基于状态空间的量子计算机有限脉冲响应滤波
State-Space-Based FIR Filtering on a Quantum Computer
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中文总结 AI 辅助
本文提出一种基于状态空间框架的量子FIR滤波器实现，利用酉量子电路和量子延迟门，支持并行与组合，并通过模拟投影算子实现低通等有界滤波，在量子电路模拟器上验证。
中文摘要 AI 辅助
许多信号处理任务需要密集的计算。量子计算有望加速某些任务，但算法必须围绕量子力学的局限性进行设计。本文提供了有限脉冲响应（FIR）滤波器的量子实现，该滤波器是经典信号处理中广泛使用的工具。该滤波器可以并行化，并作为更大量子算法的一部分进行组合，具有利用量子振幅估计和未来容错量子硬件实现加速的潜力。为了实现这些特性，我们引入了一个状态空间框架，其中基于样本的信号处理通过酉量子电路执行。我们提出了量子延迟门作为离散时间信号处理中延迟线的量子模拟。酉电路本质上描述无损系统，但我们也通过模拟投影算子来实现低通和其他有界滤波器。FIR滤波器实现已通过量子电路模拟器进行测试和演示。
英文摘要
Many signal processing tasks require intensive computations. Quantum computing promises to accelerate certain tasks, but algorithms must be designed around the limitations of quantum mechanics. This paper provides a quantum implementation of finite impulse response (FIR) filters, which are a widely used tool in classical signal processing. The filter can be parallelized and composed as part of larger quantum algorithms, with potential for speedups using quantum amplitude estimation and future fault-tolerant quantum hardware. To accomplish these properties, we introduce a state-space framework wherein sample-based signal processing is performed with unitary quantum circuits. We present the quantum delay gate as the quantum analog of the delay line in discrete-time signal processing. Unitary circuits intrinsically describe lossless systems, but we also implement lowpass and other bounded filters by emulating a projection operator. The FIR filter implementation is tested and demonstrated with a quantum circuit simulator.
发表机构
- Aalto University（阿尔托大学）
- Università degli studi di Milano Statale（米兰大学）
机构由 AI 辅助整理，请以论文原文为准。
