Experimental quantum-computing-enhanced sensing using Grover's algorithm

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arXiv: 2609.35016v1 [quant-ph], 28 Sep 2026 · Authors: M. Ouellet, P. Sen, X. Wang, S. Roy, X. Song, V. Kremenetski, S. Prabhu, V. Fatemi, P. L. McMahon (Cornell University) · License: CC BY 4.0

Overview

Research area: Quantum computational sensing — the use of a quantum computer as part of a quantum sensor — implemented on a superconducting qubit–cavity platform. It sits at the intersection of Grover's quantum search algorithm, circuit QED (dispersive qubit–cavity coupling, SNAP gates, number-splitting spectroscopy), and detection/classification theory.

Technical level: Intermediate overall. The main text is readable with a grasp of Grover amplification and dispersive readout; the appendices (device calibration, Hamiltonian characterization, shot-estimate model) are Advanced.

Scope (one sentence): A proof-of-concept experiment showing that Grover amplitude amplification, run on a single transmon qubit coupled to a single 3D superconducting cavity, lets a sensor decide whether an unknown-frequency signal falls inside a detection band using less sensed signal than a coherent-probe baseline, for bandwidths above roughly 10 MHz.

What This Paper Is About

The task is a yes/no decision: a pulsed oscillating signal arrives at known times with an unknown center frequency, and the sensor must report whether that frequency lies inside a specified detection bandwidth or outside it. Conventional broadband sensing spends signal energy sweeping or covering all candidate frequencies; this paper tests a recent theoretical proposal that reframes the decision as a search problem and applies Grover's algorithm to amplify the response at whichever frequency the signal actually occupies.

The goal is to validate experimentally that this "Grover-based sensing" protocol works on modest near-term hardware, and to measure where — in detection bandwidth and target accuracy — it beats the natural non-Grover baseline.

Key Contributions

1. First experimental demonstration of the Grover-based sensing protocol proposed in Ref. [8], realized on a single fixed-frequency superconducting transmon qubit dispersively coupled to a single three-dimensional high-purity aluminum cavity — hardware the authors describe as modest.

2. A working continuous-bandwidth sensor built from a discrete spectrum. The qubit–cavity system offers only discrete photon-number-split transitions; the authors show that signal pulses whose spectral width is comparable to the transition spacing let frequencies between adjacent transitions drive imperfect rotations, and that Grover amplification remains robust under those non-ideal conditions.

3. A quantitative resource comparison against a coherent-probe baseline (N = 0) using total signal interrogations, defined as n_shots × (2N+1), where each Grover iteration contributes two interrogations and the final R_i(π) pulse one more. This is evaluated at target classification accuracies of 75% and 90%.

4. A measured bandwidth-scaling of the advantage, including cross-over points for N = 1 and N = 2, a superlinear growth of the advantage beyond cross-over, and extrapolated maximum attainable bandwidths for each protocol.

Main Findings

• Break-even and cross-over: The baseline outperformed the Grover protocol below roughly 10 MHz detection bandwidth. The N = 1 protocol crossed the baseline at approximately 8 MHz and the N = 2 protocol at approximately 13 MHz; above roughly 22 MHz, N = 2 also outperformed N = 1.

• Superlinear growth of advantage: Beyond break-even, the advantage grew superlinearly with detection bandwidth. The paper reports a Grover enhancement (ratio of baseline signal sensed to Grover-protocol signal sensed at equal bandwidth) of approximately 4× for 75% target accuracy and up to 18× for 90% accuracy.

• Abstract-level summary figure: The abstract states that the Grover-based protocol reduced the signal needed for an accurate decision by more than 10× for larger detection bandwidths and higher desired detection accuracy, and that the advantage held for bandwidths above 10 MHz.

• Bandwidth extension independent of resource cost: Grover amplification reaches a given sensing bandwidth at a smaller coherent-state amplitude α, avoiding the high-Fock-state non-idealities (reduced readout fidelity, breakdown of the dispersive approximation, imperfect number-selective rotations). Fits to the shot-requirement model project maximum attainable bandwidths of approximately 30 MHz (N = 0), 35 MHz (N = 1) and 68 MHz (N = 2).

