Quantum algorithms: an overview

Abstract

Quantum computers are designed to outperform standard computers by running quantum algorithms. Areas in which quantum algorithms can be applied include cryptography, search and optimisation, simulation of quantum systems, and solving large systems of linear equations. Here we briefly survey some known quantum algorithms, with an emphasis on a broad overview of their applications rather than their technical details. We include a discussion of recent developments and near-term applications of quantum algorithms.

17 pages; short survey to appear in npj Quantum Information. v2: minor corrections and clarifications

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Cited by in corpus (290)

• Quantum Computing in the NISQ era and beyond
• Noisy intermediate-scale quantum (NISQ) algorithms
• Superconducting Qubits: Current State of Play
• Quantum information processing with superconducting circuits: a review
• Semiconductor Spin Qubits
• The European Quantum Technologies Roadmap
• New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds
• Quantum machine learning: a classical perspective
• Quantum advantage with shallow circuits
• Molecular Spin Qudits for Quantum Algorithms
• The Expressive Power of Parameterized Quantum Circuits
• Advances in Space Quantum Communications
• Distributed Quantum Computing: a Survey
• Erasure conversion for fault-tolerant quantum computing in alkaline earth Rydberg atom arrays
• Local and Distributed Quantum Computation
• Solving nonlinear differential equations with differentiable quantum circuits
• Quantum Computing based Hybrid Solution Strategies for Large-scale Discrete-Continuous Optimization Problems
• Quantum Sampling Problems, BosonSampling and Quantum Supremacy
• Ultracold polar molecules as qudits
• CutQC: Using Small Quantum Computers for Large Quantum Circuit Evaluations
• Dynamical decoupling for superconducting qubits: a performance survey
• Computational advantage of quantum random sampling
• On the impact of quantum computing technology on future developments in high-performance scientific computing
• Quantum Algorithm Implementations for Beginners
• Statistical Assertions for Validating Patterns and Finding Bugs in Quantum Programs
• Continuous-variable quantum computing in the quantum optical frequency comb
• The impact of classical control electronics on qubit fidelity
• Quantum Software Engineering: Landscapes and Horizons
• Realizing Quantum Convolutional Neural Networks on a Superconducting Quantum Processor to Recognize Quantum Phases
• Gaussian Boson Sampling for perfect matchings of arbitrary graphs
• Measuring Analytic Gradients of General Quantum Evolution with the Stochastic Parameter Shift Rule
• Quantum Blockchain using entanglement in time
• Recent advances for quantum classifiers
• Variational Quantum Algorithms for Computational Fluid Dynamics
• Variational Quantum Unsampling on a Quantum Photonic Processor
• Scalable High-Performance Fluxonium Quantum Processor
• Biology and medicine in the landscape of quantum advantages
• Quantum bits with Josephson junctions
• Simulating Quantum Materials with Digital Quantum Computers
• Improved success probability with greater circuit depth for the quantum approximate optimization algorithm
• Quantum algorithm for association rules mining
• Quantum algorithm for association rules mining
• Scalable quantum computing with qudits on a graph
• Neural-Network Decoders for Quantum Error Correction using Surface Codes:A Space Exploration of the Hardware Cost-Performance Trade-Offs
• Understanding quantum machine learning also requires rethinking generalization
• Prospects of Quantum Computing for Molecular Sciences
• Universal fidelity reduction of quantum operations from weak dissipation
• Classification with Quantum Machine Learning: A Survey
• Measurement Error Mitigation in Quantum Computers Through Classical Bit-Flip Correction
• The challenge and opportunities of quantum literacy for future education and transdisciplinary problem-solving
• The Quantum Socket: Three-Dimensional Wiring for Extensible Quantum Computing
• A CMOS dynamic random access architecture for radio-frequency readout of quantum devices
• Quantum linear systems algorithms: a primer
• Demonstration of algorithmic quantum speedup
• Portfolio Optimization with Digitized-Counterdiabatic Quantum Algorithms
• Simultaneous execution of quantum circuits on current and near-future NISQ systems
