Near-Term Quantum Computing Techniques: Variational Quantum Algorithms, Error Mitigation, Circuit Compilation, Benchmarking and Classical Simulation

Abstract

Quantum computing is a game-changing technology for global academia, research centers and industries including computational science, mathematics, finance, pharmaceutical, materials science, chemistry and cryptography. Although it has seen a major boost in the last decade, we are still a long way from reaching the maturity of a full-fledged quantum computer. That said, we will be in the Noisy-Intermediate Scale Quantum (NISQ) era for a long time, working on dozens or even thousands of qubits quantum computing systems. An outstanding challenge, then, is to come up with an application that can reliably carry out a nontrivial task of interest on the near-term quantum devices with non-negligible quantum noise. To address this challenge, several near-term quantum computing techniques, including variational quantum algorithms, error mitigation, quantum circuit compilation and benchmarking protocols, have been proposed to characterize and mitigate errors, and to implement algorithms with a certain resistance to noise, so as to enhance the capabilities of near-term quantum devices and explore the boundaries of their ability to realize useful applications. Besides, the development of near-term quantum devices is inseparable from the efficient classical simulation, which plays a vital role in quantum algorithm design and verification, error-tolerant verification and other applications. This review will provide a thorough introduction of these near-term quantum computing techniques, report on their progress, and finally discuss the future prospect of these techniques, which we hope will motivate researchers to undertake additional studies in this field.

arXiv commentPlease feel free to email He-Liang Huang with any comments, questions, suggestions or concerns

References in corpus (274)

• Quantum Computing in the NISQ era and beyond
• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Quantum Machine Learning
• A variational eigenvalue solver on a quantum processor
• Elementary gates for quantum computation
• The density-matrix renormalization group in the age of matrix product states
• Quantum Computing
• Quantum algorithm for solving linear systems of equations
• Variational Quantum Algorithms
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• Supervised learning with quantum enhanced feature spaces
• Efficient classical simulation of slightly entangled quantum computations
• Quantum computational advantage using photons
• Barren plateaus in quantum neural network training landscapes
• The theory of variational hybrid quantum-classical algorithms
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• A Quantum Engineer's Guide to Superconducting Qubits
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Dynamical Decoupling of Open Quantum Systems
• Noisy intermediate-scale quantum (NISQ) algorithms
• Quantum machine learning in feature Hilbert spaces
• Efficient simulation of one-dimensional quantum many-body systems
• Quantum Circuit Learning
• Improved Simulation of Stabilizer Circuits
• Quantum Chemistry in the Age of Quantum Computing
• Superconducting Qubits: Current State of Play
• Quantum Convolutional Neural Networks
• Integrated Photonic Quantum Technologies
• Quantum principal component analysis
• Error mitigation for short-depth quantum circuits
• Trapped-Ion Quantum Computing: Progress and Challenges
• Quantum computing with trapped ions
• Characterizing Quantum Supremacy in Near-Term Devices
• Time-dependent density-matrix renormalization-group using adaptive effective Hilbert spaces
• Predicting Many Properties of a Quantum System from Very Few Measurements
• Strong quantum computational advantage using a superconducting quantum processor
• Entanglement renormalization
• Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuits
• Evaluating analytic gradients on quantum hardware
• Randomized Benchmarking of Quantum Gates
• An adaptive variational algorithm for exact molecular simulations on a quantum computer
• Quantum random access memory
• Extending the computational reach of a noisy superconducting quantum processor
• Noise-Induced Barren Plateaus in Variational Quantum Algorithms
• From the Quantum Approximate Optimization Algorithm to a Quantum Alternating Operator Ansatz
• Robust randomized benchmarking of quantum processes
• Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
• Hartree-Fock on a superconducting qubit quantum computer
• Validating quantum computers using randomized model circuits
• Realizing Repeated Quantum Error Correction in a Distance-Three Surface Code
