shown in our simulation, our
combined method can achieve low estimation bias with a sampling cost multiple
times smaller than quasi-probability while without needing to be able to adjust
the hardware error rate as required in canonical error extrapolation.

本文介绍了一个使用多指数误差外推和结合单指数外推、准概率和对称性验证等误差缓解技术的方法来缓解实际量子计算机中的噪声的方法，并经过数值模拟验证其在缓解 Pauli 噪声上的有效性。