The ground-state criticality of many-body systems is a resource for quantum-enhanced sensing, namely, the Heisenberg precision limit, provided that one has access to the whole system. We show that, for partial accessibility, the sensing capabilities of a block of spins in the ground state reduces to the sub-Heisenberg limit. To compensate for this, we drive the Hamiltonian periodically and use a local steady state for quantum sensing. Remarkably, the steady-state sensing shows a significant enhancement in precision compared to the ground state and even achieves super-Heisenberg scaling for low frequencies. The origin of this precision enhancement is related to the closing of the Floquet quasienergy gap. It is in close correspondence with the vanishing of the energy gap at criticality for ground-state sensing with global accessibility. The proposal is general to all the integrable models and can be implemented on existing quantum devices.
The ground-state criticality of many-body systems is a resource for quantum-enhanced sensing, namely, the Heisenberg precision limit, provided that one has access to the whole system. We show that, for partial accessibility, the sensing capabilities of a block of spins in the ground state reduces to the sub-Heisenberg limit. To compensate for this, we drive the Hamiltonian periodically and use a local steady state for quantum sensing. Remarkably, the steady-state sensing shows a significant enhancement in precision compared to the ground state and even achieves super-Heisenberg scaling for low frequencies. The origin of this precision enhancement is related to the closing of the Floquet quasienergy gap. It is in close correspondence with the vanishing of the energy gap at criticality for ground-state sensing with global accessibility. The proposal is general to all the integrable models and can be implemented on existing quantum devices.
Quantum sensing is inevitably an elegant example of the supremacy of quantum technologies over their classical counterparts. One of the desired endeavors of quantum metrology is AC field sensing. Here, by means of analytical and numerical analysis, we show that integrable many-body systems can be exploited efficiently for detecting the amplitude of an AC field. Unlike the conventional strategies in using the ground states in critical many-body probes for parameter estimation, we only consider partial access to a subsystem. Due to the periodicity of the dynamics, any local block of the system saturates to a steady state which allows achieving sensing precision well beyond the classical limit, almost reaching the Heisenberg bound. We associate the enhanced quantum precision to closing of the Floquet gap, resembling the features of quantum sensing in the ground state of critical systems. We show that the proposed protocol can also be realized in near-term quantum simulators, e.g. ion-traps, with a limited number of qubits. We show that in such systems a simple block magnetization measurement and a Bayesian inference estimator can achieve very high precision AC field sensing.
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.
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 Letter, 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.
We investigate the physical requirements to reach the ultimate limits of ground-state metrology -- i.e., the estimation of an unknown parameter θ of an N-body Hamiltonian via measurements on its ground state -- using many-body probes featuring either short-range or long-range interactions. We characterize the conditions to saturate two fundamental limits of the quantum Fisher information Fθ: the static ground-state bound Fθ≲N2/Δ2, where Δ is the spectral gap, and the dynamical Heisenberg limit Fθ≲N2τ2, where τ is the total protocol duration. To saturate the static limit, we argue that short-range interacting systems require a spectral gap that closes with N. At second-order quantum critical points this leads to a universal condition on the critical exponents, ν(d+z)=1, which can be approached arbitrarily closely, as we show for the XXZ chain; cat-like ground states at first-order transitions provide an alternative route to static optimality. In contrast, we find that all-to-all interacting models can achieve optimality even in gapped regimes. Furthermore, reaching the dynamical bound is tightly related to the ground-state preparation time; we demonstrate that its optimal, inverse-gap profile can be obtained via local adiabatic protocols. By analyzing paradigmatic systems -- the transverse-field Ising chain, the XXZ chain, a squeezing Hamiltonian, and the two-mode Bose-Hubbard model -- we identify specific many-body probes capable of approaching both limits. Overall, our results provide a theoretical basis for the design of (local) many-body ground-state sensors operating at the ultimate limits of quantum precision.
Most quantum metrology protocols harness highly entangled probe states and globally accessible measurements to surpass the standard quantum limit. However, it is challenging to satisfy these requirements in realistic many-body sensors. We demonstrate that both of these constraints can be overcome in quantum chaotic sensors. Crucially, we establish that even in the presence of partial measurement accessibility, chaotic dynamics enables initial unentangled states to exhibit Heisenberg scaling of the quantum Fisher information, Iα with time. In the weakly chaotic regime, we identify spin-coherent states placed at the edge of the regular islands in the mixed classical phase space as optimal initial states for enhanced sensitivity. On the other hand, in the strongly chaotic regime, Iα is insensitive to the choice of the initial state. Notably, quantum-enhanced sensitivity is achieved even when a very low fraction (∼5%) of the qubits are accessible. These results establish quantum chaos as a robust resource for quantum-enhanced sensing under realistic accessibility constraints on accessibility.
Quantum sensors based on critical many-body systems are known to exhibit enhanced sensing capability. Such enhancements typically scale algebraically with the probe size. Going beyond algebraic advantage and reaching exponential scaling has remained elusive when all the resources, such as the preparation time, are taken into account. In this work, we show that many-body systems featuring first order quantum phase transitions can indeed achieve exponential scaling of sensitivity, thanks to their exponential energy gap closing. Remarkably, even after considering the preparation time using local adiabatic driving, the exponential scaling is sustained. Our results are demonstrated through comprehensive analysis of three paradigmatic models exhibiting first order phase transitions, namely Grover, p-spin, and biclique models. We show that this scaling survives moderate decoherence during state preparation and also can be optimally measured in experimentally available basis. Our findings comply with the fundamental bounds and we show that one can harness the exponential advantage through an adaptive strategy even away from the phase transition point.