Simulating chemistry using quantum computers

Abstract

The difficulty of simulating quantum systems, well-known to quantum chemists, prompted the idea of quantum computation. One can avoid the steep scaling associated with the exact simulation of increasingly large quantum systems on conventional computers, by mapping the quantum system to another, more controllable one. In this review, we discuss to what extent the ideas in quantum computation, now a well-established field, have been applied to chemical problems. We describe algorithms that achieve significant advantages for the electronic-structure problem, the simulation of chemical dynamics, protein folding, and other tasks. Although theory is still ahead of experiment, we outline recent advances that have led to the first chemical calculations on small quantum information processors.

27 pages. Submitted to Ann. Rev. Phys. Chem

References in corpus (85)

• Fault-tolerant quantum computation by anyons
• Non-Abelian Anyons and Topological Quantum Computation
• Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
• Elementary gates for quantum computation
• Quantum Computing
• Quantum-enhanced measurements: beating the standard quantum limit
• Review article: Linear optical quantum computing
• Measurement-based quantum computation with cluster states
• Simulated Quantum Computation of Molecular Energies
• Quantum random walks - an introductory overview
• Optical Quantum Computing
• Demonstration of Two-Qubit Algorithms with a Superconducting Quantum Processor
• Universal computation by quantum walk
• Superconducting Circuits and Quantum Information
• A quantum algorithm providing exponential speed increase for finding eigenvalues and eigenvectors
• Towards Quantum Chemistry on a Quantum Computer
• Probing the Superfluid to Mott Insulator Transition at the Single Atom Level
• Simulation of Many-Body Fermi Systems on a Universal Quantum Computer
• Quantum simulation of the Dirac equation
• Efficient quantum algorithms for simulating sparse Hamiltonians
• Quantum Computation by Adiabatic Evolution
• Universal quantum computation using the discrete time quantum walk
• Quantum measurements and the Abelian Stabilizer Problem
• Polynomial-time quantum algorithm for the simulation of chemical dynamics
• Efficient Simulation of Quantum Systems by Quantum Computers
• Simulating Physical Phenomena by Quantum Networks
• Quantum Algorithms for Fermionic Simulations
• Quantum Metropolis Sampling
• Experimental Investigation of an Eight Qubit Unit Cell in a Superconducting Optimization Processor
• Computational Complexity of interacting electrons and fundamental limitations of Density Functional Theory
• Creating superpositions that correspond to efficiently integrable probability distributions
• Finding Exponential Product Formulas of Higher Orders
• Simple proof of equivalence between adiabatic quantum computation and the circuit model
• Sampling from the thermal quantum Gibbs state and evaluating partition functions with a quantum computer
• Optimal Quantum Measurements of Expectation Values of Observables
• The problem of equilibration and the computation of correlation functions on a quantum computer
• Consistency of the Adiabatic Theorem
• Experimental Demonstration of a Robust and Scalable Flux Qubit
• Quantum Simulations with Cold Trapped Ions
• Quantum Simulations on a Quantum Computer
• Quantum Simulations of Classical Annealing Processes
• A scalable control system for a superconducting adiabatic quantum optimization processor
• Simulations of Many-Body Quantum Systems by a Quantum Computer
• On the construction of model Hamiltonians for adiabatic quantum computation and its application to finding low energy conformations of lattice protein models
• Using Quantum Computers for Quantum Simulation
• Speed-up via Quantum Sampling
• Sufficiency Criterion for the Validity of the Adiabatic Approximation
• Preparing ground states of quantum many-body systems on a quantum computer
• Simulating quantum mechanics on a quantum computer
• Fast quantum algorithm for numerical gradient estimation
• Quantum Phase Transition of Ground-state Entanglement in a Heisenberg Spin Chain Simulated in an NMR Quantum Computer
• A scalable readout system for a superconducting adiabatic quantum optimization system
• Calculating the Thermal Rate Constant with Exponential Speed-Up on a Quantum Computer
• Quantum NP - A Survey
• First Order Quantum Phase Transition in Adiabatic Quantum Computation
• Quantum Algorithm for Obtaining the Energy Spectrum of Molecular Systems
• Polynomial-Time Simulation of Pairing Models on a Quantum Computer
• Universal simulation of Markovian quantum dynamics
• Limitations of Quantum Simulation Examined by Simulating a Pairing Hamiltonian using Nuclear Magnetic Resonance
• A Compound Josephson Junction Coupler for Flux Qubits With Minimal Crosstalk
• The quantitative condition is necessary in guaranteeing the validity of the adiabatic approximation
• Quantum simulation of the single-particle Schrodinger equation
• Adiabatic Quantum Computing for Random Satisfiability Problems
• A Quantum Approach to Classical Statistical Mechanics
• Quantum Algorithm for Molecular Properties and Geometry Optimization
• Liquid state NMR simulations of quantum many-body problems
• Training a Large Scale Classifier with the Quantum Adiabatic Algorithm
• Image recognition with an adiabatic quantum computer I. Mapping to quadratic unconstrained binary optimization
• Adiabatic Quantum Simulators
• Preparation of many-body states for quantum simulation
• Resource Requirements for Fault-Tolerant Quantum Simulation: The Transverse Ising Model Ground State
• Efficient quantum algorithm for preparing molecular-system-like states on a quantum computer
• Eigenvector Approximation Leading to Exponential Speedup of Quantum Eigenvalue Calculation
• Quantum Computing of Quantum Chaos in the Kicked Rotator Model
• Modelling chemical reactions using semiconductor quantum dots
• Adiabatic Quantum Algorithms for the NP-Complete Maximum-Weight Independent Set, Exact Cover and 3SAT Problems
• Wavefunction preparation and resampling using a quantum computer
• Scalable Superconducting Architecture for Adiabatic Quantum Computation
• Simulation of Classical Thermal States on a Quantum Computer: A Transfer Matrix Approach
• Error sensitivity of a Quantum Simulator I: a first example
• Quantum information processing using nuclear and electron magnetic resonance: review and prospects
• Quantum Networks for Generating Arbitrary Quantum States
• Observation of Co-tunneling in Pairs of Coupled Flux Qubits
• Quantum Computational Method of Finding the Ground State Energy and Expectation Values
• Quantum Adiabatic Algorithms, Small Gaps, and Different Paths