• Asymptotic Quantum Algorithm for the Toeplitz Systems
• Quantum algorithm for visual tracking
• On applications of quantum computing to plasma simulations
• Attacking the Quantum Internet
• Dimensional Expressivity Analysis of Parametric Quantum Circuits
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• Conditional quantum operation of two exchange-coupled single-donor spin qubits in a MOS-compatible silicon device
• Quantum Computers for Weather and Climate Prediction: The Good, the Bad and the Noisy
• Quantum speedup of branch-and-bound algorithms
• Fast multi-qubit gates through simultaneous two-qubit gates
• Overcoming I/O bottleneck in superconducting quantum computing: multiplexed qubit control with ultra-low-power, base-temperature cryo-CMOS multiplexer
• Quantum Computing: An Overview Across the System Stack
• Lindblad Tomography of a Superconducting Quantum Processor
• QASMBench: A Low-level QASM Benchmark Suite for NISQ Evaluation and Simulation
• Time scale for adiabaticity breakdown in driven many-body systems and orthogonality catastrophe
• Validating Quantum-Classical Programming Models with Tensor Network Simulations
• Machine learning \& artificial intelligence in the quantum domain
• Complex Quantum Networks: a Topical Review
• Predicting quantum advantage by quantum walk with convolutional neural networks
• Two-Unitary Decomposition Algorithm and Open Quantum System Simulation
• Gradient-based closed-loop quantum optimal control in a solid-state two-qubit system
• Entanglement and coherence in Bernstein-Vazirani algorithm
• Quantum Computing for Fusion Energy Science Applications
• Analysis of The Vehicle Routing Problem Solved via Hybrid Quantum Algorithms in Presence of Noisy Channels
• Quantum-inspired Complex Convolutional Neural Networks
• Characterizing the Reproducibility of Noisy Quantum Circuits
• Classically simulating near-term partially-distinguishable and lossy boson sampling
• Quantum Deep Reinforcement Learning for Robot Navigation Tasks
• Quantum state preparation protocol for encoding classical data into the amplitudes of a quantum information processing register's wave function
• A Cooper-Pair Box Coupled to Two Resonators: An Architecture for a Quantum Refrigerator
• A brief introduction to quantum algorithms
• Quantum processing by remote quantum control
• Fault-Tolerant One-Bit Addition with the Smallest Interesting Colour Code
• Understanding Quantum Control Processor Capabilities and Limitations through Circuit Characterization
• Quantum circuits design for evaluating transcendental functions based on a function-value binary expansion method
• Qubernetes: Towards a Unified Cloud-Native Execution Platform for Hybrid Classic-Quantum Computing
• Applying quantum approximate optimization to the heterogeneous vehicle routing problem
• Continuous-variable quantum Gaussian process regression and quantum singular value decomposition of non-sparse low rank matrices
• Analyzing the impact of time-correlated noise on zero-noise extrapolation
• Gradient-descent quantum process tomography by learning Kraus operators
• Spin-boson quantum phase transition in multilevel superconducting qubits
• Just Like the Real Thing: Fast Weak Simulation of Quantum Computation
• One-particle Green's functions from the quantum equation of motion algorithm
• A universal scheme for robust self-testing in the prepare-and-measure scenario
• Experimental Bayesian calibration of trapped ion entangling operations
• Wire Recycling for Quantum Circuit Optimization
• Entanglement Production and Convergence Properties of the Variational Quantum Eigensolver
• Qubit-Efficient Randomized Quantum Algorithms for Linear Algebra
• The XYZ${}^2$ hexagonal stabilizer code
• Hungarian Qubit Assignment for Optimized Mapping of Quantum Circuits on Multi-Core Architectures
• CMOS Quantum Computing: Toward A Quantum Computer System-on-Chip
• A symbolic approach to discrete structural optimization using quantum annealing
• Harnessing Quantum Extreme Learning Machines for image classification
• Deterministic quantum search with adjustable parameters: implementations and applications
• Data re-uploading with a single qudit
• Memory compression and thermal efficiency of quantum implementations of non-deterministic hidden Markov models
• Multilayer ion trap with three-dimensional microwave circuitry for scalable quantum logic applications
• A quantum-inspired tensor network method for constrained combinatorial optimization problems
