Integrating quantum sensors with bespoke quantum error correction

物理量，如时间、相位和纠缠不能直接测量，而必须通过间接测量来推断。这种间接测量的一个重要类别是参数估计。理想的量子传感器可以以前所未有的精度估计物理量，但实际的量子传感器由于噪声而失去了量子优势。在量子传感器中加入量子纠错码是一种极具吸引力的理论降噪方法，但在实际应用中存在诸多困难。也就是说，大多数量子纠错码(1)在实际物理系统中不容易制备，(2)在不完善的量子纠错过程中引入的误差会超过它们所纠正的误差，(3)在量子纠错过程中会破坏要测量的信号。大多数量子纠错方案是通过抽象传感器的物理特性来研究的，而量子传感器的研究通常是在没有量子纠错的情况下进行的。主流方法将量子传感器和量子纠错组件视为单独优化的黑匣子。本项目旨在打破量子纠错黑盒和量子传感器黑盒之间的界限，通过优化定制的量子纠错码，将它们整合成一个整体的量子纠错集成量子传感器。在优化量子传感器中使用定制量子纠错码可以克服的一个关键问题是，当前在优化量子传感器量子纠错码方面的数值方法的顽固性。这些数值方法没有在量子纠错码上施加先验结构，并且存在粒子数量呈指数增长的运行时间。通过选择可以用可处理的参数数量来描述的定制量子代码，量子传感器可以以可扩展的方式对这些代码进行数值优化。该项目将考虑的一个著名的定制量子纠错码家族是对称码。这些代码在潜在粒子的任何排列下都是不变的，并且除了在其数值优化中的可扩展性之外，还具有其他实用优势。首先，对称码是在物理设备中近期实现的非常有前途的候选者，因为它们的全局域可控性可以允许它们在近期设备中进行可扩展的物理实现，而在这些设备中，无串扰的寻址性是很困难的。其次，这种对称码可以纠正无法追踪的粒子损失，这是传统量子纠错码无法纠正的。该项目将找到最佳的定制量子纠错码，最大限度地发挥经典场量子估计中的量子优势，同时也易于在实际物理系统中制备。将对称码的性能与其他系列定制量子纠错码的性能进行比较。在量子传感器精度的数学优化方面，该项目将采取综合方法。即，确定量子传感器的物理约束，如允许的量子比特数、工作温度和能量预算，并找到量子传感器的最佳量子纠错码。在此过程中，该项目将提供如何利用现有量子硬件提高量子传感器灵敏度的理论蓝图。

Physical quantities such as time, phase, and entanglement cannot be measured directly, but instead must be inferred through indirect measurements. An important category of such indirect measurements is parameter estimation. Ideal quantum sensors would estimate physical quantities with unprecedented precision, but practical quantum sensors lose their quantum advantage because of noise. Incorporating quantum error correction codes into quantum sensors is an attractive theoretical approach to reduce noise, but is beset with practical difficulties. Namely, most quantum error correction codes (1) cannot be readily prepared in actual physical systems, (2) would introduce more errors than they correct during imperfect quantum error correction, and (3) can destroy the signal meant to be measured during quantum error correction.Most quantum error correction schemes are studied by abstracting away the physics of sensors, while quantum sensors are typically studied in the absence of quantum error correction. Mainstream approaches treat both quantum sensors and quantum error correction components as black boxes to be optimised separately. This project aims to break down the boundary between the quantum error correction black box and the quantum sensor black box, and integrate them to make an overall quantum error correction-integrated quantum sensor, by optimising over bespoke quantum error correction codes.A critical problem that using bespoke quantum error correction codes in optimising quantum sensors can overcome is the intractability of current numerical approaches in optimising quantum error correction codes for quantum sensors. These numerical methods impose no apriori structure on quantum error correction codes, and suffer from a runtime that increases exponentially in the number of particles. By choosing bespoke quantum codes that can be described with a tractable number of parameters, quantum sensors can be numerically optimised with respect to these codes in a scalable way.A prominent family of bespoke quantum error correction codes that this project will consider are symmetric codes. These codes are invariant under any permutation of the underlying particles, and have other practical advantages apart from the scalability in their numerical optimisations. First symmetric codes are very promising candidates for near-term implementation in physical devices, because their controllability by global fields could allow for their scalable physical implementations in near-term devices where addressability without cross-talk is difficult. Second, such symmetric codes can correct untracked particle losses, which are impossible to correct using conventional quantum error correction codes.This project will find optimal bespoke quantum error correction codes that maximise the quantum advantage attainable in the quantum estimation of classical fields, while also being easy to prepare in actual physical systems. The performance of symmetric codes will be compared with the performance of other families of bespoke quantum error correction codes. In the mathematical optimisation of the quantum sensor's precision, the project will take an integrated approach. Namely, the physical constraints of the quantum sensor such as the number of allowed qubits, operating temperature, and energy budget will be fixed, and the best quantum error correction codes for quantum sensors will be found. In doing so, this project will provide theoretical blueprints on how sensitivities of quantum sensors may be improved using existing quantum hardware.