• Exact and Approximate Unitary 2-Designs: Constructions and Applications
• Photonic quantum information processing: a review
• Optimized Dynamical Decoupling in a Model Quantum Memory
• Photonic quantum information processing: a concise review
• Tensor renormalization group approach to 2D classical lattice models
• Classical simulation of quantum many-body systems with a tree tensor network
• Quantum generative adversarial learning
• Noise tailoring for scalable quantum computation via randomized compiling
• Hybrid quantum-classical algorithms and quantum error mitigation
• Hybrid Quantum-Classical Hierarchy for Mitigation of Decoherence and Determination of Excited States
• Quantum generative adversarial networks
• Scalable Noise Estimation with Random Unitary Operators
• Accurate determination of tensor network state of quantum lattice models in two dimensions
• Simulating quantum computation by contracting tensor networks
• Experimental Demonstration of Blind Quantum Computing
• Universal blind quantum computation
• Quantum Approximate Optimization of Non-Planar Graph Problems on a Planar Superconducting Processor
• Quantum Natural Gradient
• Variational Quantum Computation of Excited States
• A blueprint for demonstrating quantum supremacy with superconducting qubits
• Quantum Optimization of Maximum Independent Set using Rydberg Atom Arrays
• Generalized Unitary Coupled Cluster Wavefunctions for Quantum Computation
• Phase-Programmable Gaussian Boson Sampling Using Stimulated Squeezed Light
• Efficient measurement of quantum gate error by interleaved randomized benchmarking
• ProjectQ: An Open Source Software Framework for Quantum Computing
• qubit-ADAPT-VQE: An adaptive algorithm for constructing hardware-efficient ansatze on a quantum processor
• Coarse-graining renormalization by higher-order singular value decomposition
• Cloud Quantum Computing of an Atomic Nucleus
• Quantum Circuits for General Multiqubit Gates
• Simulation of two dimensional quantum systems on an infinite lattice revisited: corner transfer matrix for tensor contraction
• Superconducting Quantum Computing: A Review
• Measuring measurement
• Mitigating measurement errors in multi-qubit experiments
• Realization of an Error-Correcting Surface Code with Superconducting Qubits
• Quantum certification and benchmarking
• QAOA for Max-Cut requires hundreds of qubits for quantum speed-up
• Variational quantum algorithms for nonlinear problems
• Simulation of strongly correlated fermions in two spatial dimensions with fermionic Projected Entangled-Pair States
• Mixed-state entanglement from local randomized measurements
• Qulacs: a fast and versatile quantum circuit simulator for research purpose
• Characterization of addressability by simultaneous randomized benchmarking
• Quantum Computation of Electronic Transitions using a Variational Quantum Eigensolver
• Subspace-search variational quantum eigensolver for excited states
• General parameter-shift rules for quantum gradients
• Cryogenic Control Architecture for Large-Scale Quantum Computing
• Self-Consistent Quantum Process Tomography
• Minimal Universal Two-qubit Quantum Circuits
• Hybrid Quantum-Classical Convolutional Neural Networks
• Hybrid Quantum-Classical Approach to Quantum Optimal Control
• Warm-starting quantum optimization
• Polynomial-time T-depth Optimization of Clifford+T circuits via Matroid Partitioning
• Experimental Quantum Generative Adversarial Networks for Image Generation
• Scalable mitigation of measurement errors on quantum computers
• Symmetrised Characterisation of Noisy Quantum Processes
• Simulating Large Quantum Circuits on a Small Quantum Computer
• The General Quantum Interference Principle and the Duality Computer
• Towards a Distributed Quantum Computing Ecosystem
• Variational quantum algorithms for discovering Hamiltonian spectra
• Second Renormalization of Tensor-Network States
• QuEST and High Performance Simulation of Quantum Computers
• Characterizing large-scale quantum computers via cycle benchmarking
• Efficient and Noise Resilient Measurements for Quantum Chemistry on Near-Term Quantum Computers
• Error-mitigated digital quantum simulation
• Low-cost error mitigation by symmetry verification
• Learning-based quantum error mitigation
• Efficient decomposition of quantum gates
• Accelerated Variational Quantum Eigensolver
• A quantum-inspired classical algorithm for recommendation systems
• Quantum circuits of T-depth one
• Mitigation of readout noise in near-term quantum devices by classical post-processing based on detector tomography
• Synthesis of Quantum Circuits for Linear Nearest Neighbor Architectures
• Massive Parallel Quantum Computer Simulator
