Variational-State Quantum Metrology

Abstract

Quantum technologies exploit entanglement to enhance various tasks beyond their classical limits including computation, communication and measurements. Quantum metrology aims to increase the precision of a measured quantity that is estimated in the presence of statistical errors using entangled quantum states. We present a novel approach for finding (near) optimal states for metrology in the presence of noise, using variational techniques as a tool for efficiently searching the classically intractable high-dimensional space of quantum states. We comprehensively explore systems consisting of up to 9 qubits and find new highly entangled states that are not symmetric under permutations and non-trivially outperform previously known states up to a constant factor 2. We consider a range of environmental noise models; while passive quantum states cannot achieve a fundamentally superior scaling (as established by prior asymptotic results) we do observe a significant absolute quantum advantage. We finally outline a possible experimental setup for variational quantum metrology which can be implemented in near-term hardware.

arXiv comment31 pages, 10 figures -- added more discussion about, e.g., the optimisation and the ansatz structure

References in corpus (58)

• A variational eigenvalue solver on a quantum processor
• Advances in Quantum Metrology
• Quantum-enhanced measurements: beating the standard quantum limit
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• The theory of variational hybrid quantum-classical algorithms
• Logic gates at the surface code threshold: Superconducting qubits poised for fault-tolerant quantum computing
• Quantum metrology with nonclassical states of atomic ensembles
• Quantum Circuit Learning
• On the Improvement of Frequency Stardards with Quantum Entanglement
• General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology
• State preservation by repetitive error detection in a superconducting quantum circuit
• Quantum spin squeezing
• Quantum metrology from a quantum information science perspective
• Scalable Quantum Simulation of Molecular Energies
• High-fidelity two-qubit quantum logic gates using trapped calcium-43 ions
• High-fidelity quantum logic gates using trapped-ion hyperfine qubits
• The elusive Heisenberg limit in quantum enhanced metrology
• Quantum Fisher information matrix and multiparameter estimation
• Efficient variational quantum simulator incorporating active error minimisation
• Quantum optimization using variational algorithms on near-term quantum devices
• Quantum Metrology in Non-Markovian Environments
• Realization of Three-Qubit Quantum Error Correction with Superconducting Circuits
• Global entanglement in multiparticle systems
• A subpicotesla diamond magnetometer
• Improved quantum metrology using quantum error-correction
• Optimal states and almost optimal adaptive measurements for quantum interferometry
• Dividing Quantum Channels
• Quantum Error Correction for Metrology
• QuEST and High Performance Simulation of Quantum Computers
• Characterizing the entanglement of symmetric many-particle spin-1/2 systems
• Phase-space formulation of quantum mechanics and quantum state reconstruction for physical systems with Lie-group symmetries
• Approximate quantum error correction can lead to better codes
• Stochastic gradient descent for hybrid quantum-classical optimization
• Magnet field sensing beyond the standard quantum limit under the effect of decoherence
• Increasing sensing resolution with error correction
• Efficient tools for quantum metrology with uncorrelated noise
• Procedures for Converting among Lindblad, Kraus and Matrix Representations of Quantum Dynamical Semigroups
• Force-detected nuclear magnetic resonance: Recent advances and future challenges
• Qubit metrology and decoherence
• Wigner Functions for Arbitrary Quantum Systems
• Quantum Fisher information for density matrices with arbitrary ranks
• An Adaptive Optimizer for Measurement-Frugal Variational Algorithms
• Entanglement Evolution in a Non-Markovian Environment
• Variational-State Quantum Metrology
• Ultrasensitive magnetic field detection using a single artificial atom
• Flexible resources for quantum metrology
• Random bosonic states for robust quantum metrology
• Measurement cost of metric-aware variational quantum algorithms
• A search algorithm for quantum state engineering and metrology
• Continuous phase-space representations for finite-dimensional quantum states and their tomography
• Matrix product states for quantum metrology
• Optimal quantum states for frequency estimation
• Quantum Error-Correction-Enhanced Magnetometer Overcoming the Limit Imposed by Relaxation
• Sensing in the Presence of Observed Environments
• Channel-Optimized Quantum Error Correction
• Electron paramagnetic resonance spectroscopy using a single artificial atom
• Continuous phase spaces and the time evolution of spins: star products and spin-weighted spherical harmonics
• Time evolution of coupled spin systems in a generalized Wigner representation

Cited by in corpus (69)