• A Tool For Debugging Quantum Circuits
• Quantum Hocus Pocus
• Adiabatic Quantum Kitchen Sinks for Learning Kernels Using Randomized Features
• On the expressivity of embedding quantum kernels
• Opening the Black Box Inside Grover's Algorithm
• Phase diagram of quantum generalized Potts-Hopfield neural networks
• Quantum algorithms for scientific computing
• Multiple transitions between normal and hyperballistic diffusion in quantum walks with time-dependent jumps
• Entangling power of multipartite unitary gates
• Timing constraints imposed by classical digital control systems on photonic implementations of measurement-based quantum computing
• Avoiding local minima in Variational Quantum Algorithms with Neural Networks
• Nearly optimal quantum algorithm for generating the ground state of a free quantum field theory
• Quantum State Tomography with Conditional Generative Adversarial Networks
• Complexity and efficiency of minimum entropy production probability paths from quantum dynamical evolutions
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• Experimental Quantum Computing to Solve Network DC Power Flow Problem
• As Accurate as Needed, as Efficient as Possible: Approximations in DD-based Quantum Circuit Simulation
• Scalable on-chip multiplexing of silicon single and double quantum dots
• Quantum mean centering for block-encoding-based quantum algorithm
• Independent stabilizer Rényi entropy and entanglement fluctuations in random unitary circuits
• What can we learn from quantum convolutional neural networks?
• Impact of decoherence on the fidelity of quantum gates leaving the computational subspace
• Quantum circuit compilation and hybrid computation using Pauli-based computation
• Robust inference of memory structure for efficient quantum modelling of stochastic processes
• Quantum Computing and Tensor Networks for Laminate Design: A Novel Approach to Stacking Sequence Retrieval
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• Stationary States in Quantum Walk Search
• Resource Optimized Quantum Architectures for Surface Code Implementations of Magic-State Distillation
• Quantum Algorithms for Inverse Participation Ratio Estimation in multi-qubit and multi-qudit systems
• Solving The Vehicle Routing Problem via Quantum Support Vector Machines
• Stabilizing entanglement in two-mode Gaussian states
• Quantum Computing Solution of DC Power Flow
• Quantifying the difference between many-body quantum states
• Quantum Expectation-Maximization for Gaussian Mixture Models
• Combinatorial Optimization with Quantum Computers
• Comparative study of quantum error correction strategies for the heavy-hexagonal lattice
• Nonstabilizerness dynamics in many-body localized systems
• Classification and reconstruction of optical quantum states with deep neural networks
• Experimental demonstration of a measurement-based realisation of a quantum channel
• A tensor network discriminator architecture for classification of quantum data on quantum computers
• Implementation of quantum stochastic walks for function approximation, two-dimensional data classification, and sequence classification
• Heralded entangling quantum gate via cavity-assisted photon scattering
• Full-Stack Quantum Software in Practice: Ecosystem, Stakeholders and Challenges
• Resource-aware System Architecture Model for Implementation of Quantum aided Byzantine Agreement on Quantum Repeater Networks
• Mitigating coherent leakage of superconducting qubits in a large-scale quantum socket
• Approximation of Quantum States Using Decision Diagrams
• A novel approach for quantum financial simulation and quantum state preparation
• Stochastic approach for quantum metrology with generic Hamiltonians
• Extending the reach of quantum computing for materials science with machine learning potentials
• A Photonic Parameter-shift Rule: Enabling Gradient Computation for Photonic Quantum Computers
• Programmable adiabatic demagnetization for systems with trivial and topological excitations
• Negative correlations can play a positive role in disordered quantum walks
• Numerical solution of nonlinear Schrödinger equation by a hybrid pseudospectral-variational quantum algorithm
• Noise-robust ground state energy estimates from deep quantum circuits
• Taming numerical errors in simulations of continuous variable non-Gaussian state preparation
• Quantum-walk search in motion
• Quantum error correction under numerically exact open-quantum-system dynamics
