Quantum-enhanced mean value estimation via adaptive measurement
arXiv:2210.15624 · doi:10.22331/q-2024-09-09-1463
Abstract
Quantum-enhanced (i.e., higher performance by quantum effects than any classical methods) mean value estimation of observables is a fundamental task in various quantum technologies; in particular, it is an essential subroutine in quantum computing algorithms. Notably, the quantum estimation theory identifies the ultimate precision of such an estimator, which is referred to as the quantum Cramér-Rao (QCR) lower bound or equivalently the inverse of the quantum Fisher information. Because the estimation precision directly determines the performance of those quantum technological systems, it is highly demanded to develop a generic and practically implementable estimation method that achieves the QCR bound. Under imperfect conditions, however, such an ultimate and implementable estimator for quantum mean values has not been developed. In this paper, we propose a quantum-enhanced mean value estimation method in a depolarizing noisy environment that asymptotically achieves the QCR bound in the limit of a large number of qubits. To approach the QCR bound in a practical setting, the method adaptively optimizes the amplitude amplification and a specific measurement that can be implemented without any knowledge of state preparation. We provide a rigorous analysis for the statistical properties of the proposed adaptive estimator such as consistency and asymptotic normality. Furthermore, several numerical simulations are provided to demonstrate the effectiveness of the method, particularly showing that the estimator needs only a modest number of measurements to almost saturate the QCR bound.
35 pages, 9 figures. Final version
References in corpus (62)
- A variational eigenvalue solver on a quantum processor
- Quantum sensing
- Advances in Quantum Metrology
- Variational Quantum Algorithms
- Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
- Quantum Amplitude Amplification and Estimation
- Predicting Many Properties of a Quantum System from Very Few Measurements
- Hamiltonian Simulation by Qubitization
- Quantum metrology from a quantum information science perspective
- Advances in Photonic Quantum Sensing
- The elusive Heisenberg limit in quantum enhanced metrology
- Efficient variational quantum simulator incorporating active error minimisation
- Entanglement-free Heisenberg-limited phase estimation
- Using entanglement against noise in quantum metrology
- A Grand Unification of Quantum Algorithms
- Optimal states and almost optimal adaptive measurements for quantum interferometry
- Amplitude estimation without phase estimation
- Accelerated Variational Quantum Eigensolver
- Fisher information in quantum statistics
- Optimal Quantum Measurements of Expectation Values of Observables
- Variational Quantum State Diagonalization
- Efficient Bayesian Phase Estimation
- Iterative Quantum Amplitude Estimation
- How to perform the most accurate possible phase measurements
- Quantum phase estimation of multiple eigenvalues for small-scale (noisy) experiments
- Hardware-efficient variational quantum algorithms for time evolution
- Quantum Fisher information for states in exponential form
- Variational Quantum State Eigensolver
- Quantum error mitigation as a universal error-minimization technique: applications from NISQ to FTQC eras
- Demonstrating Heisenberg-limited unambiguous phase estimation without adaptive measurements
- Adaptive Variational Quantum Dynamics Simulations
- Measurement reduction in variational quantum algorithms
- Quantum Approximate Counting, Simplified
- Simple expression for the quantum Fisher information matrix
- Parity Measurement is Sufficient for Phase Estimation at the Quantum Cramer-Rao Bound for Path-Symmetric States
- A case study of variational quantum algorithms for a job shop scheduling problem
- Minimizing estimation runtime on noisy quantum computers
- Experimental Demonstration of Adaptive Quantum State Estimation
- Low depth algorithms for quantum amplitude estimation
- Applications of Quantum Computing for Investigations of Electronic Transitions in Phenylsulfonyl-carbazole TADF Emitters
- Quantum Algorithms for Estimating Physical Quantities using Block-Encodings
- Using adaptiveness and causal superpositions against noise in quantum metrology
- Faster Amplitude Estimation
- Nearly Optimal Quantum Algorithm for Estimating Multiple Expectation Values
- Multiple phase estimation for arbitrary pure states under white noise
- Amplitude estimation via maximum likelihood on noisy quantum computer
- Achieving Heisenberg scaling with maximally entangled states: an analytic upper bound for the attainable root mean square error
- Heisenberg-limited quantum phase estimation of multiple eigenvalues with few control qubits
- Quantum metrology of noisy spreading channels
- Experimental multiparameter quantum metrology in adaptive regime
- Simulating Time Evolution with Fully Optimized Single-Qubit Gates on Parameterized Quantum Circuits
- Variational quantum algorithm for unconstrained black box binary optimization: Application to feature selection
- Modified Grover operator for amplitude estimation
- Quantum computation speedup limits from quantum metrological precision bounds
- Non-asymptotic Heisenberg scaling: experimental metrology for a wide resources range
- Power of One Bit of Quantum Information in Quantum Metrology
- Randomized gap and amplitude estimation
- Approximate Solutions of Combinatorial Problems via Quantum Relaxations
- Noisy quantum amplitude estimation without noise estimation
- Quantum Amplitude Estimation in the Presence of Noise
- Can shallow quantum circuits scramble local noise into global white noise?
- Improved maximum-likelihood quantum amplitude estimation