  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.
