Quantum Chemistry in the Age of Quantum Computing

Abstract

Practical challenges in simulating quantum systems on classical computers have been widely recognized in the quantum physics and quantum chemistry communities over the past century. Although many approximation methods have been introduced, the complexity of quantum mechanics remains hard to appease. The advent of quantum computation brings new pathways to navigate this challenging complexity landscape. By manipulating quantum states of matter and taking advantage of their unique features such as superposition and entanglement, quantum computers promise to efficiently deliver accurate results for many important problems in quantum chemistry such as the electronic structure of molecules. In the past two decades significant advances have been made in developing algorithms and physical hardware for quantum computing, heralding a revolution in simulation of quantum systems. This article is an overview of the algorithms and results that are relevant for quantum chemistry. The intended audience is both quantum chemists who seek to learn more about quantum computing, and quantum computing researchers who would like to explore applications in quantum chemistry.

194 pages, 13 figures, 5 tables and 404 references. Fixed formatting issues from the previous version. Comments welcome

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• Accurate and Efficient Quantum Computations of Molecular Properties Using Daubechies Wavelet Molecular Orbitals: A Benchmark Study against Experimental Data
• On-Premises Superconducting Quantum Computer for Education and Research
• Benchmarking the Variational Quantum Eigensolver through Simulation of the Ground State Energy of Prebiotic Molecules on High-Performance Computers
• Faster quantum chemistry simulations on a quantum computer with improved tensor factorization and active volume compilation
• Optimal scheduling in probabilistic imaginary-time evolution on a quantum computer
• A Perspective on Quantum Computing Applications in Quantum Chemistry using 25--100 Logical Qubits
• Fermionic correlation functions from randomized measurements in programmable atomic quantum devices
• Speeding up qubit control with bipolar single-flux-quantum pulse sequences
• Strong-Weak Duality via Jordan-Wigner Transformation: Using Fermionic Methods for Strongly Correlated $su(2)$ Spin Systems
• Complexity of Supersymmetric Systems and the Cohomology Problem
• Exponentially faster implementations of Select(H) for fermionic Hamiltonians
• Fully quantum algorithm for lattice Boltzmann methods with application to partial differential equations
• Efficient and precise quantum simulation of ultra-relativistic quark-nucleus scattering
• Noise-Resistant Quantum State Compression Readout
• Quantum Computing and Tensor Networks for Laminate Design: A Novel Approach to Stacking Sequence Retrieval
• Beyond unital noise in variational quantum algorithms: noise-induced barren plateaus and limit sets
• Digital quantum simulation of linear and nonlinear optical elements
• Subspace methods for the simulation of molecular response properties on a quantum computer
• SimuQ: A Framework for Programming Quantum Hamiltonian Simulation with Analog Compilation
• Tensor-network-assisted variational quantum algorithm
• Hybrid quantum variational algorithm for simulating open quantum systems with near-term devices
• Variational quantum iterative power algorithms for global optimization
• Quantum Gaussian process model of potential energy surface for a polyatomic molecule
• Algorithmic Shadow Spectroscopy
• On the sampling complexity of open quantum systems
• Benchmarking quantum gates and circuits
• Randomized adaptive quantum state preparation
• Computational protocol to evaluate electron-phonon interactions within density matrix perturbation theory
• Density functionals and Kohn-Sham potentials with minimal wavefunction preparations on a quantum computer
• Optimizing Variational Quantum Algorithms with qBang: Efficiently Interweaving Metric and Momentum to Navigate Flat Energy Landscapes
• Non-Unitary Quantum Machine Learning
• Molecular Dynamics on Quantum Annealers
• An Optimization Case Study for solving a Transport Robot Scheduling Problem on Quantum-Hybrid and Quantum-Inspired Hardware
• Scattering phase shifts from a quantum computer
• Robustness to spontaneous emission of a variational quantum algorithm
• Quantum-selected configuration interaction with time-evolved state
• Physically motivated improvements of Variational Quantum Eigensolvers
• Quantum simulation of colour in perturbative quantum chromodynamics
• Natural orbitals and sparsity of quantum mutual information
• Adaptive variational preparation of the Fermi-Hubbard eigenstates
• A Quantum Computing Approach for the Unit Commitment Problem
• Beyond MP2 initialization for unitary coupled cluster quantum circuits
• Optimizing Gate Decomposition for High-Level Quantum Programming
• A Quantum Computing Implementation of Nuclear-Electronic Orbital (NEO) Theory: Towards an Exact pre-Born-Oppenheimer Formulation of Molecular Quantum Systems
• Partitioning Quantum Chemistry Simulations with Clifford Circuits
• Leveraging Analog Quantum Computing with Neutral Atoms for Solvent Configuration Prediction in Drug Discovery
• Towards chemical accuracy with shallow quantum circuits: A Clifford-based Hamiltonian engineering approach
• The variational quantum eigensolver self-consistent field method within a polarizable embedded framework
• Can shallow quantum circuits scramble local noise into global white noise?
