Fisher Information in Noisy Intermediate-Scale Quantum Applications

Abstract

The recent advent of noisy intermediate-scale quantum devices, especially near-term quantum computers, has sparked extensive research efforts concerned with their possible applications. At the forefront of the considered approaches are variational methods that use parametrized quantum circuits. The classical and quantum Fisher information are firmly rooted in the field of quantum sensing and have proven to be versatile tools to study such parametrized quantum systems. Their utility in the study of other applications of noisy intermediate-scale quantum devices, however, has only been discovered recently. Hoping to stimulate more such applications, this article aims to further popularize classical and quantum Fisher information as useful tools for near-term applications beyond quantum sensing. We start with a tutorial that builds an intuitive understanding of classical and quantum Fisher information and outlines how both quantities can be calculated on near-term devices. We also elucidate their relationship and how they are influenced by noise processes. Next, we give an overview of the core results of the quantum sensing literature and proceed to a comprehensive review of recent applications in variational quantum algorithms and quantum machine learning.

30 pages, 3 figures, quantumarticle, comments warmly welcome

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Cited by in corpus (74)

• General parameter-shift rules for quantum gradients
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• Theoretical Guarantees for Permutation-Equivariant Quantum Neural Networks
• Review: Quantum Metrology and Sensing with Many-Body Systems
• Quantum circuits for measuring weak values, Kirkwood--Dirac quasiprobability distributions, and state spectra
• Unifying speed limit, thermodynamic uncertainty relation and Heisenberg principle via bulk-boundary correspondence
• Quantum machine learning of large datasets using randomized measurements
• Probe incompatibility in multiparameter noisy quantum metrology
• Quantum Neural Network Classifiers: A Tutorial
• Symmetry enhanced variational quantum spin eigensolver
• Quantum Transfer Learning for Real-World, Small, and High-Dimensional Datasets
• Fisher information universally identifies quantum resources
• Noisy intermediate-scale quantum algorithm for semidefinite programming
• Integrable quantum many-body sensors for AC field sensing
• Stark localization as a resource for weak-field sensing with super-Heisenberg precision
• Error Bounds for Variational Quantum Time Evolution
• Information geometry under hierarchical quantum measurement
• Effects of noise on the overparametrization of quantum neural networks
• Tackling Sampling Noise in Physical Systems for Machine Learning Applications: Fundamental Limits and Eigentasks
• Modular Many-Body Quantum Sensors
• Quantum variational learning for quantum error-correcting codes
• Variational quantum algorithm for unconstrained black box binary optimization: Application to feature selection
• Generalization of Quantum Machine Learning Models Using Quantum Fisher Information Metric
• A Practical Introduction to Benchmarking and Characterization of Quantum Computers
• Exponential clustering of bipartite quantum entanglement at arbitrary temperatures
• Inference-Based Quantum Sensing
• Current Trends in Global Quantum Metrology
• Long-range interacting Stark many-body probes with Super-Heisenberg precision
• Natural parameterized quantum circuit
• Metrological robustness of high photon number optical cat states
• Quantum metrology in the finite-sample regime
• Optimizing Variational Quantum Algorithms with qBang: Efficiently Interweaving Metric and Momentum to Navigate Flat Energy Landscapes
• Krylov shadow tomography: Efficient estimation of quantum Fisher information
• Beyond one-axis twisting: Simultaneous spin-momentum squeezing
• Overcoming Quantum Metrology Singularity through Sequential Measurements
• Stochastic approach for quantum metrology with generic Hamiltonians
• A hybrid quantum algorithm to detect conical intersections
• Accelerating quantum imaginary-time evolution with random measurements
• Learning a quantum channel from its steady-state
• Two-dimensional coherent spectrum of high-spin models via a quantum computing approach
• Random Natural Gradient
• Adaptive variational quantum dynamics simulations with compressed circuits and fewer measurements
• Variational quantum simulation of long-range interacting systems
• Generic Two-Mode Gaussian States as Quantum Sensors
• Adaptive variational quantum computing approaches for Green's functions and nonlinear susceptibilities
• Characterization of overparametrization in the simulation of realistic quantum systems
• Exploiting subspace constraints and ab initio variational methods for quantum chemistry
• Backpropagation scaling in parameterised quantum circuits
• Quantum Natural Gradient with Geodesic Corrections for Small Shallow Quantum Circuits
• Quantum Enhanced Sensitivity through Many-Body Bloch Oscillations
• Data-Dependent Generalization Bounds for Parameterized Quantum Models Under Noise
• Estimation of Quantum Fisher Information via Stein's Identity in Variational Quantum Algorithms
• Policy Gradients using Variational Quantum Circuits
• Non-Gaussian Dissipative Quantum Thermometry Beyond Gaussian Bounds
• Iterative optimization in quantum metrology and entanglement theory using semidefinite programming
• NISQ algorithm for the matrix elements of a generic observable
• Modified Conjugate Quantum Natural Gradient
• Evolved Quantum Boltzmann Machines
• Optimized readout strategies for neutral atom quantum processors
• Efficient Berry Phase Calculation via Adaptive Variational Quantum Computing Approach
• Variational simulation of higher-spin systems on qubit-based quantum simulators
• Quantum natural gradient with thermal-state initialization
• Superiority of Krylov shadow tomography in estimating quantum Fisher information: From bounds to exactness
• Precision Bounds for Characterising Quantum Measurements
• Information geometry of bosonic Gaussian thermal states
• Quantum feature-map learning with reduced resource overhead
• Exploring Entanglement and Parameter Sensitivity in QAOA through Quantum Fisher Information
• Disentangling quantum autoencoder
• The fuzzy bit
• Natural gradient and parameter estimation for quantum Boltzmann machines
• Quantum Speed Limits and the Ultimate Scaling of the Quantum Sensors