Multiparameter quantum metrology with postselection measurements

Ho, Le Bin; Kondo, Yasushi

doi:10.1063/5.0024555

Cited by 11 publications

(5 citation statements)

References 88 publications

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“…In the estimation theory, the estimated values φ(x) are obtained by a certain estimator wherein different estimator strategies, such as maximum-likelihood estimation 74,75 , least square 76 , may yield different precision. The estimation precision can be characterized in terms of covariance matrix 33…”

Section: Quantum Parameters Estimation For General Hamiltoniansmentioning

confidence: 99%

“…So far, it has been demonstrated the quantum-enhanced beyond the Heisenberg limit with nonlinear interaction 4,22,23 , interaction-based 24,25 , and even without entanglement 26 . The studies of quantum metrology under noisy environments [27][28][29] , post-selection measurements [30][31][32][33] , and quantum error correction [34][35][36][37] are also extensively reported.…”

Section: Introductionmentioning

confidence: 99%

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Stochastic parameter-shift rule for quantum metrology with general Hamiltonians

2022

Preprint

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Recently, quantum metrology with multiplicative Hamiltonians has been proposed in the variational quantum algorithms, from which the estimation precision can be adaptively optimized via the variational circuits. Systems with general Hamiltonians, however, still lack these variational schemes. This work introduces a quantum-circuit-based approach for studying quantum metrology with general Hamiltonians. We present a stochastic parameter-shift rule for the derivatives of the evolved quantum state under the parameterized gates in the circuit, whereby the quantum Fisher information can be obtained. Here the parameters are those we wish to estimate. We find that our scheme can be executed in universal quantum computers under the family of parameterized gates. Moreover, in the examples of the magnetic field estimation, we show the consistency between the results obtained from the stochastic parameter-shift rule and the exact results, while the results obtained from the standard parameter-shift rule slightly deviate from the exact ones. Our work sheds new light on studying quantum metrology with general Hamiltonians using quantum circuit algorithms.

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Section: Quantum Parameters Estimation For General Hamiltoniansmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Stochastic parameter-shift rule for quantum metrology with general Hamiltonians

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…This type of tradeoff is present in other quantum estimation tasks including the measurment of a phase and a phase diffusion parameter (Altorio et al, 2015;Roccia et al, 2017;Szczykulska et al, 2017;Vidrighin et al, 2014). Possible methods to circumvent these tradeoffs include having the parameters be correlated (Birchall et al, 2020) and using postselection (Ho and Kondo, 2021).…”

Section: Phase and Lossmentioning

confidence: 99%

Quantum Polarimetry

Goldberg

2021

Preprint

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Polarization is one of light's most versatile degrees of freedom for both classical and quantum applications. The ability to measure light's state of polarization and changes therein is thus essential; this is the science of polarimetry. It has become ever more apparent in recent years that the quantum nature of light's polarization properties is crucial, from explaining experiments with single or few photons to understanding the implications of quantum theory on classical polarization properties. We present a self-contained overview of quantum polarimetry, including discussions of classical and quantum polarization, their transformations, and measurements thereof. We use this platform to elucidate key concepts that are neglected when polarization and polarimetry are considered only from classical perspectives.

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“…So far, it has been demonstrated the quantum-enhanced beyond the Heisenberg limit with nonlinear interaction 4,22,23 , interaction-based 24,25 , and even without entanglement 26 . The studies of quantum metrology under noisy environments [27][28][29] , postselection measurements [30][31][32][33] , and quantum error correction [34][35][36][37] are also extensively reported.…”

Section: Introductionmentioning

confidence: 99%

Stochastic parameter-shift rule for quantum metrology with general Hamiltonians

Ho¹

2022

Preprint

Self Cite

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Recently, quantum metrology with multiplicative Hamiltonians has been proposed in the variational quantum algorithms, from which the estimation precision can be adaptively optimized via the variational circuits. For systems with general Hamiltonians, however, still lack these variational schemes. In this work, we introduce a quantum-circuit-based approach for studying quantum metrology with general Hamiltonians. We introduce the stochastic parameter-shift rule for the derivatives of the evolved quantum state under the parameterized gates in the circuit, whereby the quantum Fisher information can be obtained. Here the parameters are those we wish to estimate. We find that under the family of the parameterized gates, our scheme can be executed in universal quantum computers. Moreover, in the examples of the magnetic field estimation, we show the consistency between the results obtained from the stochastic parameter-shift rule and the exact results while the standard parameter-shift rule slightly deviates from the exact ones. Our work sheds new light for studying quantum metrology with general Hamiltonians using quantum circuit algorithms.

show abstract

Multiparameter quantum metrology with postselection measurements

Cited by 11 publications

References 88 publications

Stochastic parameter-shift rule for quantum metrology with general Hamiltonians

Stochastic parameter-shift rule for quantum metrology with general Hamiltonians

Quantum Polarimetry

Stochastic parameter-shift rule for quantum metrology with general Hamiltonians

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