https://doi.org/10.1140/epjqt/s40507-023-00195-w
Research
A stochastic evaluation of quantum Fisher information matrix with generic Hamiltonians
1
Frontier Research Institute for Interdisciplinary Sciences, Tohoku University, Sendai, Japan
2
Department of Applied Physics, Graduate School of Engineering, Tohoku University, Sendai, Japan
Received:
24
May
2023
Accepted:
9
September
2023
Published online:
19
September
2023
Quantum Fisher information matrix (QFIM) is a fundamental quantity in quantum physics, which closely links to diverse fields such as quantum metrology, phase transitions, entanglement witness, and quantum speed limit. It is crucial in quantum parameter estimation, central to the ultimate Cramér-Rao bound. Recently, the evaluation of QFIM using quantum circuit algorithms has been proposed for systems with multiplicative parameters Hamiltonian. However, systems with generic Hamiltonians still lack these proposed schemes. This work introduces a quantum-circuit-based approach for evaluating QFIM with generic Hamiltonians. We present a time-dependent stochastic parameter-shift rule for the derivatives of evolved quantum states, whereby the QFIM can be obtained. The scheme can be executed in universal quantum computers under the family of parameterized gates. In magnetic field estimations, we demonstrate the consistency between the results obtained from the stochastic parameter-shift rule and the exact results, while the results obtained from a standard parameter-shift rule slightly deviate from the exact ones. Our work sheds new light on studying QFIM with generic Hamiltonians using quantum circuit algorithms.
Key words: Quantum metrology / Generic Hamiltonian / Fisher information / Stochastic parameter-shift rule / Variational algorithm / Quantum circuit
© The Author(s) 2023
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