通过改进测量方式，大幅减少求解非线性微分方程所需的量子电路次数。
Differential equation quantum solvers: engineering measurements to reduce cost
- 采用先测量后计算的策略，设计可优化的代价算子。
- 在1维和2维问题上实现约100倍的电路评估次数降低。
- 适合资源受限的现有量子硬件进行复杂微分方程求解。
量子计算机被提出用于高效求解非线性微分方程（DEs），这在众多技术和科学领域中具有基础意义。然而，关键挑战在于设计硬件感知的协议，以高效利用有限的量子资源。本文聚焦于源自科学机器学习的可微量子电路（DQC）这一有前景的变分方法，特别关注其电路评估次数的开销。在混合量子/经典算法中，每次循环的量子硬件接口与运行时间对总耗时的影响远超相对廉价的经典后处理。为此，我们提出并测试了两种高样本效率的求解协议，实现了量子电路评估次数的指数级节省。这些协议基于‘先测量’思路，重新设计从DQC中提取信息的方式，引入类似随机测量工具箱（即经典阴影）的工程化代价算子。在单维和双维微分方程的基准模拟中，报告了高达约100倍的电路评估次数减少。因此，这些协议有望使现有量子硬件实现更大、更复杂的非线性微分方程演示。
原文摘要 · Abstract (English)
Quantum computers have been proposed as a solution for efficiently solving non-linear differential equations (DEs), a fundamental task across diverse technological and scientific domains. However, a crucial milestone in this regard is to design protocols that are hardware-aware, making efficient use of limited available quantum resources. We focus here on promising variational methods derived from scientific machine learning: differentiable quantum circuits (DQC), addressing specifically their cost in number of circuit evaluations. Reducing the number of quantum circuit evaluations is particularly valuable in hybrid quantum/classical protocols, where the time required to interface and run quantum hardware at each cycle can impact the total wall-time much more than relatively inexpensive classical post-processing overhead. Here, we propose and test two sample-efficient protocols for solving non-linear DEs, achieving exponential savings in quantum circuit evaluations. These protocols are based on redesigning the extraction of information from DQC in a ``measure-first" approach, by introducing engineered cost operators similar to the randomized-measurement toolbox (i.e. classical shadows). In benchmark simulations on one and two-dimensional DEs, we report up to $\sim$ 100 fold reductions in circuit evaluations. Our protocols thus hold the promise to unlock larger and more challenging non-linear differential equation demonstrations with existing quantum hardware.
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