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

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.