On the Speed-up of Wave-like Dark Matter Searches with Entangled Qubits

TL;DR

This work analyzes wave-like dark matter searches using entangled qubits, showing that phase-based readout preserves the search bandwidth while delivering a genuine scan-rate advantage that scales with $n_q^2$ in favorable regimes. It derives coherence-time and error-rate requirements, develops a detailed noise-model framework, and provides a quantitative cavity-vs-qubit benchmark for dark photons, indicating that entangled states of order $n_q \sim 100$ can rival photon-counting cavities for masses $m_{DM} \gtrsim 30{-}40~\mu\text{eV}$. The results highlight the practical trade-offs between qubit volume, coherence, and gate errors, and suggest error-mitigation strategies (e.g., spectator qubits, potential quantum error correction) to extend quantum advantage. Overall, the paper defines concrete parameter regimes and scalability paths for leveraging entangled quantum sensors in future dark matter searches, especially at higher masses where cavity-volume scaling is more challenging.

Abstract

Qubit-based sensing platforms offer promising new directions for wave-like dark matter searches. Recent proposals demonstrate that entangled qubits can achieve quadratic scaling of the signal in the number of qubits. In this work we expand on these proposals to analyze the bandwidth and scan rate performance of entangled qubit protocols across different error regimes. We find that the phase-based readout of entangled protocols preserves the search bandwidth independent of qubit number, in contrast to power-based detection schemes, thereby achieving a genuine scan-rate advantage. We derive coherence time and error rate requirements for qubit systems to realize this advantage. Applying our analysis to dark photon searches, we find that entangled states of approximately 100 qubits can become competitive with benchmark photon-counting cavity experiments for masses $\gtrsim 30{-}40~μ{\rm eV}$, provided sufficiently low error rates are achieved. The advantage increases at higher masses where cavity volume scaling becomes less favorable.

Figures (6)

• Figure 1: Quantum circuit implementing the entangled-state protocol for DM detection. The circuit shows: (i) preparation of GHZ-like entangled state using Hadamard and CNOT gates, (ii) exposure to DM (the $U_\mathrm{DM}$ "gate"), and (iii) phase transfer via CNOT gates to transfer the phase information to the signal qubit for measurement. In the absence of DM the signal qubit will be in $|0\rangle$. The other ("spectator") qubits will be in $|0\rangle$ states at the end the protocol, but can be monitored to detect errors. Dotted boxes show the state of the system in various stages of the protocol.
• Figure 2: Left: signal probability in the entangled-state protocol (normalized by $n_q^2$) as a function of detuning $\Delta_{\omega}$. Right: bandwidth of the entangled-state protocol as a function of $n_q$. We have fixed $\eta t_{\rm exp}= 0.01$ in both plots.
• Figure 3: Bandwidth of the entangled-state protocol as a function of $t_{\rm exp}$ (solid cyan) and numerical fit (yellow dashed). We have fixed $n_q =10$ and assumed $t_{\rm exp} \leq \tau_\mathrm{\small DM}$.
• Figure 4: Scan rate scaling with $n_q$ for entangled (cyan) and unentangled parallel (orange) protocols. The entangled protocol exhibits following regimes: $n_q^4$ scaling when readout-error dominates, $n_q^3$ scaling when errors scale with $n_q$, $n_q^2$ scaling beyond the red line when $t_{\rm exp} \approx \tau_\mathrm{\small GHZ} < \tau_\mathrm{\small DM}$, and linear scaling beyond $n_q^{\rm max} = p_{\rm max}/p_{\rm g}$. Dashed lines show earlier transition for higher gate error rates.
• Figure 5: Scan rates for cavities and the entangled-state protocol (normalized by the single-qubit scan rate) as a function of DM mass. The benchmark effective volume for the qubit $V_\mathrm{eff}=1$ mm$^3$ is taken to be independent of frequency, whereas the cavity volume is taken to scale as $\omega^{-3}$. We use ref. dixit2021searching as the benchmark for photon-counting cavity searches with the error rate of 0.1%. For the thermal cavity, we assume an effective temperature of $10 ~ {\rm mK}$. In panel (a) we assume high qubit coherence and gate fidelity such that the exposure time is set by $\tau_\mathrm{\small DM}$ and the single-qubit error probability is below 0.25%. In panel (b) we fix the qubit coherence $\tau_q \sim$ 1 ms, and set the exposure time to be $\min [ \tau_\mathrm{\small DM}, \tau_\mathrm{\small GHZ} ]$.