Quantum systems of infinite dimension, such as bosonic oscillators, provide vast resources for quantum sensing. Yet, a general theory on how to manipulate such bosonic modes for sensing beyond parameter estimation is unknown. We present a general algorithmic framework, quantum signal processing interferometry (QSPI), for quantum sensing at the fundamental limits of quantum mechanics by generalizing Ramsey-type interferometry. Our QSPI sensing protocol relies on performing nonlinear polynomial transformations on the oscillator's quadrature operators by generalizing quantum signal processing (QSP) from qubits to hybrid qubit-oscillator systems. We use our QSPI sensing framework to make efficient binary decisions on a displacement channel in the single-shot limit. Theoretical analysis suggests the sensing accuracy, given a single-shot qubit measurement, scales inversely with the sensing time or circuit depth of the algorithm. We further concatenate a series of such binary decisions to perform parameter estimation in a bit-by-bit fashion. Numerical simulations are performed to support these statements. Our QSPI protocol offers a unified framework for quantum sensing using continuous-variable bosonic systems beyond parameter estimation and establishes a promising avenue toward efficient and scalable quantum control and quantum sensing schemes beyond the NISQ era.

中文翻译：

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单次量子信号处理干涉测量


无限维度的量子系统，例如玻色子振荡器，为量子传感提供了大量资源。然而，关于如何操纵这种玻色子模式进行参数估计之外的传感的一般理论尚不清楚。我们提出了一种通用算法框架，即量子信号处理干涉测量（QSPI），通过推广拉姆齐型干涉测量来实现量子力学基本极限下的量子传感。我们的 QSPI 传感协议依赖于通过将量子信号处理 (QSP) 从量子位推广到混合量子位振荡器系统来对振荡器的正交算子执行非线性多项式变换。我们使用 QSPI 传感框架在单次极限内的位移通道上做出有效的二元决策。理论分析表明，在单次量子位测量的情况下，传感精度与算法的传感时间或电路深度成反比。我们进一步连接一系列此类二元决策，以逐位方式执行参数估计。进行数值模拟来支持这些陈述。我们的 QSPI 协议为使用参数估计之外的连续可变玻色子系统的量子传感提供了一个统一的框架，并为超越 NISQ 时代的高效、可扩展的量子控制和量子传感方案建立了一条有前途的途径。