• Algorithm-Oriented Qubit Mapping for Variational Quantum Algorithms
• Fermionic Simulators for Enhanced Scalability of Variational Quantum Simulation
• Quantum state preparation for multivariate functions
• Quantum Computation of Eigenvalues within Target Intervals
• Experimental demonstration of a high-fidelity virtual two-qubit gate
• Quantum Computing for Atomic and Molecular Resonances
• Resource estimations for the Hamiltonian simulation in correlated electron materials
• Solving an Industrially Relevant Quantum Chemistry Problem on Quantum Hardware
• Data-driven discovery of statistically relevant information in quantum simulators
• Simulation of a Diels-Alder Reaction on a Quantum Computer
• Classical and quantum machine learning applications in spintronics
• Analytical formulation of the second-order derivative of energy for orbital-optimized variational quantum eigensolver: application to polarizability
• Quantum algorithms for generator coordinate methods
• State preparation of AGP on a quantum computer without number projection
• Quantum supremacy and quantum phase transitions
• Bayesian phase difference estimation algorithm for direct calculation of fine structure splitting: accelerated simulation of relativistic and quantum many-body effects
• Calculating the many-body density of states on a digital quantum computer
• Quantum Eigenvector Continuation for Chemistry Applications
• Extending the reach of quantum computing for materials science with machine learning potentials
• Hückel Molecular Orbital Theory on a Quantum Computer: A Scalable System-Agnostic Variational Implementation with Compact Encoding
• Calculation of the ground-state Stark effect in small molecules using the variational quantum eigensolver
• Near-term Efficient Quantum Algorithms for Entanglement Analysis
• Parallel Quantum Algorithm for Hamiltonian Simulation
• Variational approach to photonic quantum circuits via the parameter shift rule
• Quantum-machine-assisted Drug Discovery
• Programmable adiabatic demagnetization for systems with trivial and topological excitations
• Towards Efficient Quantum Computing for Quantum Chemistry: Reducing Circuit Complexity with Transcorrelated and Adaptive Ansatz Techniques
• Concatenation Schemes for Topological Fault-tolerant Quantum Error Correction
• Hubbard physics with Rydberg atoms: using a quantum spin simulator to simulate strong fermionic correlations
• Scalable simulation of non-equilibrium quantum dynamics via classically optimised unitary circuits
• Engineering analog quantum chemistry Hamiltonians using cold atoms in optical lattices
• Error-tolerant quantum convolutional neural networks for symmetry-protected topological phases
• TFermion: A non-Clifford gate cost assessment library of quantum phase estimation algorithms for quantum chemistry
• Distributed Quantum Computing for Chemical Applications
• Workflow for practical quantum chemical calculations with quantum phase estimation algorithm: electronic ground and π-π* excited states of benzene and its derivatives†
• Virtual distillation with noise dilution
• Quantum annealing approach to Ionic Diffusion in Solid
• Mapping renormalized coupled cluster methods to quantum computers through a compact unitary representation of non-unitary operators
• Noise-robust ground state energy estimates from deep quantum circuits
• Application of the Diamond Gate in Quantum Fourier Transformations and Quantum Machine Learning
• Optimizing the Electrical Interface for Large-Scale Color-Center Quantum Processors
• Simulating time evolution on distributed quantum computers
• Exponentially improved efficient machine learning for quantum many-body states with provable guarantees
• More quantum chemistry with fewer qubits
• Cutting a Wire with Non-Maximally Entangled States
• Hamiltonian learning from time dynamics using variational algorithms
• Expressive Quantum Supervised Machine Learning using Kerr-nonlinear Parametric Oscillators
• Characterization of quantum states based on creation complexity
• Ultrafast Hybrid Fermion-to-Qubit mapping
• Classical Pre-optimization Approach for ADAPT-VQE: Maximizing the Potential of High-Performance Computing Resources to Improve Quantum Simulation of Chemical Applications
• Calculation of core-excited and core-ionized states using variational quantum deflation method and applications to photocatalyst modelling
• Variational quantum computing for quantum simulation: principles, implementations, and challenges
