The Phase Ordering Problem for Quantum Circuit Compilation

量子电路编译的相序问题

• 批准号: 2744426
• 金额: --
• 依托单位: University of Oxford
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2022
• 资助国家: 英国
• 起止时间: 2022 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2744426
• 关键词: Phase; Ordering; Problem; Quantum; Circuit

By leveraging the laws of quantum mechanics, quantum computing potentially allows us to perform tasks faster than a classical computer. Current devices are noisy, so algorithmsdesigned for fault-tolerant quantum computers cannot be reliably performed. Improvements made upon the resources required to execute such algorithms will enable larger tasks to beaccurately solved on a quantum computer, bringing us closer to quantum advantage. This proposal presents directions of research in programming language theory and circuit compilation, with the aim of designing new tools for quantum computing research and development.Although impressive progress has been made in developing new quantum algorithms and hardware, in practice quantum programs are still defined using circuits, which are akin to assembly code in classical computing. This is not a sensible way to design large-scale quantum applications, as it prevents the programmer from expressing their ideas in a modular, reusable manner. To fully take advantage of quantum advantage, it is necessary to develop semantics for classical-quantum programming. The algebraic framework proposed by Prof. Sam Staton [1], which characterises the unclonability of quantum information using linear type theory, is a good foundation for implementing a classical-quantum programming language which can use algebraic effects to separate the local classical computation from external quantum computation that permits only linear use of resources. This separation will enable the development of more advanced, less error-prone software that is easier to analyse for acompiler.Although ZX-calculus has enabled the development of new and effective rewrite rules for simplifying circuits [2], there is a lack of research in how to select and apply such rewriterules: many papers on circuit compilation propose new rewrite rules and combine them into a greedy routine without leveraging existing rewrite rules. In general, diagrammaticrewriting is a non-confluent operation, so the order in which the compilation phases are applied can severely impact the results. Meanwhile, this problem of phase ordering has beenmore thoroughly studied in the field of classical compilation [3]. My plan is to use pauliopt, a Pauli gadget based library developed by Dr. Stefano Gogioso and me during my master'sthesis, as a framework for implementing the new optimisation routines that I will develop over the course of the DPhil. As a starting point, I will use machine learning to find theoptimal compilation phase ordering of a given circuit. Then, I will incorporate other phase gadget rewrite rules such as the spider nest identities, which have been naively applied toachieve state-of-the-art T-count reduction.In my opinion, the development of open-source software is crucial to the field of quantum computing, so my papers that propose algorithms are accompanied with implemented code.[4, 5] To demonstrate their effcacy and benefits, the techniques developed over the course of the DPhil will be accompanied with implementation and experiments. In particular, Iwill focus on applying QML techniques to NLP, a field I have gained experience in from my work and undergraduate studies. With the excellent resources and supervision that Oxfordprovides, I believe I will be able to achieve state-of-the-art results and advance the field of quantum computing.My project falls within EPSRC Quantum Technologies area.

通过利用量子力学定律，量子计算可能使我们能够比经典计算机更快地执行任务。当前的设备噪声很大，因此为容错量子计算机设计的算法无法可靠地执行。对执行此类算法所需资源的改进将使量子计算机能够准确解决更大的任务，使我们更接近量子优势。该提案提出了编程语言理论和电路编译的研究方向，旨在为量子计算研究和开发设计新的工具。尽管在开发新的量子算法和硬件方面取得了令人瞩目的进展，但实际上量子程序仍然使用电路，类似于经典计算中的汇编代码。这不是设计大规模量子应用的明智方法，因为它阻止程序员以模块化、可重用的方式表达他们的想法。为了充分利用量子优势，有必要开发经典量子编程的语义。 Sam Staton教授提出的代数框架[1]利用线性类型理论描述了量子信息的不可复制性，为实现经典量子编程语言奠定了良好的基础，该语言可以利用代数效应将局部经典计算与外部计算分开。只允许线性使用资源的量子计算。这种分离将有助于开发更先进、更不易出错的软件，更容易为编译器进行分析。尽管 ZX-calculus 已经能够开发新的有效重写规则来简化电路 [2]，但仍缺乏研究在如何选择和应用此类重写规则方面：许多有关电路编译的论文提出了新的重写规则，并将它们组合成贪婪例程，而不利用现有的重写规则。一般来说，图解重写是一种非融合操作，因此编译阶段的应用顺序会严重影响结果。同时，这个相序问题在经典编译领域得到了更深入的研究[3]。我的计划是使用 pauliopt，这是一个由 Stefano Gogioso 博士和我在硕士论文期间开发的基于 Pauli gadget 的库，作为实现我将在 DPhil 课程中开发的新优化例程的框架。作为起点，我将使用机器学习来找到给定电路的最佳编译阶段顺序。然后，我将结合其他阶段小工具重写规则，例如蜘蛛巢身份，这些规则已被天真地应用于实现最先进的 T 计数减少。 在我看来，开源软件的开发对于量子计算领域，所以我提出算法的论文都附有实现的代码。[4, 5] 为了证明其功效和优点，在博士学位课程中开发的技术将附有实现和实验。特别是，我将专注于将 QML 技术应用到 NLP 中，这是我从工作和本科学习中获得的经验。凭借牛津大学提供的优质资源和监督，我相信我将能够取得最先进的成果并推进量子计算领域的发展。我的项目属于 EPSRC 量子技术领域。