• Stochastic gradient descent for hybrid quantum-classical optimization
• Unbiasing Fermionic Quantum Monte Carlo with a Quantum Computer
• Efficient learning of quantum noise
• Algorithms for finite Projected Entangled Pair States
• Solving nonlinear differential equations with differentiable quantum circuits
• Efficient estimation of Pauli observables by derandomization
• Noise Resilience of Variational Quantum Compiling
• Digital zero noise extrapolation for quantum error mitigation
• Hyper-optimized tensor network contraction
• Renormalization of tensor-network states
• Variational algorithms for linear algebra
• Model-free readout-error mitigation for quantum expectation values
• Fundamental limits of quantum error mitigation
• Mitigating depolarizing noise on quantum computers with noise-estimation circuits
• Quantum generative adversarial network for generating discrete distribution
• Exact synthesis of multiqubit Clifford+T circuits
• Resource Efficient Zero Noise Extrapolation with Identity Insertions
• Differentiable Quantum Architecture Search
• Hardware-efficient variational quantum algorithms for time evolution
• A flexible high-performance simulator for verifying and benchmarking quantum circuits implemented on real hardware
• Three Qubit Randomized Benchmarking
• Avoiding local minima in variational quantum eigensolvers with the natural gradient optimizer
• Variational Quantum Eigensolver with Fewer Qubits
• Measuring the Capabilities of Quantum Computers
• Solving the sampling problem of the Sycamore quantum circuits
• Detector Tomography on IBM 5-qubit Quantum Computers and Mitigation of Imperfect Measurement
• A general framework for randomized benchmarking
• Yao.jl: Extensible, Efficient Framework for Quantum Algorithm Design
• Variational Quantum algorithm for Poisson equation
• Avoiding barren plateaus using classical shadows
• Quantum computation with universal error mitigation on superconducting quantum processor
• Randomized Benchmarking of Multi-Qubit Gates
• Error Mitigation by Symmetry Verification on a Variational Quantum Eigensolver
• Filtering variational quantum algorithms for combinatorial optimization
• Compiler Design for Distributed Quantum Computing
• Reducing qubit requirements for quantum simulation using molecular point group symmetries
• Decoding quantum errors with subspace expansions
• Establishing the Quantum Supremacy Frontier with a 281 Pflop/s Simulation
• Adaptive Variational Quantum Dynamics Simulations
• Quantum autoencoders to denoise quantum data
• Low-depth gradient measurements can improve convergence in variational hybrid quantum-classical algorithms
• Efficient estimation of Pauli channels
• Orbital optimized unitary coupled cluster theory for quantum computer
• Realizing Quantum Convolutional Neural Networks on a Superconducting Quantum Processor to Recognize Quantum Phases
• Diabatic gates for frequency-tunable superconducting qubits
• Direct randomized benchmarking for multi-qubit devices
• Efficient error models for fault-tolerant architectures and the Pauli twirling approximation
• Quantum circuit optimizations for NISQ architectures
• Error-Mitigated Quantum Gates Exceeding Physical Fidelities in a Trapped-Ion System
• Hybrid quantum-classical algorithms for approximate graph coloring
• Simple Mitigation of Global Depolarizing Errors in Quantum Simulations
• Experimental Realization of a Quantum Autoencoder: The Compression of Qutrits via Machine Learning
• Experimental Blind Quantum Computing for a Classical Client
• Characterizing Universal Gate Sets via Dihedral Benchmarking
• Calculating energy derivatives for quantum chemistry on a quantum computer
• Measuring Analytic Gradients of General Quantum Evolution with the Stochastic Parameter Shift Rule
• Mitigating realistic noise in practical noisy intermediate-scale quantum devices
• Neural Predictor based Quantum Architecture Search
• Learning to Optimize Variational Quantum Circuits to Solve Combinatorial Problems
• Calculation of the Green's function on near-term quantum computers
• Training A Quantum Optimizer
• Scalable randomized benchmarking of non-Clifford gates
• A measurement-based variational quantum eigensolver
• General-purpose quantum circuit simulator with Projected Entangled-Pair States and the quantum supremacy frontier
• Unified approach to data-driven quantum error mitigation
• Generalized quantum subspace expansion
• Multi-exponential Error Extrapolation and Combining Error Mitigation Techniques for NISQ Applications
• A state-averaged orbital-optimized hybrid quantum-classical algorithm for a democratic description of ground and excited states
• How many qubits are needed for quantum computational supremacy?