• Classical simulation of boson sampling with sparse output
• Efficient Strategies for Reducing Sampling Error in Quantum Krylov Subspace Diagonalization
• Tensor-based quantum phase difference estimation for large-scale demonstration
• Parameterized Two-Qubit Gates for Enhanced Variational Quantum Eigensolver
• Understanding polaritonic chemistry from ab initio quantum electrodynamics
• A full circuit-based quantum algorithm for excited-states in quantum chemistry
• Hybrid Quantum Machine Learning Assisted Classification of COVID-19 from Computed Tomography Scans
• Asymmetric quantum multicast network coding: asymmetric optimal cloning over quantum networks
• The Coming Decades of Quantum Simulation
• Gradients and frequency profiles of quantum re-uploading models
• Calculating the energy profile of an enzymatic reaction on a quantum computer
• A multiple-circuit approach to quantum resource reduction with application to the quantum lattice Boltzmann method
• A Quantum Simulation Approach to Implementing Nuclear Density Functional Theory via Imaginary Time Evolution
• Shortcut to Chemically Accurate Quantum Computing via Density-based Basis-set Correction
• A Comprehensive Cross-Model Framework for Benchmarking the Performance of Quantum Hamiltonian Simulations
• Unleashed from Constrained Optimization: Quantum Computing for Quantum Chemistry Employing Generator Coordinate Inspired Method
• Projective Quantum Phase Difference Estimation Algorithm for the Direct Computation of Eigenenergy Gaps on a Quantum Computer
• Measuring Trotter error and its application to precision-guaranteed Hamiltonian simulations
• Simulation of a feedback-based algorithm for quantum optimization for a realistic neutral atom system with an optimized small-angle controlled-phase gate
• Coupled cluster method tailored with quantum computing
• On connectivity-dependent resource requirements for digital quantum simulation of $d$-level particles
• QUBO.jl: A Julia Ecosystem for Quadratic Unconstrained Binary Optimization
• Quantum computational study of chloride ion attack on chloromethane for chemical accuracy and quantum noise effects with UCCSD and k-UpCCGSD ansatzes
• Riemannian quantum circuit optimization based on matrix product operators
• Greedy Gradient-free Adaptive Variational Quantum Algorithms on a Noisy Intermediate Scale Quantum Computer
• Stabilization of Discrete Time-Crystaline Response on a Superconducting Quantum Computer by increasing the Interaction Range
• A Classically Efficient Quantum Scalable Fermi-Hubbard Benchmark
• Flexibility of the factorized form of the unitary coupled cluster ansatz
• Quantum random access memory with transmon-controlled phonon routing
• A Study on Quantum Graph Neural Networks Applied to Molecular Physics
• Efficient ground-state energy estimation and certification on early fault-tolerant quantum computers
• Direct pulse-level compilation of arbitrary quantum logic gates on superconducting qutrits
• Lattice Hamiltonians and Stray Interactions Within Quantum Processors
• Characterizing conical intersections of nucleobases on quantum computers
• Cryogenic Optical-to-Microwave Conversion Using Si Photonic Integrated Circuit Ge Photodiodes
• Quantum computing for genomics: conceptual challenges and practical perspectives
• Quantum simulation costs for Suzuki-Trotter decomposition of quantum many-body lattice models
• Size-consistency and orbital-invariance issues revealed by VQE-UCCSD calculations with the FMO scheme
• Parameterization and optimizability of pulse-level VQEs
• Roadmap for quantum simulation of the fractional quantum Hall effect
• Routing in Quantum Networks with End-to-End Knowledge
• SHARC-VQE: Simplified Hamiltonian Approach with Refinement and Correction enabled Variational Quantum Eigensolver for Molecular Simulation
• Red-QAOA: Efficient Variational Optimization through Circuit Reduction
• Optimization of the Variational Quantum Eigensolver for Quantum Chemistry Applications
• Error mitigation, optimization, and extrapolation on a trapped ion testbed
• Optimization strategies in WAHTOR algorithm for quantum computing empirical ansatz: a comparative study
• Experimental implementation of arbitrary entangled operations
• Digital Quantum Simulation and Circuit Learning for the Generation of Coherent States
• Symmetric Trotterization in digital quantum simulation of quantum spin dynamics
• Comparison of encoding schemes for quantum computing of $S>1/2$ spin chains
