具有量子错误检测功能的量子近似优化的性能

Zichang He, David Amaro, Ruslan Shaydulin, Marco Pistoia
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引用次数: 0

摘要

必须扩大量子算法的规模,以解决现实世界中的应用问题。要做到这一点,就必须克服当今硬件上存在的噪声。量子近似优化算法(QAOA)对资源的要求不高,而且在某些问题上的渐进速度超过了最先进的经典算法,因此是一种很有前景的扩展候选算法。然而,要利用 QAOA 实现优于经典算法的性能,相信需要一定的容错能力。在本文中,我们利用 $[[k+2,k,2]]$ ``冰山''错误检测代码演示了 QAOA 的部分容错实现。我们发现,在困离子量子计算机上处理逻辑量子比特高达 20 美元的问题时,与未编码电路相比,用冰山代码对电路进行编码能提高算法性能。此外,我们还提出并校准了一个用于预测代码性能的模型,并用它来描述冰山代码的极限,并将其性能推断到错误率更高的未来硬件上。特别是,我们展示了如何利用我们的模型来确定 QAOA 在未来硬件上优于 Goemans-Williamson 算法的必要条件。我们的成果展示了迄今为止在实际应用中受部分容错量子错误检测保护的最大通用量子计算算法,为利用量子计算机解决现实世界的应用问题铺平了道路。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Performance of Quantum Approximate Optimization with Quantum Error Detection
Quantum algorithms must be scaled up to tackle real-world applications. Doing so requires overcoming the noise present on today's hardware. The quantum approximate optimization algorithm (QAOA) is a promising candidate for scaling up due to its modest resource requirements and documented asymptotic speedup over state-of-the-art classical algorithms for some problems. However, achieving better-than-classical performance with QAOA is believed to require fault tolerance. In this paper, we demonstrate a partially fault-tolerant implementation of QAOA using the $[[k+2,k,2]]$ ``Iceberg'' error detection code. We observe that encoding the circuit with the Iceberg code improves the algorithmic performance as compared to the unencoded circuit for problems with up to $20$ logical qubits on a trapped-ion quantum computer. Additionally, we propose and calibrate a model for predicting the code performance, and use it to characterize the limits of the Iceberg code and extrapolate its performance to future hardware with improved error rates. In particular, we show how our model can be used to determine necessary conditions for QAOA to outperform Goemans-Williamson algorithm on future hardware. Our results demonstrate the largest universal quantum computing algorithm protected by partially fault-tolerant quantum error detection on practical applications to date, paving the way towards solving real-world applications with quantum computers.
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