Exponential quantum advantage for learning signals with a single qubit
AuthorsIshaan Kannan, Sridhar Prabhu, Saeed A. Khan, Mandar M. Sohoni, Xingrui Song, Saswata Roy, Alen Senanian, Valla Fatemi, Peter L. McMahon, Jordan Cotler
Resources
A single controllable qubit dramatically cuts the measurements needed to learn classical signals, suggesting powerful near-term applications for quantum-enhanced sensing.
Key results
The superconducting cavity–transmon experiment demonstrated Fourier-signal learning through k = 20.
QFS required 100× fewer shots than a two-mode-entangled receiver.
What the paper found
This paper shows that a conventional bosonic sensor can gain an exponential learning advantage from just one controllable ancilla qubit. Its Quantum Phase-Space Inference, or QΨ, framework uses accessible feature information to derive tight lower bounds for conventional protocols and design matching quantum feature-sensing algorithms. For a signal’s kth Fourier coefficient, energy-constrained Gaussian sensing requires exp(Ω(k)) queries, while a single-qubit echoed conditional-displacement protocol needs only O(k) queries. In a superconducting cavity–transmon experiment reaching k = 20, the qubit-assisted method achieved comparable classification with roughly 100 shots, reducing measurement requirements by seven orders of magnitude relative to conventional Gaussian sensing. The same architecture can preserve temporal information in the qubit: an m-point temporal correlator requires O(1) signal queries with one long-lived memory qubit, versus exp(Ω(m)) without coherent memory. Numerical studies extend the idea to axionic dark-matter streams, where QFS quadratically improves weak-field characterization, and to wireless receivers: for 64-QAM, a three-qubit QFS receiver used 100× fewer shots than a two-mode-entangled receiver and 100× fewer than a classical heterodyne receiver. The central claim is that near-term quantum advantage need not rely on large entangled processors; programmable non-Gaussian control, quantum memory, and modest circuit depth can make classical signal features exponentially more accessible.
Original abstract
Quantum technology has the potential to transform scientific discovery, but quantum advantages often require processing capabilities well beyond the reach of experimental platforms. We show that coupling a single controllable qubit to an otherwise conventional sensor can exponentially reduce the number of measurements required to learn classical signals. These rigorous quantum advantages apply to fundamental sensing tasks, including learning Fourier coefficients, extracting temporal correlations from time-varying signals, and estimating transformations of physical observables. Using a superconducting cavity--qubit architecture, we experimentally demonstrate $10^7$-fold reductions in the number of measurements required for Fourier-amplitude and time-varying signal learning. Our $\textit{quantum feature sensing}$ algorithms further enable orders-of-magnitude improvements in simulations of weak-signal dark matter detection and wireless communication applications. These quantum advantages are derived from Quantum Phase-Space Inference (Q$Ψ$), a unifying theory of quantum-enhanced experiments that simultaneously converts a set of experimental objectives and constraints into tight lower bounds and optimal quantum-enhanced learning algorithms while producing a certificate of quantum advantage. Q$Ψ$ extends beyond the regimes captured by quantum Fisher information and provides a framework for systematically identifying rigorous quantum advantages in practical experimental tasks. Together, our results establish that near-term quantum technology can exponentially enhance our ability to learn from classical signals.
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