Cited by in corpus (165)

• Quantum Simulation
• The theory of variational hybrid quantum-classical algorithms
• Quantum computational chemistry
• Quantum walks: a comprehensive review
• Scalable Quantum Simulation of Molecular Energies
• Elucidating Reaction Mechanisms on Quantum Computers
• Quantum optimization using variational algorithms on near-term quantum devices
• Efficient variational quantum simulator incorporating active error minimisation
• Universal digital quantum simulation with trapped ions
• Toward the first quantum simulation with quantum speedup
• Hybrid Quantum-Classical Hierarchy for Mitigation of Decoherence and Determination of Excited States
• Quantum chemistry calculations on a trapped-ion quantum simulator
• Boson Sampling for Molecular Vibronic Spectra
• Quantum Implementation of Unitary Coupled Cluster for Simulating Molecular Electronic Structure
• Gate count estimates for performing quantum chemistry on small quantum computers
• Low Depth Quantum Simulation of Electronic Structure
• Variational quantum simulation of general processes
• From transistor to trapped-ion computers for quantum chemistry
• A case study in programming a quantum annealer for hard operational planning problems
• Quantum Simulation with Interacting Photons
• Layered architecture for quantum computing
• Adiabatic Quantum Simulation of Quantum Chemistry
• A quantum algorithm for evolving open quantum dynamics on quantum computing devices
• Hardware-efficient variational quantum algorithms for time evolution
• Quantum Simulation of Helium Hydride in a Solid-State Spin Register
• A Quantum-Quantum Metropolis Algorithm
• Simulating chemistry efficiently on fault-tolerant quantum computers
• Quantum Machine Learning for Electronic Structure Calculations
• Analog quantum chemistry simulation
• Exploiting locality in quantum computation for quantum chemistry
• Quantum algorithm for simulating the dynamics of an open quantum system
• Quantum simulator of an open quantum system using superconducting qubits: exciton transport in photosynthetic complexes
• Simulating quantum statistics with entangled photons: a continuous transition from bosons to fermions
• Quantum Computing for Molecular Biology
• Approximate Quantum Fourier Transform with $O(n\log (n))$ T gates
• Adiabatic state preparation study of methylene
• Classically optimized Hamiltonian simulation
• Simulating Quantum Materials with Digital Quantum Computers
• Quantum Analog-Digital Conversion
• Automatic spin-chain learning to explore the quantum speed limit
• Toward scalable simulations of Lattice Gauge Theories on quantum computers
• Practical approximation of single-qubit unitaries by single-qubit quantum Clifford and T circuits
• Demon-like Algorithmic Quantum Cooling and its Realization with Quantum Optics
• Quantum Chemistry Simulations of Dominant Products in Lithium-Sulfur Batteries
• Single-particle digitization strategy for quantum computation of a ${\varphi }^4$ scalar field theory
• Computational Complexity in Electronic Structure
• Quantum Fourier Transform Has Small Entanglement
• Solving Quantum Ground-State Problems with Nuclear Magnetic Resonance
• Digital Quantum Simulation of the Statistical Mechanics of a Frustrated Magnet
• Decomposition of Unitary Matrices for Finding Quantum Circuits: Application to Molecular Hamiltonians
• Quantum Hamiltonian-Based Models and the Variational Quantum Thermalizer Algorithm
• Measurement cost of metric-aware variational quantum algorithms
• Evidence of Kardar-Parisi-Zhang scaling on a digital quantum simulator
• Optimizing qubit resources for quantum chemistry simulations in second quantization on a quantum computer
• Quantum natural gradient generalised to noisy and non-unitary circuits
• Infrared-dressed entanglement of cold open-shell polar molecules for universal matchgate quantum computing
• Ordering of Trotterization: Impact on Errors in Quantum Simulation of Electronic Structure
• Introduction to Quantum Algorithms for Physics and Chemistry
• Practical adaptive quantum tomography
• Accelerated Randomized Benchmarking