• Correlation-Informed Permutation of Qubits for Reducing Ansatz Depth in VQE
• Quantum Circuit Transformation Based on Simulated Annealing and Heuristic Search
• Error mitigation via verified phase estimation
• Towards a Larger Molecular Simulation on the Quantum Computer: Up to 28 Qubits Systems Accelerated by Point Group Symmetry
• Reinforcement Learning assisted Quantum Optimization
• Machine Learning Phase Transitions with a Quantum Processor
• Extending quantum probabilistic error cancellation by noise scaling
• Measurement Error Mitigation in Quantum Computers Through Classical Bit-Flip Correction
• Variational Quantum Eigensolver with Reduced Circuit Complexity
• Toward Practical Quantum Embedding Simulation of Realistic Chemical Systems on Near-term Quantum Computers
• Theory of analytical energy derivatives for the variational quantum eigensolver
• Optimal resource cost for error mitigation
• Variational Quantum-Neural Hybrid Eigensolver
• Demonstration of Adiabatic Variational Quantum Computing with a Superconducting Quantum Coprocessor
• Recovering noise-free quantum observables
• Error mitigation for variational quantum algorithms through mid-circuit measurements
• Constructing Smaller Pauli Twirling Sets for Arbitrary Error Channels
• Variational Quantum Circuits for Quantum State Tomography
• Rigorous measurement error correction
• The Dominant Eigenvector of a Noisy Quantum State
• Quantum Error Mitigation using Symmetry Expansion
• Mutual information-assisted Adaptive Variational Quantum Eigensolver
• Analyzing the Performance of Variational Quantum Factoring on a Superconducting Quantum Processor
• Dual-state purification for practical quantum error mitigation
• Emulating quantum teleportation of a Majorana zero mode qubit
• Realization of a quantum autoencoder for lossless compression of quantum data
• Simulating periodic systems on quantum computer
• Adaptive variational quantum eigensolvers for highly excited states
• Noise-Assisted Quantum Autoencoder
• Quantum Analytic Descent
• Noise-Resilient Variational Hybrid Quantum-Classical Optimization
• Variational inference with a quantum computer
• Chemistry on quantum computers with virtual quantum subspace expansion
• Benchmarking adaptive variational quantum eigensolvers
• Light Cone Matrix Product
• Variational quantum simulations of stochastic differential equations
• Variational Quantum Algorithm for Non-equilibrium Steady States
• Variational quantum amplitude estimation
• A Quantum Algorithm to Calculate Band Structure at the EOM Level of Theory
• Demonstration of Topological Data Analysis on a Quantum Processor
• An efficient adaptive variational quantum solver of the Schrodinger equation based on reduced density matrices
• Non-linear quantum-classical scheme to simulate non-equilibrium strongly correlated fermionic many-body dynamics
• Natural Evolutionary Strategies for Variational Quantum Computation
• Validating Quantum-Classical Programming Models with Tensor Network Simulations
• To quantum or not to quantum: towards algorithm selection in near-term quantum optimization
• Computationally Efficient Zero Noise Extrapolation for Quantum Gate Error Mitigation
• Quantum autoencoders with enhanced data encoding
• Modeling and mitigation of cross-talk effects in readout noise with applications to the Quantum Approximate Optimization Algorithm
• Randomized benchmarking for individual quantum gates
• Computation of molecular excited states on IBM quantum computers using a discriminative variational quantum eigensolver
• Optimising Matrix Product State Simulations of Shor's Algorithm
• Variational quantum process tomography
• Optimized Dynamical Decoupling via Genetic Algorithms
• Active Readout Error Mitigation
• General solution to inhomogeneous dephasing and smooth pulse dynamical decoupling
• Random circuit block-encoded matrix and a proposal of quantum LINPACK benchmark