• Empirical response characterization: Measured qubit-excitation probability versus sensing frequency was recorded for α = 5.82 and N = 0, 1, 2 and 3. Under ideal amplification the addressed-state population is P_N(i, α) = sin²[(2N+1) arcsin √p_i]; simulations including finite pulse durations reproduce the measured response. Amplification both raises the excitation probability and widens the frequency range classified as in-band.

• Role of pulse duration: The main resource analysis used a signal-pulse duration of 0.25/χ. The advantage persisted for longer, more spectrally resolved pulses of 0.5/χ and 1/χ. A separate sweep with L = 1/4χ, 1/2χ, 1/χ, 2/χ and 4/χ (with χ/2π ≈ 0.86 MHz) showed the transition from comb-like, individually resolved number-split transitions to a continuous sensing window as pulses shorten.

• Scaling relations: The response center follows f_c ≃ χ|α|² and the sensing-window FWHM scales approximately as 4|α|χ√(ln 2), i.e. roughly linearly in α. Deviations arise from finite pulse selectivity, which adds a pulse-limited contribution to the bandwidth and compounds over successive iterations, giving a weak dependence of bandwidth on N.

• Reported device parameters: readout resonator 2π × 8846.60 MHz; transmon g–e 2π × 6266.86 MHz; cavity 2π × 7045.53 MHz; T₁ = 51 µs; T₂* = 24 µs; cavity T₁,c = 85.8 µs; ground-state readout error 5%; excited-state readout error 10%; χ = 2π × 0.8607 MHz; K = 2π × 1.22 kHz; displacement calibration coefficient A = 89.72.

Methodology in Plain English

Encoding frequency into photon number. A fixed-frequency qubit is coupled to a cavity so that the qubit's transition frequency shifts by a known amount for each additional photon in the cavity (the dispersive shift χ). Each cavity photon-number state |i⟩ therefore corresponds to its own resolvable qubit transition frequency f_ge,i. An incoming signal at one of those frequencies selectively drives only the matching transition. The authors drive the qubit around a closed 2π path on the Bloch sphere, which stamps a π phase onto that one Fock component — a SNAP gate. This gate is the "oracle" that marks the state addressed by the signal.

The probe. Rather than an equal superposition of Fock states, they prepare a coherent state D(α)|0⟩ by resonantly driving the cavity, giving Poisson-distributed populations p_i with mean photon number n̄ = |α|². This simplifies the amplitude amplification but makes the response nonuniform across the sensing range — the authors note the enhancement would likely be larger with a uniform superposition.

One Grover iteration. The marked-state reflection is S_π^(i) = R_i(2π) = I − 2|i,g⟩⟨i,g|. The reflection about the initial probe is built from displacements around a vacuum-selective SNAP gate: S_π^(α) = D(α) R_0(2π) D(−α) = I − 2|α,g⟩⟨α,g|. Their product G = S_π^(α) S_π^(i) is one iteration (Fig. 2a of the paper).

Reading out the decision. After N iterations, a final signal-frequency pulse R_i(π) excites the qubit conditioned on the cavity occupying state |i⟩. An in-band signal has already been amplified, so the qubit-excitation probability P_e is high; an out-of-band signal gives a low P_e. Only a small number of qubit measurements is needed — the full photon-number distribution is never reconstructed — at the cost of one extra interaction with the signal.

Defining the baseline fairly. The baseline is the same coherent-state preparation and final signal-dependent rotation but with no intermediate Grover reflections (N = 0). For each protocol the coherent-state amplitude α is adjusted so comparisons occur at the same sensing bandwidth. Bandwidth Δf is defined as the FWHM of the measured qubit-excitation response; frequencies inside form class 1 and neighboring out-of-band frequencies class 0. Signal frequencies were sampled over [f_ge,0 + χ, f_ge,0 − 4.5 f_c].

Statistics. Each reported point is the mean over 100 trials with standard deviation error bars; in each trial 1,000 points are randomly drawn from a dataset of 10,000 points, with 800 used for training and 200 for validation. Dashed curves are fits to a shot-estimate model given in the appendix.

Why This Matters

Impact on research. The paper supplies experimental evidence that a quantum algorithm can deliver a metrological advantage on hardware far smaller than fault-tolerant computation would demand, because the scarce resource in sensing is the signal, not the computing time — a contrast the authors draw explicitly with database search, where they say near-term practical advantage looks prohibitive even in the fault-tolerant setting. It also demonstrates that Grover amplification tolerates the imperfect, non-π, partially selective rotations that a continuous bandwidth requires.

