Optimal Thermometers with Spin Networks

Abstract

The heat capacity $\mathcal{C}$ of a given probe is a fundamental quantity that determines, among other properties, the maximum precision in temperature estimation. In turn, $\mathcal{C}$ is limited by a quadratic scaling with the number of constituents of the probe, which provides a fundamental limit in quantum thermometry. Achieving this fundamental bound with realistic probes, i.e. experimentally amenable, remains an open problem. In this work, we tackle the problem of engineering optimal thermometers by using networks of spins. Restricting ourselves to two-body interactions, we derive general properties of the optimal configurations and exploit machine-learning techniques to find the optimal couplings. This leads to simple architectures, which we show analytically to approximate the theoretical maximal value of $\mathcal{C}$ and maintain the optimal scaling for short- and long-range interactions. Our models can be encoded in currently available quantum annealers, and find application in other tasks requiring Hamiltonian engineering, ranging from quantum heat engines to adiabatic Grover's search.

10 (+16) pages

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• Current Trends in Global Quantum Metrology
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• Mixing thermal coherent states for precision and range enhancement in quantum thermometry
• Quantum Chaos in Random Ising Networks
• Topological quantum thermometry
• Optimizing quantum sensing networks via genetic algorithms and deep learning
• From dynamical to steady-state many-body metrology: Precision limits and their attainability with two-body interactions
• Low-temperature Quantum Metrology Enhanced by Strong Couplings
• Optimal limits of continuously monitored thermometers and their Hamiltonian structure
• Configuration-dependent precision in magnetometry and thermometry using multi-qubit quantum sensors
• Optimal strategies for transient and equilibrium quantum thermometry using Gaussian and non-Gaussian probes
• Minimizing Dissipation via Interacting Environments: Quadratic Convergence to Landauer Bound
• Nonequilibrium thermometry via an ensemble of initially correlated qubits