Fisher Information in Noisy Intermediate-Scale Quantum Applications
arXiv:2103.15191 · doi:10.22331/q-2021-09-09-539
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.
arXiv comment30 pages, 3 figures, quantumarticle, comments warmly welcome
References in corpus (56)
- Quantum Computing in the NISQ era and beyond
- Supplementary information for "Quantum supremacy using a programmable superconducting processor"
- Quantum Machine Learning
- Variational Quantum Algorithms
- Supervised learning with quantum enhanced feature spaces
- The theory of variational hybrid quantum-classical algorithms
- Noisy intermediate-scale quantum (NISQ) algorithms
- Quantum Circuit Learning
- An introduction to quantum machine learning
- Quantum Resource Theories
- Predicting Many Properties of a Quantum System from Very Few Measurements
- Parameterized quantum circuits as machine learning models
- Evaluating analytic gradients on quantum hardware
- The power of quantum neural networks
- On the Improvement of Frequency Stardards with Quantum Entanglement
- The elusive Heisenberg limit in quantum enhanced metrology
- Quantum Fisher information matrix and multiparameter estimation
- Quantum autoencoders for efficient compression of quantum data
- Quantum Natural Gradient
- Compatibility in Multiparameter Quantum Metrology
- Achieving the Heisenberg limit in quantum metrology using quantum error correction
- Generalized Geometric Quantum Speed Limits
- A Geometric Perspective on Quantum Parameter Estimation
- A perspective on multiparameter quantum metrology: from theoretical tools to applications in quantum imaging
- Fisher information in quantum statistics
- Optimal measurements for simultaneous quantum estimation of multiple phases
- Multi-parameter estimation beyond Quantum Fisher Information
- Estimating the gradient and higher-order derivatives on quantum hardware
- Avoiding local minima in variational quantum eigensolvers with the natural gradient optimizer
- Variational spin-squeezing algorithms on programmable quantum sensors
- Relating out-of-time-order correlations to entanglement via multiple-quantum coherences
- Capacity and quantum geometry of parametrized quantum circuits
- Discontinuities of the quantum Fisher information and the Bures metric
- A variational toolbox for quantum multi-parameter estimation
- Machine learning quantum states in the NISQ era
- Variational-State Quantum Metrology
- Simultaneous Perturbation Stochastic Approximation of the Quantum Fisher Information
- Optimal measurements for quantum multiparameter estimation with general states
- Incorporating Heisenberg's Uncertainty Principle into Quantum Multiparameter Estimation
- Quantum Fisher information from randomized measurements
- Quantum Semiparametric Estimation
- Minimizing estimation runtime on noisy quantum computers
- Fidelity susceptibility and quantum Fisher information for density operators with arbitrary ranks
- Precision Limits in Quantum Metrology with Open Quantum Systems
- A Scalable Maximum Likelihood Method for Quantum State Tomography
- Measurement cost of metric-aware variational quantum algorithms
- Detecting metrologically useful asymmetry and entanglement by a few local measurements
- Optimal probes and error-correction schemes in multi-parameter quantum metrology
- Using Quantum Metrological Bounds in Quantum Error Correction: A Simple Proof of the Approximate Eastin-Knill Theorem
- On the discontinuity of the quantum Fisher information for quantum statistical models with parameter dependent rank
- Incompatibility in Quantum Parameter Estimation
- Witnessing multipartite entanglement by detecting asymmetry
- Geometric distinguishability measures limit quantum channel estimation and discrimination
- Optimal universal programming of unitary gates
- Sub-Quantum Fisher Information
- Generalized Measure of Quantum Fisher Information
Cited by in corpus (75)
- Noisy intermediate-scale quantum (NISQ) algorithms
- General parameter-shift rules for quantum gradients
- Theory of overparametrization in quantum neural networks
- Quantum criticality under decoherence or weak measurement
- Avoiding barren plateaus using classical shadows
- Simultaneous Perturbation Stochastic Approximation of the Quantum Fisher Information
- 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
- Exponential clustering of bipartite quantum entanglement at arbitrary temperatures
- A Practical Introduction to Benchmarking and Characterization of Quantum Computers
- 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
- 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
- Quantum metrology in the finite-sample regime
- Beyond one-axis twisting: Simultaneous spin-momentum squeezing
- Stochastic approach for quantum metrology with generic Hamiltonians
- Overcoming Quantum Metrology Singularity through Sequential Measurements
- A hybrid quantum algorithm to detect conical intersections
- Accelerating quantum imaginary-time evolution with random measurements
- Two-dimensional coherent spectrum of high-spin models via a quantum computing approach
- Learning a quantum channel from its steady-state
- Variational quantum simulation of long-range interacting systems
- Random Natural Gradient
- Adaptive variational quantum dynamics simulations with compressed circuits and fewer measurements
- Generic Two-Mode Gaussian States as Quantum Sensors
- Characterization of overparametrization in the simulation of realistic quantum systems
- Adaptive variational quantum computing approaches for Green's functions and nonlinear susceptibilities
- Quantum Natural Gradient with Geodesic Corrections for Small Shallow Quantum Circuits
- Exploiting subspace constraints and ab initio variational methods for quantum chemistry
- Backpropagation scaling in parameterised quantum circuits
- Estimation of Quantum Fisher Information via Stein's Identity in Variational Quantum Algorithms
- Data-Dependent Generalization Bounds for Parameterized Quantum Models Under Noise
- Quantum Enhanced Sensitivity through Many-Body Bloch Oscillations
- Iterative optimization in quantum metrology and entanglement theory using semidefinite programming
- Modified Conjugate Quantum Natural Gradient
- Evolved Quantum Boltzmann Machines
- NISQ algorithm for the matrix elements of a generic observable
- Policy Gradients using Variational Quantum Circuits
- Non-Gaussian Dissipative Quantum Thermometry Beyond Gaussian Bounds
- Optimized readout strategies for neutral atom quantum processors
- Efficient Berry Phase Calculation via Adaptive Variational Quantum Computing Approach
- Superiority of Krylov shadow tomography in estimating quantum Fisher information: From bounds to exactness
- Quantum natural gradient with thermal-state initialization
- Variational simulation of higher-spin systems on qubit-based quantum simulators
- Precision Bounds for Characterising Quantum Measurements
- Quantum Speed Limits and the Ultimate Scaling of the Quantum Sensors
- Information geometry of bosonic Gaussian thermal states
- Natural gradient and parameter estimation for quantum Boltzmann machines
- 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