Classical simulation and verification of quantum computation using matchgates and magic states

使用匹配门和魔法状态进行量子计算的经典模拟和验证

• 批准号: 2746767
• 金额: --
• 依托单位: University of Cambridge
• 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-2746767
• 关键词: Classical; simulation; verification; quantum; computation

Quantum computers allow one to explore computational regimes which are believed to be beyond the reach of current classical computing. Therefore, it is unlikely that universal quantum computers can be efficiently simulated by classical probabilistic algorithms. This is in part because the state-of-the-art classical simulators which rely on the power of modern supercomputers struggle to simulate any quantum system beyond 50 qubits. At the same time, certain quantum information processing tasks do not require computational universality. In some scenarios, there are provable benefits, such as an exponential reduction in communication resources for some distributed computing tasks (e.g. Raz 1999) and in quantum cryptography, the ability to communicate with unconditional security against eavesdropping. To realize quantum computation in a circuit model one has to pick a universal gate set. One of the most prominent gatesets which enables universal quantum computation is made of Clifford + T gates. Clifford gates are efficiently classically simulatable, however, when you add a special single-qubit T gate you regain the full power of quantum computation. In 2016, Bravyi et al. introduced a quantity called stabilizer rank. It helps reduce this exponential scaling by significantly decreasing the scaling of resources required to classically simulate quantum systems. The ability to classically simulate generic quantum computations, while unlikely to be possible for a large number of qubits, is of great importance in the noisy intermediate-term quantum computation (NISQ). Another very natural gateset which enables universal quantum computation is made of so-called Matchgates + Magic states. Matchgates are an especially multiflorous class of two-qubit nearest neighbour quantum gates, defined by a set of algebraic constraints. They occur for example in the theory of perfect matchings of graphs, non-interacting fermions, and one-dimensional spin chains. The goal of the project is to study the analogous notion to stabilizer rank for matchgates - the so-called Gaussian rank and study the computational complexity of approximating this quantity. Currently, nearly nothing is known about Gaussian rank and unlike its stabilizer counterpart, the decompositions of n copies of magic states in terms of Gaussian states for n>3 are not known. This problem presents a unique set of challenges suitable for a strong PhD student and would require a combination of techniques: from numerical exploration for a small number of qubits to proof-based techniques which rely on the unique structural properties of Gaussian states. Computing the exact Gaussian rank for a large number of copies of magic states has a number of important applications for the emerging small-to-medium scale quantum computers. First, it would enable one to verify quantum computations for a non-trivial number of qubits (20-300), which is likely to be the milestoneSecond, it would provide unique insights into the complexity of fermionic linear optics and its abilities to achieve universal quantum computations when supplemented with magic states. Thirdly, it would allow one to design novel quantum error-correcting codes as well as efficient classical decoders.

量子计算机允许人们探索被认为超出当前经典计算的计算制度。因此，不可能通过经典概率算法有效地模拟通用量子计算机。这部分是因为依赖现代超级计算机力量的最先进的古典模拟器难以模拟50码数以上的任何量子系统。同时，某些量子信息处理任务不需要计算普遍性。在某些情况下，有可证明的好处，例如某些分布式计算任务的通信资源的指数减少（例如Raz 1999）和量子密码学，即具有无条件安全性与窃听的无条件安全性的能力。 要在电路模型中实现量子计算，必须选择一个通用门集。启用通用量子计算的最突出的门之一是由Clifford + T门制成。 Clifford Gates在经典上是有效的，但是，当您添加特殊的单位t门时，您会重新获得量子计算的全部功能。在2016年，Bravyi等人。引入了称为稳定器等级的数量。它通过显着降低古典模拟量子系统所需的资源规模来帮助减少这种指数缩放。在嘈杂的中期量子量子计算（NISQ）中，经典模拟通用量子计算的能力非常重要。另一个非常自然的闸门，可以使通用量子计算由所谓的对照头 +魔术状态组成。匹配设备是一个特别多的两分Quitit最近的邻居量子门，由一组代数约束定义。例如，在图，非相互作用的费米和一维旋转链的完美匹配理论中发生。该项目的目的是研究对其有的类似概念，以稳定匹配的稳定器等级 - 所谓的高斯等级，并研究近似值的计算复杂性。目前，关于高斯等级几乎一无所知，与其稳定器的对应物不同，n> 3的n> 3副本的n副本的分解是不知道的。这个问题提出了一组适合强大的博士生的挑战，需要采用多种技术：从少量Qubits的数值探索到依赖高斯州独特的结构特性的基于证明的技术。计算大量魔术状态副本的确切高斯等级为新兴的小型至中等量表量子计算机具有许多重要应用。首先，它将能够验证非平凡数量的Qubits（20-300）的量子计算，这可能是里程碑，它将为费尔米激素线性光学器件的复杂性及其能力提供独特的见解，并在补充魔术状态后实现通用量子计算的能力。第三，它将允许人们设计新颖的量子误差校正代码以及有效的经典解码器。