Real-world applications (the paper names only the first explicitly; the others are the general sensing contexts the protocol targets):

• Dark-matter searches, where signals would arise at the cryogenic operating temperature of the superconducting system (tens of millikelvin) and could be sensed without the attenuation that degraded absolute sensitivity here.
• Binary spectral anomaly detection — deciding whether an unknown-frequency tone is present inside a specified band, the exact task demonstrated.
• Signal-frequency identification — flagged as future work: instead of yes/no, identify which discrete frequency bin a signal falls into.
• Multi-tone detection — flagged as future work: the equivalent of the multiple-marked-items case, when signals comprising several frequencies arrive simultaneously.

Industry relevance. The protocol runs on one qubit and one cavity, which is a far smaller footprint than computational quantum advantage would require, and it repurposes existing superconducting control stacks (the authors use a Xilinx ZCU216 board, a traveling-wave parametric amplifier from MIT Lincoln Laboratory, and a Bluefors dilution refrigerator). The authors also identify cryogenic sensing as the setting where their platform's lack of attenuation would not be a drawback.

Future Directions

1. Replace the coherent state with a uniform Fock-state superposition, which the authors suggest could yield a greater Grover enhancement than the coherent-state approximation, and which they note may be engineerable rather than merely assumed.

2. More Grover iterations. The demonstration was capped at two iterations by qubit coherence time (T₂* = 24 µs, T₁ = 51 µs); more iterations could enable greater detection bandwidth and larger advantage.

3. Broader tasks and signal models. Identify which discrete frequency bin a signal occupies, implement the quantum-signal-processing step from the original proposal to discretize accumulated phases, compute functions of the sensed frequency beyond the rectangular binary window, and handle simultaneous multi-frequency signals.

4. Address the protocol's assumptions. The scheme presumes the signal arrives at known, synchronizable times and repeats as often as needed, whereas many practical signals are transient; the baseline used has not been proven to be the best possible non-Grover protocol; and whether room-temperature-origin signals can be sensed practically through the attenuation chain remains an open question. The paper also notes a closely related contemporaneous work (Ref. [29]) that uses mutual information and counts of resolved discrete frequency bins as its advantage metrics, rather than sensing time on a continuous-bandwidth yes/no task.

Target Audience

Researchers and graduate students in superconducting quantum computing and circuit QED who want a concrete near-term application of a quantum algorithm; quantum-sensing specialists interested in decision-oriented (rather than parameter-estimation) metrology; and metrology or detector-physics groups evaluating whether cryogenic quantum sensors could serve searches such as dark-matter detection. Experimentalists will find the calibration and wiring appendices (device parameters in Table 1, number-splitting and displacement calibration, Kerr characterization) directly reusable. Readers wanting only the conceptual result can read the abstract, Fig. 1 and Fig. 3; the full protocol details and the shot-estimate model require the appendices.

Data and code are available at https://doi.org/10.5281/zenodo.23000895.

Authors’ abstract

The combination of quantum sensing with quantum computing to provide an enhancement over conventional quantum sensing has recently emerged as a promising potential application of quantum computing that could give advantages without needing large-scale or fault-tolerant hardware. In this work, we report an experimental demonstration of a recent theoretical proposal to repurpose Grover's search algorithm to improve the ability to detect signals with unknown frequency within a large detection bandwidth. Our experiments were based on a system comprising a single superconducting qubit coupled to a single superconducting cavity, highlighting the modest hardware requirements for realizing the protocol. We found that Grover-based sensing was able to outperform the natural non-Grover baseline for our experimental platform for detection bandwidths $>$10~MHz, with an advantage that empirically grew superlinearly with the bandwidth beyond that break-even point. The use of the Grover-based protocol reduced the amount of signal that needed to be sensed to make an accurate detection decision by more than 10$\times$ for choices of larger detection bandwidth and higher desired detection accuracy. Our results provide a proof-of-principle validation that Grover-based quantum computational sensing can be realized in near-term hardware and provide a metrological advantage well beyond break-even in spite of the additional protocol complexity.