• Quantum Algorithm for Vibronic Dynamics: Case Study on Singlet Fission Solar Cell Design
• Exploring Ground States of Fermi-Hubbard Model on Honeycomb Lattices with Counterdiabaticity
• Matrix product state ansatz for the variational quantum solution of the Heisenberg model on Kagome geometries
• Accurate harmonic vibrational frequencies for diatomic molecules via quantum computing
• QSlack: A slack-variable approach for variational quantum semi-definite programming
• Mitigating Quantum Gate Errors for Variational Eigensolvers Using Hardware-Inspired Zero-Noise Extrapolation
• Differentiable matrix product states for simulating variational quantum computational chemistry
• Quantum computing quantum Monte Carlo algorithm
• Near-term quantum algorithm for computing molecular and materials properties based on recursive variational series methods
• Improved resource-tunable near-term quantum algorithms for transition probabilities, with applications in physics and variational quantum linear algebra
• Calculation of Gibbs partition function with imaginary time evolution on near-term quantum computers
• Quantum algorithm for calculation of transition amplitudes in hybrid tensor networks
• Deep variational quantum eigensolver for excited states and its application to quantum chemistry calculation of periodic materials
• Hamiltonian-based graph-state ansatz for variational quantum algorithms
• Refining resource estimation for the quantum computation of vibrational molecular spectra through Trotter error analysis
• From Heisenberg to Hubbard: An initial state for the shallow quantum simulation of correlated electrons
• Quantum Computing in Pharma: A Multilayer Embedding Approach for Near Future Applications
• Resonance triplet dynamics in the quenched unitary Bose gas
• Comparing planar quantum computing platforms at the quantum speed limit
• Non-Iterative Disentangled Unitary Coupled-Cluster based on Lie-algebraic structure
• Quantum Zeno approach for molecular energies with maximum commuting initialHamiltonians
• Practical techniques for high-precision measurements on near-term quantum hardware and applications in molecular energy estimation
• A quantum random access memory (QRAM) using a polynomial encoding of binary strings
• The Role of Quantum Computing in Advancing Scientific High-Performance Computing: A perspective from the ADAC Institute
• A comparison of three ways to measure time-dependent densities with quantum simulators
• Demonstration of Hardware Efficient Photonic Variational Quantum Algorithm
• Multireference error mitigation for quantum computation of chemistry
• Quantum-assisted variational Monte Carlo
• Composable Programming of Hybrid Workflows for Quantum Simulation
• Ladder Operator Block-Encoding
• Sequence of penalties method to study excited states using VQE
• Large-scale Efficient Molecule Geometry Optimization with Hybrid Quantum-Classical Computing
• qlbm -- A Quantum Lattice Boltzmann Software Framework
• Hardware-efficient quantum phase estimation via local control
• Continuous monitoring for noisy intermediate-scale quantum processors
• Optimized numerical gradient and Hessian estimation for variational quantum algorithms
• Quantum Reservoir Computing for Realized Volatility Forecasting
• Stable many-body resonances in open quantum systems
• Full-Dimensional Schrödinger Wavefunction Calculations using Tensors and Quantum Computers: the Cartesian component-separated approach
• Quantum variational solving of the Wheeler-DeWitt equation
• Ultra-Fast All-Electrical Universal Nano-Qubits
• Simulating polaritonic ground states on noisy quantum devices
• Constructing Local Bases for a Deep Variational Quantum Eigensolver for Molecular Systems
• Systematic many-fermion Hamiltonian input scheme and spectral calculations on quantum computers
• Multiqubit state learning with entangling quantum generative adversarial networks
• Sparse-Hamiltonian approach to the time evolution of molecules on quantum computers
• Sampling Electronic Fock States using Determinant Quantum Monte Carlo
• Compact Multi-Threshold Quantum Information Driven Ansatz For Strongly Interactive Lattice Spin Models
• Harnessing Quantum Computing for Energy Materials: Opportunities and Challenges
• Demonstration of a variational quantum eigensolver with a solid-state spin system under ambient conditions
• Quantum many-body simulation of finite-temperature systems with sampling a series expansion of a quantum imaginary-time evolution
• Simulating quantum field theories on gate-based quantum computers