• Hidden Inverses: Coherent Error Cancellation at the Circuit Level
• Readout Rebalancing for Near Term Quantum Computers
• Rolling quantum dice with a superconducting qubit
• A Neural-Network Variational Quantum Algorithm for Many-Body Dynamics
• Approximate Randomized Benchmarking for Finite Groups
• Experimental Implementation of a Quantum Autoencoder via Quantum Adders
• Generalization of the output of variational quantum eigensolver by parameter interpolation with low-depth ansatz
• Quantum readout error mitigation via deep learning
• A Variational Quantum Attack for AES-like Symmetric Cryptography
• Quantum Teleportation-Inspired Algorithm for Sampling Large Random Quantum Circuits
• Verifying Random Quantum Circuits with Arbitrary Geometry Using Tensor Network States Algorithm
• Experimental implementation of non-Clifford interleaved randomized benchmarking with a controlled-S gate
• Optimizing a Polynomial Function on a Quantum Simulator
• A scheme for automatic differentiation of complex loss functions
• Quantum Error Mitigation Relying on Permutation Filtering
• Multi-round QAOA and advanced mixers on a trapped-ion quantum computer
• Mitigating algorithmic errors in quantum optimization through energy extrapolation
• Evaluating the Q-score of Quantum Annealers
• Natural evolution strategies and variational Monte Carlo
• Simulating the Dynamics of Single Photons in BosonSampling Devices with Matrix Product States
• Variational Quantum Cloning: Improving Practicality for Quantum Cryptanalysis
• How to enhance quantum generative adversarial learning of noisy information
• Lifetime-based Optimization for Simulating Quantum Circuits on a New Sunway Supercomputer
• Quantum error reduction with deep neural network applied at the post-processing stage
• Probabilistic Eigensolver with a Trapped-Ion Quantum Processor
• Optimal digital dynamical decoupling for general decoherence via Walsh modulation
• Evaluating the Resilience of Variational Quantum Algorithms to Leakage Noise

Cited by in corpus (22)

• Quantum Neuronal Sensing of Quantum Many-Body States on a 61-Qubit Programmable Superconducting Processor
• Quantum Neural Networks for Power Flow Analysis
• A duplication-free quantum neural network for universal approximation
• Continuous variable quantum communication with 40 pairs of entangled sideband
• Resource frugal optimizer for quantum machine learning
• Synergistic Dynamical Decoupling and Circuit Design for Enhanced Algorithm Performance on Near-Term Quantum Devices
• Mitigating Quantum Errors via Truncated Neumann Series
• Optimal Parameter Configurations for Sequential Optimization of Variational Quantum Eigensolver
• Parameter-Parallel Distributed Variational Quantum Algorithm
• Improving the Performance of Digitized Counterdiabatic Quantum Optimization via Algorithm-Oriented Qubit Mapping
• Superconducting Quantum Simulation for Many-Body Physics beyond Equilibrium
• Quantum homotopy analysis method with quantum-compatible linearization for nonlinear partial differential equations
• Single-Layer Digitized-Counterdiabatic Quantum Optimization for $p$-spin Models
• High-fidelity dimer excitations using quantum hardware
• Application of Quantum Pre-Processing Filter for Binary Image Classification with Small Samples
• Quantum Advantage: A Single Qubit's Experimental Edge in Classical Data Storage
• Tomography-assisted noisy quantum circuit simulator using matrix product density operators
• Constraint-Aware Quantum Optimization via Hamming Weight Operators
• Suppressing decoherence in quantum state transfer with unitary operations
• Circuit-Noise-Resilient Virtual Distillation
• Cheaper and more noise-resilient quantum state preparation using eigenvector continuation
• The Dual Role of Low-Weight Pauli Propagation: A Flawed Simulator but a Powerful Initializer for Variational Quantum Algorithms