Towards Enhanced Verification of Near-Term Small-Scale Quantum Systems with Restricted Architectures

该项目的重点是为受限的低复杂度量子架构开发量子验证技术，特别是模拟量子模拟器。人们普遍认为，量子计算机将能够解决经典难以解决的问题。量子验证是量子计算的一个领域，旨在回答这样一个问题：如果量子计算机解决了一个经典无法解决的问题，那么如何验证结果是正确的？这个问题针对的是高度复杂的系统。然而，从低复杂度量子系统的角度考虑这个问题，我们可以将验证重新定义为系统性能的度量和特定情况下系统中存在的噪声的表征。量子模拟器是模拟另一个物理量子设备的工程量子系统。虽然大多数量子计算和量子模拟的架构处理离散变量，量子逻辑门（数字），模拟量子模拟器涉及所谓的时间演化算子，因此与当前用于数字量子计算机/模拟器的量子验证技术不兼容。该项目的目标是开发一种量子验证技术，该技术可以评估模拟量子模拟器的性能，超出当前测试模拟器计算可靠性的技术范围。量子模拟器对于理解多体量子系统的动力学、量子信息、纠缠和某些物理现象的特定性质至关重要。因此，在模拟量子模拟器中建立信任作为物理量子系统的仿真是非常重要的。当模拟量子模拟器被设计成产生远程相互作用时，当前的技术在较短的时间尺度和少量的量子比特上失败了。该项目的目的是开发一种独立于系统大小的技术，该技术可以部分消除远程量子模拟器时间演化中存在的噪声量，从而对系统性能进行一些测量。通过这种方式，一个看起来运行正常的模拟量子模拟器可以作为其他模拟器的基准，并可以建立对模拟器的信心。重点放在随机基准测试上，这是一种实验协议，用于测量量子计算机在运行长时间随机选择的计算时存在的错误的平均强度。它只被应用于数字量子系统，通过将理论适应模拟机制，已经创建了模拟随机基准测试的协议，希望它可以通过实验实现，以证明噪声可以部分表征模拟量子模拟器的远程相互作用和更大的系统尺寸。这将是量子模拟、多体量子物理和基准测试的一个重要里程碑，因为它将量子计算技术与低复杂度的量子模拟器结合在一起。目前，研究的重点是一个一维模拟量子模拟器，该模拟器是一个被囚禁的钙离子串，模拟随机基准测试的经典模拟正在进行中。未来的发展方向包括在实验上实现模拟随机基准测试和将模拟随机基准测试应用于里德堡原子。最终的目标是将联合收割机模拟随机基准测试协议与当前的量子验证思想相结合，这样我们就可以突出噪声的最大贡献者以及哪种类型的计算性能最好，而不是获得系统中错误的平均强度的度量。

The focus of this project is to develop a quantum verification technique for restricted low-complexity quantum architectures, specifically analogue quantum simulators. It is widely accepted that quantum computers will be able to solve problems that are classically intractable. Quantum verification is the field of quantum computing that aims to answer the question: If a quantum computer solves a problem that can not be solved classically, how does one verify that the outcome is correct? This question is aimed at systems of high complexity. However, thinking of this question in terms of low-complexity quantum systems, we can redefine verification as a measure of the systems performance and a characterisation of the noise present in the system for specific instances.Quantum simulators are engineered quantum systems that emulate another physical quantum device. Although most architectures for quantum computing and quantum simulation deal with discrete variables, quantum logic gates (digital), analogue quantum simulators involve something called a time-evolution operator and are therefore not compatible with current quantum verification techniques used for digital quantum computers/simulators. The goal of this project is to develop a quantum verification technique that can evaluate the performance of an analogue quantum simulator beyond the scope of current techniques that test for reliability in the simulators computation. Analogue quantum simulators are vital in terms of understanding dynamics of many-body quantum systems, quantum information, entanglement and specific properties of certain physical phenomena. Therefore, establishing confidence in an analogue quantum simulator as an emulation of a physical quantum system is incredibly important. When analogue quantum simulators are engineered to create long-range interactions, current techniques fail at shorter time-scales and for a small amount of qubits. The aim of this project is to develop a technique independent of system size that can partially characterise the amount of noise present in the time-evolution of a long-range quantum simulator, and thereby have some measure of the systems performance. In this way, an analogue quantum simulator that seems to be performing correctly can act as a benchmark for other simulators and can establish confidence in your simulator. Focus was put on randomized benchmarking, which is an experimental protocol used to measure the average strength of errors present in a quantum computer when running long randomly-chosen computations. It has only been applied to digital quantum systems, by adapting the theory to the analogue regime a protocol for analogue randomized benchmarking has been created, with the hope that it may be implemented experimentally in order to demonstrate that noise can be partially characterised for an analogue quantum simulator for long-range interactions and larger system sizes. This would be an important milestone in quantum simulation, many-body quantum physics and benchmarking as it combines techniques used for quantum computation with low-complexity quantum simulators.So far, focus has been put on a one dimensional analogue quantum simulator that is a string of trapped calcium-ions, and classical simulations of analogue randomized benchmarking on this system are underway. Future directions include implementing analogue randomized benchmarking experimentally and applying analogue randomized benchmarking to Rydberg atoms. Eventually the goal is to combine the analogue randomized benchmarking protocol with current quantum verification ideas so that rather than obtaining a measure of the average strength of errors in the system, we can highlight where the biggest contributors to noise occur and for what type of computation performance is best.