• Virtual distillation with noise dilution
• Improving the Time Stability of Superconducting Planar Resonators
• Digital quantum simulation of the BCS model with a central-spin-like quantum processor
• Integrating quantum and classical computing for multi-energy system optimization using Benders decomposition
• A quantum computing concept for 1-D elastic wave simulation with exponential speedup
• A quantum information theoretic analysis of reinforcement learning-assisted quantum architecture search
• Benchmarking Quantum Computers: Towards a Standard Performance Evaluation Approach
• A quantum procedure for map generation
• Characterization of quantum states based on creation complexity
• Fault-tolerant quantum speedup from constant depth quantum circuits
• Characterization of Broadband Purcell Filters with Compact Footprint for Fast Multiplexed Superconducting Qubit Readout
• Quantum Machine Learning and its Supremacy in High Energy Physics
• Observability of fidelity decay at the Lyapunov rate in few-qubit quantum simulations
• Demonstration of Algorithmic Quantum Speedup for an Abelian Hidden Subgroup Problem
• In the shadow of the Hadamard test: Using the garbage state for good and further modifications
• Gradient-descent methods for fast quantum state tomography
• Integrated multiplexed microwave readout of silicon quantum dots in a cryogenic CMOS chip
• Quantum error cancellation in photonic systems -- undoing photon losses
• A Quantum Search Decoder for Natural Language Processing
• Dimension reduction and redundancy removal through successive Schmidt decompositions
• Discrete-time quantum walk dispersion control through long-range correlations
• Best-approximation error for parametric quantum circuits
• Simulating thermodynamic properties of dinuclear metal complexes using Variational Quantum Algorithms
• Digital-Analog Counterdiabatic Quantum Optimization with Trapped Ions
• Quantum computing for genomics: conceptual challenges and practical perspectives
• Segmented Composite Design of Robust Single-Qubit Quantum Gates
• TeleSABRE: Layout Synthesis in Multi-Core Quantum Systems with Teleport Interconnect
• Measurement based 2-qubit unitary gates for pairs of Nitrogen-Vacancy centers in diamond
• Biased Random Access Codes
• Hermitian-preserving ansatz and variational open quantum eigensolver
• Universal Translationally-Invariant Hamiltonians
• A Generalization of Bernstein-Vazirani Algorithm to Qudit Systems
• Software Architecture Challenges in Integrating Hybrid Classical-Quantum Systems
• Hybrid Quantum Neural Networks with Variational Quantum Regressor for Enhancing QSPR Modeling of CO2-Capturing Amine
• Rigorous noise reduction with quantum autoencoders
• Quantum Circuit Distillation and Compression
• Methods for Classically Simulating Noisy Networked Quantum Architectures
• Modular quantum signal processing in many variables
• Succinct quantum testers for closeness and $k$-wise uniformity of probability distributions
• Continuous dynamical decoupling and decoherence-free subspaces for qubits with tunable interaction
• Ion trap with gold-plated alumina: substrate and surface characterization
• A Generalized Circuit for the Hamiltonian Dynamics Through the Truncated Series
• Distributed quantum error correction based on hyperbolic Floquet codes
• Quantum Feasibility Labeling for NP-complete Vertex Coloring Problem
• Quantum Algorithm Cards: Streamlining the development of hybrid classical-quantum applications
• Out of the Loop: Structural Approximation of Optimisation Landscapes and non-Iterative Quantum Optimisation
• Spectral Gap Optimization for Enhanced Adiabatic State Preparation
• Optimized numerical gradient and Hessian estimation for variational quantum algorithms
• Quantum Decomposition Algorithm For Master Equations of Stochastic Processes: The Damped Spin Case
• High-Density Qubit Wiring: Pin-Chip Bonding for Fully Vertical Interconnects
• Cosine series quantum sampling method with applications in signal and image processing
• Topics in Quantum Networking
• Proximal quantum control of spin and spin ensemble with highly localized control field from skyrmions
• Quantum computation of nonlinear maps
• Dissipative learning of a quantum classifier
• Investigation of the spin dynamics of quantum spin dimers with Dzyaloshinsky-Moriya interaction
• On the Effects of Small Graph Perturbations in the MaxCut Problem by QAOA
• A quantum algorithm for linear autonomous differential equations via Padé approximation