• Contextuality Test of the Nonclassicality of Variational Quantum Eigensolvers
• Resolving Correlated States of Benzyne on a Quantum Computer with an Error-Mitigated Quantum Contracted Eigenvalue Solver
• Quantum Bootstrapping via Compressed Quantum Hamiltonian Learning
• Floating Point Representations in Quantum Circuit Synthesis
• Resource-Efficient Quantum Computing by Breaking Abstractions
• Relativistic quantum chemistry on quantum computers
• A Trotter-Suzuki approximation for Lie groups with applications to Hamiltonian simulation
• Quantum gates and architecture for the quantum simulation of the Fermi-Hubbard model
• Experimental simulation of quantum tunneling in small systems
• Algorithm for the solution of the Dirac equation on digital quantum computers
• Generalization of the output of variational quantum eigensolver by parameter interpolation with low-depth ansatz
• Universal Programmable Quantum Circuit Schemes to Emulate an Operator
• Fault-tolerant Operations for Universal Blind Quantum Computation
• Twist: Sound Reasoning for Purity and Entanglement in Quantum Programs
• Linear and logarithmic time compositions of quantum many-body operators
• Ab Initio Molecular Dynamics on Quantum Computers
• Local convertibility and the quantum simulation of edge states in many-body systems
• Tower: Data Structures in Quantum Superposition
• Exact quantum dynamics developments for floppy molecular systems and complexes
• Simulating Time Evolution with Fully Optimized Single-Qubit Gates on Parameterized Quantum Circuits
• A Universal Quantum Circuit Scheme For Finding Complex Eigenvalues
• Quantum simulations of one dimensional quantum systems
• Optimal Trotterization in universal quantum simulators under faulty control
• Emulating Molecular Orbitals and Electronic Dynamics with Ultracold Atoms
• Simulating Molecular Spectroscopy with Circuit Quantum Electrodynamics
• Spin-free quantum computational simulations and symmetry adapted states
• Quantum Algorithms for Quantum Chemistry based on the sparsity of the CI-matrix
• Quantum Simulation of Tunneling in Small Systems
• Simulating the Transverse Ising Model on a Quantum Computer: Error Correction with the Surface Code
• Simulating Non-Markovian Quantum Dynamics on NISQ Computers Using the Hierarchical Equations of Motion
• Spin Star as Switch for Quantum Networks
• Quantum Simulation of 2D Quantum Chemistry in Optical Lattices
• Quantum chemistry and charge transport in biomolecules with superconducting circuits
• Hardware-efficient fermionic simulation with a cavity-QED system
• Engineered Open Systems and Quantum Simulations with Atoms and Ions
• Fault-tolerant fermionic quantum computation based on color code
• Site-resolved imaging of beryllium ion crystals in a high-optical-access Penning trap with inbore optomechanics
• ScQ cloud quantum computation for generating Greenberger-Horne-Zeilinger states of up to 10 qubits
• Quantum algorithms for scientific computing
• Experimental Demonstration of Quantum Tunneling in IBM Quantum Computer
• Simulating the same physics with two distinct Hamiltonians
• Efficient Two-Electron Ansatz for Benchmarking Quantum Chemistry on a Quantum Computer
• Accurate and Efficient Quantum Computations of Molecular Properties Using Daubechies Wavelet Molecular Orbitals: A Benchmark Study against Experimental Data
• Nitrogen-Vacancy Center as Open-Quantum-System Simulator
• A unified framework of transformations based on the Jordan-Wigner transformation
• Thermodynamic Entanglement of Magnonic Condensates
• Development of Zero-Noise Extrapolated Projection Based Quantum Algorithm for Accurate Evaluation of Molecular Energetics in Noisy Quantum Devices
• Scalable Qubit Representations of Neutrino Mixing Matrices
• Discovering optimal fermion-qubit mappings through algorithmic enumeration
• Measurement-Based Time Evolution for Quantum Simulation of Fermionic Systems
• Computational complexity of time-dependent density functional theory
• Adiabatic quantum simulations with driven superconducting qubits
• Hybrid quantum variational algorithm for simulating open quantum systems with near-term devices
