Towards Heisenberg limit without critical slowing down via quantum reinforcement learning

TL;DR

This work proposes a quantum reinforcement learning-enhanced critical sensing protocol for quantum many-body systems with exotic phase diagrams that can robustly achieve Heisenberg and super-Heisenberg limits, even in noisy environments with practical Pauli measurements.

Abstract

Critical ground states of quantum many-body systems have emerged as vital resources for quantum-enhanced sensing. Traditional methods to prepare these states often rely on adiabatic evolution, which may diminish the quantum sensing advantage. In this work, we propose a quantum reinforcement learning (QRL)-enhanced critical sensing protocol for quantum many-body systems with exotic phase diagrams. Starting from product states and utilizing QRL-discovered gate sequences, we explore sensing accuracy in the presence of unknown external magnetic fields, covering both local and global regimes. Our results demonstrate that QRL-learned sequences reach the finite quantum speed limit and generalize effectively across systems of arbitrary size, ensuring accuracy regardless of preparation time. This method can robustly achieve Heisenberg and super-Heisenberg limits, even in noisy environments with practical Pauli measurements. Our study highlights the efficacy of QRL in enabling precise quantum state preparation, thereby advancing scalable, high-accuracy quantum critical sensing.

Figures (4)

• Figure 1: Schematic of the quantum reinforcement learning critical sensing (QRLCS) protocol.
• Figure 2: (a) Gate sequence learning by QRL, where the positive (negative) sign on the y-axis indicates the duration of the corresponding actions as positive (negative) time. (b) Total fidelity $F$ of the target state as a function of the number of steps (number of gates), and the total fidelity threshold $F^* = 0.85$ is marked by the black dashed line. (c) Fidelity of critical ground states of arbitrary spin length $L$ prepared from the action sequence in (a). Ising model's sensing performance of different protocols for the local (d) and global (e) case, where the probes of QRLCS are prepared from the action sequence in (a)
• Figure 3: (M)XY model's sensing performance under measurement operator $\sum\nolimits_{i = 1}^L {{\bm{\sigma} _z}}$ of QRLCS for the local (a) and global (b) case. (c) Schematic of a simple MXY chain. (d) The fidelity between the critical ground state of the MXY model and that of the XY model.
• Figure 4: MXY model's sensing performance under optimal single-site measurement of noisy QRLCS for the local (a) and global (b) case. The inset in the upper left corner of (a) shows the effect of noise intensity on accuracy limit of QRLCS, where scaling denotes the exponent $a$ in $\mathcal{F_{C}} \propto L^a$.