Rare-Event Quantum Sensing using Logical Qubits

TL;DR

This work tackles sensing rare, weak signals in the presence of local Markovian noise by leveraging quantum error correction to convert sporadic pulses into a higher-order logical phase. The authors develop a full framework around both the 3-qubit repetition code and the Steane code to show how syndrome extraction nonlinear processing yields a logical phase that scales as $\epsilon^3$ per pulse, while substantially extending coherence through error correction. They derive the logical QFI expressions, reveal favorable scaling regimes (including short-time Heisenberg-like scaling with logical blocks), and compare against standard physical Ramsey and classical error-detection strategies, demonstrating conditions under which QEC-enhanced sensing outperforms conventional methods. The results suggest practical routes to detect rare events—relevant to dark matter searches or gravitational-wave sensing—using coded quantum sensors, while highlighting tradeoffs with pulse duration, clock speed, and syndrome-fidelity requirements.

Abstract

We present a novel protocol to detect rare signals in a noisy environment using quantum error correction (QEC). The key feature of our protocol is the discrimination between signal and noise through distinct higher-order correlations, realized by the non-linear processing that occurs during syndrome extraction in QEC. In this scheme, QEC has two effects: First, it sacrifices part of the signal $ε$ by recording a reduced, stochastic, logical phase $φ_L = \mathcal{O}(ε^3)$. Second, it corrects the physical noise and extends the (logical) coherence time for signal acquisition. For rare signals occurring at random times in the presence of local Markovian noise, we explicitly demonstrate an improved sensitivity of our approach over more conventional sensing strategies.

Figures (4)

• Figure 1: QEC-enhanced logical sensing scheme. ($a$) We entangle physical sensors and form quantum codes, for example a 7-qubit Steane code, to improve the sensing performance in the presence of local Markovian decoherence with strength $\gamma$. ($b$) We consider the task of sensing a random rare (with known rate $R$) and weak signal $\omega(t)$ in the form of short pulses with area $\epsilon$ and duration $\sigma_t$.
• Figure 2: Sensing strategies. We compare three different sensing strategies: ($a$) Physical sensing (Ramsey): Physical quantum sensors are initialized and measured in repeated cycles of duration $\Delta t \sim 1/\gamma$, where $\gamma$ is the physical decoherence rate. ($b$) Physical sensing with classical error detection: We initialize a pair of physical sensors as $\ket{++}$, forming a classical repetition code. For small exposure time $\Delta t \ll 1/\gamma$, we can exclude (single) physical noise errors by only recording collective qubit flips where $X_1=X_2=-1$. ($c$) QEC-enhanced logical sensing: We perform syndrome extraction and correction steps in intervals $\delta t \ll 1/\gamma$, to extend the (logical) sensing interval, $\Delta t_L =1/\Gamma \gg 1/\gamma$, where $\Gamma$ is the logical decoherence rate. During this time, the logical sensor picks up an average phase $\Phi_L \propto R\Delta t_L\epsilon^3$ from multiple, coherently added signal pulses. All three sensing strategies can be enhanced using entanglement between multiple physical/logical sensors.
• Figure 3: Logical sensing protocol. ($a$) Our quantum sensor is built from a quantum-error-correcting code, e.g. a $[[7,1,3]]$ Steane code. ($b$) QEC Ramsey cycle: We prepare the logical state $\ket{+_L}$, then sense the signal for a duration $\Delta t_L$ interspersed with syndrome extraction in intervals of $\delta t$, and, finally, apply a logical projective measurement (choosing the optimal operating/bias point). ($c$) Syndrome extraction is performed, e.g., by coupling stabilizers to noiseless ancillas, and it converts the signal to a probabilistic logical gate, with logical phase $\phi_L^+/\phi_L^-$ depending on stabilizer outcomes with probabilities $p_+/p_-$. ($d$) We numerically demonstrate this stochastic acquisition of an average logical signal with phase $\Phi_L \propto R\Delta t_L \epsilon^3$. Our numerical example shows data for $T=100$, $\delta t=10^{-3}$, $R=30$, $\epsilon= 0.005\times 2\pi$, $\gamma = 0$, and $50$ runs; the dashed lines indicates the analytical estimate $\Phi_L\pm (R\Delta t_L)\sigma_{\Phi_L}$.
• Figure 4: Sensitivity. Quantitative comparison of different sensing strategies. ($a$) Logical QFI $F^\mathrm{tot}_\mathrm{L}$ for $M$ repetitions with $\Delta t_L = T/M$. The blue curve is optimal for given total sensing time $T$ and logical decoherence $\Gamma$. ($b$) Sensing performances versus signal rate $R$. Logical sensing outperforms physical sensing for small $R$ and $\delta t \rightarrow 0$. The dashed vertical line signals the crossover from $R$ to $R^2$ scaling. ($c$) Similarly, for $\delta t\rightarrow 0$, logical sensing outperforms physical sensing for small $\epsilon$. The vertical line signals a crossover to $\epsilon$-independence. ($d$) Error-detection yields the best asymptotic sensitivity scaling with qubit number $n$. For fixed $n$, logical sensing outperforms other strategies for sufficiently small $\epsilon$. See SM for numerical parameters SM.