• Variational Quantum Algorithms
• Noisy intermediate-scale quantum (NISQ) algorithms
• Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuits
• Noise-Induced Barren Plateaus in Variational Quantum Algorithms
• Hybrid quantum-classical algorithms and quantum error mitigation
• Variational Quantum Linear Solver
• Solving nonlinear differential equations with differentiable quantum circuits
• Exponential Error Suppression for Near-Term Quantum Devices
• Fisher Information in Noisy Intermediate-Scale Quantum Applications
• A variational toolbox for quantum multi-parameter estimation
• Quantum Variational Optimization of Ramsey Interferometry and Atomic Clocks
• Variational-State Quantum Metrology
• Variational Quantum Algorithm for Estimating the Quantum Fisher Information
• Review: Quantum Metrology and Sensing with Many-Body Systems
• Asymptotic theory of quantum channel estimation
• The Parity Operator: applications in quantum metrology
• The Dominant Eigenvector of a Noisy Quantum State
• Measurement cost of metric-aware variational quantum algorithms
• Quantum metrology with imperfect measurements
• Quantum natural gradient generalised to noisy and non-unitary circuits
• Optimal and Variational Multi-Parameter Quantum Metrology and Vector Field Sensing
• Can Error Mitigation Improve Trainability of Noisy Variational Quantum Algorithms?
• Symmetry enhanced variational quantum spin eigensolver
• Quantum Error Mitigated Classical Shadows
• A semi-agnostic ansatz with variable structure for quantum machine learning
• Optimal Control for Quantum Metrology via Pontryagin's principle
• Variational waveguide QED simulators
• Variational quantum algorithm for experimental photonic multiparameter estimation
• Robust estimation of the Quantum Fisher Information on a quantum processor
• Sub-Quantum Fisher Information
• Effects of noise on the overparametrization of quantum neural networks
• Application of Pontryagin's Maximum Principle to Quantum Metrology in Dissipative Systems
• Recent advances in high-dimensional mode-locked quantum frequency combs
• Preparation of Metrological States in Dipolar-Interacting Spin Systems
• Inference-Based Quantum Sensing
• Squeezing and quantum approximate optimization
• Variational quantum solutions to the Shortest Vector Problem
• Variational determination of multi-qubit geometrical entanglement in NISQ computers
• Fast computation of spherical phase-space functions of quantum many-body states
• Fully-Optimized Quantum Metrology: Framework, Tools, and Applications
• Measurement optimization of variational quantum simulation by classical shadow and derandomization
• Private and Robust States for Distributed Quantum Sensing
• Beyond unital noise in variational quantum algorithms: noise-induced barren plateaus and limit sets
• Single-component gradient rules for variational quantum algorithms
• Optimizing Initial State of Detector Sensors in Quantum Sensor Networks
• Can shallow quantum circuits scramble local noise into global white noise?
• Near-term Efficient Quantum Algorithms for Entanglement Analysis
• Photonic quantum metrology with variational quantum optical non-linearities
• Stochastic approach for quantum metrology with generic Hamiltonians
• Qsun: an open-source platform towards practical quantum machine learning applications
• Time-energy uncertainty relation for noisy quantum metrology
• Phase Spaces, Parity Operators, and the Born-Jordan Distribution
• Optimizing one-axis twists for variational Bayesian quantum metrology
• Characterizing quantum instruments: from non-demolition measurements to quantum error correction
• Generation of genuine all-way entanglement in defect-nuclear spin systems through dynamical decoupling sequences
• Variational quantum simulation of long-range interacting systems
• Generation of photonic tensor network states with Circuit QED
• Erasure conversion for singlet-triplet spin qubits enables high-performance shuttling-based quantum error correction
• More buck-per-shot: Why learning trumps mitigation in noisy quantum sensing
• Biasing quantum trajectories for enhanced sensing
• Error Analysis of the Variational Quantum Eigensolver Algorithm
• Density matrix representation of hybrid tensor networks for noisy quantum devices
• Efficient tensor networks for control-enhanced quantum metrology
• Multi-target quantum compilation algorithm
• Photonic variational quantum eigensolver for NISQ-compatible quantum technology
• Iterative optimization in quantum metrology and entanglement theory using semidefinite programming
• Lieb-Mattis states for robust entangled differential phase sensing
• Variational simulation of higher-spin systems on qubit-based quantum simulators
• Optical Quantum Computing