Accreditation for Analogue Quantum Computing Systems

使用量子系统作为信息承载和处理单元，有望为计算提供一种新的范式，在从化学、材料科学、生物学到优化、机器学习和金融等关键任务中，它可以提供比现有“经典”计算更强大的计算能力。在过去的十年中，这种理论上的可能性已经开始成为一个非常现实的前景，政府和工业倡议已经为量子计算系统的发展做出了贡献，这些系统已经开始提供计算量子优势。如何验证或基准测试量子计算系统的性能是最重要的实践和理论问题之一，特别是在经典计算机无法在合理时间内模拟的情况下。这个问题的实际意义是显而易见的：量子计算机取得了量子优势吗？计算是否正确，或者不完美是否会损害性能优势，因此，客户是否应该向量子计算提供商付费？已经开发了许多验证和基准测试方法，每种方法都有其优点和缺点（Eisert et al Nature Reviews Physics 2020）。仅举几例：有效验证任何数字量子计算的通用方法已经开发和实现（例如Bartz， Fitzsimons, Kashefi, Walther Nature Physics 2013），但需要一个数字化的容错系统，并且需要额外的开销。如果一个人对依赖于对误差的几个假设的性能基准测试感到满意，那么随机基准测试是有效的。提高重建输出量子态的效率仍然是指数级昂贵的，但有应用(例如。“高效”断层扫描和直接保真度估计)。最近，一些方法也被用于嘈杂的中尺度量子器件（Leichtle等人PRX quantum 2021， Ferracin, Kapourniotis, Datta NJP 2019）。量子计算设备大致可以分为两类。数字量子计算机（DQC），与经典计算机类似，其可能的操作是离散的，例如它由一组有限（通用）门集合组成。模拟量子计算机（AQC）使用随时间不断进化的量子系统（在一些可调谐的相互作用下）。在AQC中，包括量子模拟器、量子退火炉（如D-Wave）和绝热量子计算机。后者目前在量子位方面的可扩展性更好，但更难应用量子纠错技术。因此，至少在短期内，AQC很可能会提供更多有用的量子优势的例子。有趣的是，虽然在验证和基准测试DQC方面已经做了大量的工作，但对于AQC却做得很少，因为这些技术通常不适用，这在研究中开辟了一个令人兴奋的空白。在这个项目中，我们将在DQC现有方法的基础上解决模拟量子计算的验证和基准测试。我们将首先专注于扩展随机基准测试模拟版本的早期结果，推广数学工具（旋转，近似2-设计等），提供理论基础并修改方法以实际实施。然后，我们将专注于其他验证方法，并探索哪些方法可以针对每个不同的模拟量子计算系统进行修改，如量子模拟器，量子退火，绝热量子计算机。

The use of quantum systems as information carrying and processing units promises a new paradigm for computation that could offer significantly greater computational power than existing "classical" computing in crucial tasks, from chemistry, material science, biology to optimisation, machine learning and finance. This theoretical possibility, during the last decade, has started to emerge as a very realistic prospect, where governmental and industrial initiatives have contributed to the development of quantum computing systems that have started offering computational quantum advantage.One of the most important practical and theoretical question is how to verify or benchmark the performance of a quantum computing system, especially where it cannot be simulated with classical computers in reasonable time. The practical relevance of this question is evident: has a quantum computer achieved quantum advantage ? Is the computation correct or do imperfections compromise the performance advantage, and thus , should a client pay a quantum computing provider?Many verification and benchmarking methods have been developed, each with their strengths and short-comings (Eisert et al Nature Reviews Physics 2020). To name a few: a universal method for verifying any digital quantum computation efficiently has been developed and realised (e.g. Bartz, Fitzsimons, Kashefi, Walther Nature Physics 2013), but requires a digital, fault-tolerant system, and requires additional overhead. If one is satisfied with a performance benchmarking that relies on several assumptions on the errors , randomised benchmarking works. Improving the efficiency of reconstructing the output quantum state is still exponentially expensive but has applications (e.g. "efficient" tomography and direct fidelity estimation). While recently some methods have also been adapted for noisy intermediate scale quantum devices (Leichtle et al PRX Quantum 2021, Ferracin, Kapourniotis, Datta NJP 2019). Quantum computing devices can broadly be grouped into two categories. Digital quantum computers (DQC), similar to classical computers the possible operations are discrete, for example it consist from a set of a finite (universal) gate set. Analogue quantum computers (AQC) that use quantum systems that evolve continuously in time (under some tuneable interaction). In AQC one includes quantum simulators, quantum annealers (such as D-Wave) and adiabatic quantum computers . The latter category currently scales better in terms of qubits but is harder to apply quantum error correction techniques. Thus, at least in the near-term, it is very likely that AQC may provide more examples of useful quantum advantage. Interestingly, while extensive work has been done in verifying and benchmarking DQC, little has been done for AQC, since the techniques do not generally apply, opening up an exciting gap in the research. In this project we will address verification and benchmarking for analogue quantum computing, building on the existing methods for DQC. We will first focus on extending early results on the analogue version of randomised benchmarking, generalising the mathematical tools (twirling, approximate 2-designs, etc), providing the theoretical basis and modifying the method to be practically implementable. We will then concentrate on other methods of verification and explore which ones can be modified for each of the different analogue quantum computing systems of interest such as quantum simulators, quantum annealing, adiabatic quantum computers.