Quantum Computing Enhanced Sensing

TL;DR

This work introduces Quantum Computing Enhanced Sensing (QSS) to detect weak, unknown-strength oscillating fields across broad bandwidths by digitizing analog signals and embedding the resulting discrete problem into a quantum-search framework. The key innovation is the Quantum Sensing Oracle (ESU) combined with quantum signal processing (QSP) and Grover search, enabling a provable speedup over conventional AC sensing and establishing the Grover-Heisenberg limit as a fundamental lower bound on sensing time. The authors also show QSS compatibility with quantum error correction, robustness under decoherence, and practical realizations across platforms such as NV centers, Rydberg systems, trapped ions, and cavity QED. A detailed proof-of-principle protocol (dQSS) and extensive simulations illustrate near-term improvements using NV-based implementations, while theoretical sections bound performance limits for QFI-based, memory-lifetime-limited, and classical-signal-processing sensing. Overall, the work positions quantum computation as a powerful, general resource for enhancing sensing capabilities with broad implications for precision metrology and quantum sensing theory.

Abstract

Quantum computing and quantum sensing represent two distinct frontiers of quantum information science. In this work, we harness quantum computing to solve a fundamental and practically important sensing problem: the detection of weak oscillating fields with unknown strength and frequency. We present a quantum computing enhanced sensing protocol that outperforms all existing approaches. Furthermore, we prove our approach is optimal by establishing the Grover-Heisenberg limit -- a fundamental lower bound on the minimum sensing time. The key idea is to robustly digitize the continuous, analog signal into a discrete operation, which is then integrated into a quantum algorithm. Our metrological gain originates from quantum computation, distinguishing our protocol from conventional sensing approaches. Indeed, we prove that broad classes of protocols based on quantum Fisher information, finite-lifetime quantum memory, or classical signal processing are strictly less powerful. Our protocol is compatible with multiple experimental platforms. We propose and analyze a proof-of-principle experiment using nitrogen-vacancy centers, where meaningful improvements are achievable using current technology. This work establishes quantum computation as a powerful new resource for advancing sensing capabilities.

Figures (3)

• Figure S1: Comparing the achievable sensitivity $B_{\min}$ and bandwidth $|\Delta \omega|$ without decoherence (a, see also FIG. 1c in main text) versus with decoherence (b). We fix the sensing time $\tau$, number of sensors $n_S$, and sensor coherence time $T_2 \sim 1/\Gamma$. Regardless of the presence of decoherence, conventional protocols with unentangled sensors achieve $B_{\min} \sim (n_S \tau)^{-1/2} |\Delta \omega|^{1/2}$ (the standard quantum limit, SQL) and conventional protocols with entangled sensors achieve $B_{\min} \sim n_S^{-1} \tau^{-1/2} |\Delta \omega|^{1/2}$ (the Heisenberg limit, HL). However, in the presence of decoherence, the minimal achievable sensitivity of conventional protocols with entangled or unentangled sensors is the same, scaling as $1/(n_S \tau T_2)^{1/2}$ (due to the reduced effective $T_2^{\text{eff}} = T_2/n_S$ of the GHZ state). Without decoherence, our quantum search sensing (QSS) algorithm achieves $B_{\min} \sim n_S^{-1} \tau^{-2/3} |\Delta \omega|^{1/3}$ (up to polylogarithmic corrections). With decoherence, for $B_{\min} \gtrsim 1/T_2$, the QSS-based protocol in this section achieves $B_{\min} \sim (n_S^2 \tau T_2)^{-1/3} |\Delta \omega|^{1/3}$ (again, up to polylogarithmic corrections), outperforming conventional approaches.
• Figure S2: Improvement factor $\mathcal{I}$ as a function of $B$ and $T_2$, for different numbers of computational qubits $n_Q$. The improvement factor is averaged over $8$ random signal frequencies, and the shaded areas indicate the variance over frequencies. The variance is only non-negligible in the large $B$ regime, where power broadening limits the protocol performance.
• Figure S3: The results of optimizing $B_{R_0}$ and $N_G$ for small system sizes $n_Q \le 7$ (different columns) over a wide range of signal strengths $B$ (horizontal axis) and coherence times $T_2$ (different colors). The optimal $B_{R_0}$ is well-captured by the simple ansatz $\widehat{B}_{R_0}$ (red line), which exceeds $B$ (blue line) over the full range of parameters. The optimal $N_G$ depends non-trivially on $n_Q$ and $T_2$.

Theorems & Definitions (24)

• Definition S1: AC Sensing
• Theorem S1: Quantum Search Sensing
• Definition S2: AC Sensing with High Frequency, Finite Dynamic Range
• Lemma S1
• Lemma S2: ESU Hamiltonian Transformation
• Lemma S3: ESU Error Bound
• Lemma S4: Corollary 6.27 in low:2017
• Proposition S1: RWA Error
• proof
• Lemma S5: Lemma 1 in burgarth:2022