Learning to Restore Heisenberg Limit in Noisy Quantum Sensing via Quantum Digital Twin

TL;DR

This work establishes quantum digital twin as a generic methodology for quantum control, proposing a noise-immune paradigm for next-generation quantum sensors compatible with NISQ-era experimental constraints.

Abstract

Quantum sensors leverage nonclassical resources to achieve sensing precision at the Heisenberg limit, surpassing the standard quantum limit attainable through classical strategies. However, a critical issue is that the environmental noise induces rapid decoherence, fundamentally limiting the realizability of the Heisenberg limit. In this Letter, we propose a quantum digital twin protocol to overcome this issue. The protocol first establishes observable-constrained state reconstruction to infer random errors in the decoherence process, and then utilizes reinforcement learning to derive adaptive compensatory control strategies. Demonstrated across discrete, continuous variable and multi-qubit circuit systems, our approach bypasses quantum state tomography's exponential overhead and discovers optimal control schemes to restore the Heisenberg limit. Unlike quantum error correction or mitigation schemes requiring precise noise characterization and ancillary qubits, our autonomous protocol achieves noise-resilient sensing through environment-adaptive control sequencing. This work establishes quantum digital twin as a generic methodology for quantum control, proposing a noise-immune paradigm for next-generation quantum sensors compatible with NISQ-era experimental constraints.

Figures (4)

• Figure 1: Schematic of the quantum digital twin sensing protocol. The dynamics predictor can be recurrent neural networks or Transformer.
• Figure 2: Results for the single atom system. (a) Dynamics and purity of the system under the continuous monitoring environment setup, where the shaded area indicates the standard deviation. $P_{\rm st}$ is the purity of the density matrix of a single trajectory, while $P_{\rm av}$ is the purity after averaging the density matrix over all trajectories. (b) Predictive performance of the digital twin model. The solid lines are the observable expectations of the real system as functions of the evolution time, and the scatters are the predicted values given by the digital twin. (c) Sensing precision of the different schemes, described by the CFI in the measurement base $\sigma_z$. (d) Evolution trajectories of the system with different schemes, represented by the observable expectation. The inset show the control actions of the different protocols.
• Figure 3: Results for the quantum circuit system. (a) Schematic of the quantum sensing circuit. (b) Purity and entropy of circuit for GHZ state case under the continuous monitoring environment setup. $P_{\rm st}$ is the purity of the density matrix of a single trajectory, while $P_{\rm av}$ is the purity after averaging the density matrix over all trajectories. (c) Predictive performance of the digital twin model. (d) Sensing precision of the different schemes, described by the CFI in the optimal measurement basis.
• Figure 4: Results for the continuous variable system. (a) Predictive performance of the digital twin model. (b) The sensing precision of all considered protocols is quantified via the CFI, evaluated through homodyne measurements. The inset shows the final state of the system using QDTS protocol in the squeezing case.