• Simulating open quantum dynamics on an NMR quantum processor using the Sz.-Nagy dilation algorithm
• Density functionals and Kohn-Sham potentials with minimal wavefunction preparations on a quantum computer
• Benchmarking quantum gates and circuits
• Quantum Gaussian process model of potential energy surface for a polyatomic molecule
• Incoherent quantum algorithm dynamics of an open system with near-term devices
• Physically motivated improvements of Variational Quantum Eigensolvers
• A Generic Compilation Strategy for the Unitary Coupled Cluster Ansatz
• Simulation of a Diels-Alder Reaction on a Quantum Computer
• Experimental demonstration of a measurement-based realisation of a quantum channel
• Calculating the many-body density of states on a digital quantum computer
• Fast-forwarding quantum simulation with real-time quantum Krylov subspace algorithms
• Scalable simulation of non-equilibrium quantum dynamics via classically optimised unitary circuits
• Simulating Vibrational Dynamics on Bosonic Quantum Devices
• Hybrid Quantum Machine Learning Assisted Classification of COVID-19 from Computed Tomography Scans
• More quantum chemistry with fewer qubits
• Multiple Network Alignment on Quantum Computers
• Quantum Fourier transform on photonic qubits using cavity QED
• Effects of Noise, Correlations and errors in the preparation of initial states in Quantum Simulations
• Improved precision scaling for simulating coupled quantum-classical dynamics
• Quantum kernel learning Model constructed with small data
• Quantum Simulation of Simple Many-Body Dynamics
• Quantum simulation costs for Suzuki-Trotter decomposition of quantum many-body lattice models
• Stabilization of Discrete Time-Crystaline Response on a Superconducting Quantum Computer by increasing the Interaction Range
• eQASM: An Executable Quantum Instruction Set Architecture
• Material matters in superconducting qubits
• Trotter simulation of vibrational Hamiltonians on a quantum computer
• A Generalized Circuit for the Hamiltonian Dynamics Through the Truncated Series
• Simulating spin systems with Majorana networks
• Efficient state initialization by a quantum spectral filtering algorithm
• Quantum Simulation of Pairing Hamiltonians with Nearest-Neighbor Interacting Qubits
• General, efficient, and robust Hamiltonian engineering
• The Enduring Relevance of Semiempirical Quantum Mechanics
• Resource optimization for fault-tolerant quantum computing
• Analyzing the spectral density of a perturbed analog quantum simulator using Keldysh formalism
• Simulation of the elementary evolution operator with the motional states of an ion in an anharmonic trap
• Context aware quantum simulation of a matrix stored in quantum memory
• Quantum many-body simulation of finite-temperature systems with sampling a series expansion of a quantum imaginary-time evolution
• Simulating Quantum Circuits with Tree Tensor Networks using Density-Matrix Renormalization Group Algorithm
• Calculating potential energy surfaces with quantum computers by measuring only the density along adiabatic transitions
• Quantum Machine Learning For Classical Data
• Experimental realization of local-to-global noise transition in a two-qubit optical simulator
• The quantum version of the shifted power method and its application in quadratic binary optimization
• Using Quantum Computers to Learn Physics
• Quantum Simulation of Molecular Collisions in the Time-Dependent Formulation
• Toward Witnessing Molecular Exciton Entanglement from Spectroscopy
• Hamiltonian Engineering in Quantum Spin Networks
• Molecular resonance identification in complex absorbing potentials via integrated quantum computing and high-throughput computing
• Nonadiabatic Self-Healing of Trotter Errors in Digitized Counterdiabatic Dynamics
• Distributed variational quantum computing with deterministic entanglement tuning
• Accelerating Fermionic System Simulation on Quantum Computers
• Quantum Eigenvalue Estimation for Irreducible Non-negative Matrices
• Approximating Ground and Excited State Energies on a Quantum Computer