Single-shot Quantum Signal Processing Interferometry
arxiv(2023)
摘要
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, i.e., the Heisenberg sensing limit, 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 binary
decisions on a displacement channel in the single-shot limit. Theoretical
analysis suggests the sensing accuracy given a single-shot qubit measurement
can approach the Heisenberg-limit scaling. 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.
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