• Integer Programming Using A Single Atom
• An Efficient Decomposition of the Carleman Linearized Burgers' Equation
• Quantum Software Ecosystem Design
• Low Depth Virtual Distillation of Quantum Circuits by Deterministic Circuit Decomposition
• Derandomization of quantum algorithm for triangle finding
• Distributed Realization of Color Codes for Quantum Error Correction
• Realizing Quantum Algorithms on Real Quantum Computing Devices
• An Energy Estimation Benchmark for Quantum Computers
• Passive verification protocol for thermal graph states
• Evolved Quantum Boltzmann Machines
• Attention-Based Deep Reinforcement Learning for Qubit Allocation in Modular Quantum Architectures
• Quantum Interference in Atomic Systems
• Exposing the hidden layers and interplay in the quantum software stack
• Computability and Complexity of Unconventional Computing Devices
• Energy-saving fast-forward scaling
• Thermal masses and trapped-ion quantum spin models: a self-consistent approach to Yukawa-type interactions in the $\lambda {\varphi }^4$ model
• Spectral stabilizability
• Generative flow-based warm start of the variational quantum eigensolver
• Graph Neural Network-Based Predictor for Optimal Quantum Hardware Selection
• Scaling Hybrid Quantum-HPC Applications with the Quantum Framework
• QTIS: A QAOA-Based Quantum Time Interval Scheduler
• Quantum Circuit Pruning: Improving Fidelity via Compilation-Aware Circuit Approximation
• Tailoring Fault-Tolerance to Quantum Algorithms
• Robustness of optimized numerical estimation schemes for noisy variational quantum algorithms
• Quantum Learning Based Nonrandom Superimposed Coding for Secure Wireless Access in 5G URLLC
• Suppressing decoherence in quantum state transfer with unitary operations
• Finding eigenvectors with a quantum variational algorithm
• Quantum Heaviside Eigen Solver
• Evidence for effectively constant shot complexity in the quantum approximate optimization algorithm without per-instance optimization
• Optimizing the Phase Estimation Algorithm Applied to the Quantum Simulation of Heisenberg-Type Hamiltonians
• Optimizing Compilation for Distributed Quantum Computing via Clustering and Annealing
• Quantum Pattern Recognition in Photonic Circuits
• Influence of errors on the transport of quantum information through distant quantum dot spin qubits
• Affect of Simulated Atmospheric Turbulence on Three Entangled Photons
• United Nation Security Council in Quantum World: Experimental Realization of Quantum Anonymous Veto Protocols using IBM Quantum Computer
• Reshaping quantum device noise via repetition code circuits
• Application of graph theory in quantum computer science
• Quantum State Tomography as a Bilevel Problem, Utilizing I-Q Plane Data
• Inference of maximum parsimony phylogenetic trees with model-based classical and quantum methods
• Dimensional Expressivity Analysis, best-approximation errors, and automated design of parametric quantum circuits
• Interference Effect of Beam Splitter Current in Iron-Pnictide Superconductors
• Considering Decoherence Errors in the Simulation of Quantum Circuits Using Decision Diagrams
• Oracle problems as communication tasks and optimization of quantum algorithms
• Power of photonic states: from quantum computation to cosmology
• Qrisp Implementation and Resource Analysis of a T-Count-Optimised Non-Restoring Quantum Square-Root Circuit
• Quantum Algorithms in Cybernetics
• When to Build Quantum Software?
• OSC-Qasm: Interfacing Music Software with Quantum Computing
• Modular quantum computing and quantum-like devices
• Quantum Computation
• Circuit connectivity boosts by quantum-classical-quantum interfaces
• Resilience-Runtime Tradeoff Relations for Quantum Algorithms
• Flying Unicorn: Developing a Game for a Quantum Computer
• Hybrid quantum recurrent neural network for remaining useful life prediction of turbofan engines
• From Information Theory Puzzles in Deletion Channels to Deniability in Quantum Cryptography
• Unitary-transformed projective squeezing: applications for circuit-knitting and state-preparation of non-Gaussian states
• A Quantum Genetic Algorithm with application to Cosmological Parameters Estimation
• Limits of Clifford Disentangling in Tensor Network States
• Generalizations of Laver tables
• The Rise of Quantum Computing -- Take a BITE for Built Environment and Urban Microclimate Research
• Revisiting quantum walk advantages: A mean hitting time perspective