Integrating quantum sensors with bespoke quantum error correction

时间、相位和纠缠等物理量不能直接测量，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。理想的量子传感器将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。将量子纠错码嵌入到量子传感器中是一种很有吸引力的理论方法，但在实际应用中存在困难。也就是说，大多数量子纠错码（1）不能在实际的物理系统中容易地制备，（2）在不完美的量子纠错期间将引入比它们纠正的更多的错误，以及（3）可以在量子纠错期间破坏要测量的信号。大多数量子纠错方案通过抽象传感器的物理来研究，而量子传感器通常在没有量子纠错的情况下进行研究。主流方法将量子传感器和量子纠错组件视为需要单独优化的黑盒。本项目旨在打破量子纠错黑匣子和量子传感器黑匣子之间的界限，将两者整合，制成一个整体的量子纠错一体化量子传感器，在优化量子传感器中使用定制的量子纠错码可以克服的一个关键问题是当前数值方法在优化量子误差中的棘手性量子传感器的校正码这些数值方法没有对量子纠错码施加先验结构，并且遭受粒子数量呈指数增长的运行时间。通过选择可以用易于处理的参数描述的定制量子码，量子传感器可以以可扩展的方式相对于这些码进行数值优化。本项目将考虑的一个突出的定制量子纠错码家族是对称码。这些代码在底层粒子的任何排列下都是不变的，并且除了其数值优化的可扩展性之外，还具有其他实际优点。首先，对称码是非常有前途的候选人在物理设备中的近期实施，因为它们的可控性的全球领域可以允许其可扩展的物理实现在短期的设备中，没有串扰的寻址能力是困难的。第二，这种对称码可以纠正未跟踪的粒子损失，这是不可能纠正使用传统的量子纠错码。该项目将找到最佳的定制量子纠错码，最大限度地提高量子优势，在经典领域的量子估计，同时也很容易在实际的物理系统准备。对称码的性能将与其他家庭的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中，该项目将采取综合方法。也就是说，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将是固定的，并找到最好的量子纠错码的量子传感器。在这样做的过程中，该项目将提供理论蓝图如何使用现有的量子硬件提高量子传感器的灵敏度。

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.