• Tight Quantum Depth Lower Bound for Solving Systems of Linear Equations
• QSteed: A Resource-Virtualized and Hardware-Aware Quantum Compilation Framework for Real Quantum Computing Processors
• Measuring Correlation and Entanglement between Molecular Orbitals on a Trapped-Ion Quantum Computer
• Simulating the Fermi-Hubbard model with long-range hopping on a quantum computer
• Limitations of Quantum Hardware for Molecular Energy Estimation Using VQE
• Almost optimal measurement scheduling of molecular Hamiltonian via finite projective plane
• Quantum Computing Beyond Ground State Electronic Structure: A Review of Progress Toward Quantum Chemistry Out of the Ground State
• Solving the Hubbard model using density matrix embedding theory and the variational quantum eigensolver
• Multi-set variational quantum dynamics algorithm for simulating nonadiabatic dynamics on quantum computers
• Coupled-cluster pairing models for radicals with strong correlations
• Quantum-computing within a bosonic context: Assessing finite basis effects on prototypical vibrational Hamiltonian spectra
• Exponential distillation of dominant eigenproperties
• Modeling Non-Covalent Interatomic Interactions on a Photonic Quantum Computer
• Practical limitations of quantum data propagation on noisy quantum processors
• Quantum Simulation of Molecular Dynamics Processes -- A Benchmark Study Using Classical Simulator and Present-Day Quantum Hardware
• Automated detection of symmetry-protected subspaces in quantum simulations
• Density matrix representation of hybrid tensor networks for noisy quantum devices
• Simulating methylamine using symmetry adapted qubit-excitation-based variational quantum eigensolver
• Scalable Quantum Computational Science: A Perspective from Block-Encodings and Polynomial Transformations
• An Energy Estimation Benchmark for Quantum Computers
• Escaping Local Minima with Quantum Coherent Cooling
• Compressed sensing enhanced by quantum approximate optimization algorithm
• Orbital Expansion Variational Quantum Eigensolver: Enabling Efficient Simulation of Molecules with Shallow Quantum Circuit
• Quantum algorithms for optimal effective theory of many-body systems
• A Synthesis of Hidden Subgroup Quantum Algorithms and Quantum Chemical Dynamics
• Averaging gate approximation error and performance of Unitary Coupled Cluster ansatz in Pre-FTQC Era
• Calculating potential energy surfaces with quantum computers by measuring only the density along adiabatic transitions
• Robustness of optimized numerical estimation schemes for noisy variational quantum algorithms
• Arbitrary Ground State Observables from Quantum Computed Moments
• Solving coupled Non-linear Schrödinger Equations via Quantum Imaginary Time Evolution
• Batched Line Search Strategy for Navigating through Barren Plateaus in Quantum Circuit Training
• On the Hardness of Measuring Magic
• Resource-efficient quantum algorithm for linear systems of equations
• A coherent approach to quantum-classical optimization
• Refined Criteria for QRAM Error Suppression via Efficient Large-Scale QRAM Simulator
• Blockwise Optimization for Projective Variational Quantum Dynamics (BLOP-VQD): Algorithm and Implementation for Lattice Systems
• Parallelized Givens Ansatz for Molecular ground-states: Bridging Accuracy and Efficiency on NISQ Platforms
• Adiabatic state preparation from general initial states
• Rovibrational energy levels of H${}_2$O by quantum computing
• Benchmarking of quantum fidelity kernels for Gaussian process regression
• Best-practice aspects of quantum-computer calculations: A case study of hydrogen molecule
• Scalable Simulation of Fermionic Encoding Performance on Noisy Quantum Computers
• Comment on arXiv:2307.08384 "Efficient Quantum State Preparation with Walsh Series"
• Optimizing Sparse SYK
• Learning Variational Quantum Circuit Parameters with Classical Artificial Intelligence for Quantum Phase Transition Detection
• Towards defending crosstalk-mediated attacks in multi-tenant quantum computing
• Accelerated spin-adapted ground state preparation with non-variational quantum algorithms
• Quantum-Classical Computing for Time-Dependent Ion-Atom Collision Dynamics: Applications to Charge Transfer Cross Section Simulations
• Energy Spectra of Compressed Quantum States
• Hamiltonian Expressibility for Ansatz Selection in Variational Quantum Algorithms
• Shot-Efficient ADAPT-VQE via Reused Pauli Measurements and Variance-Based Shot Allocation
• Entanglement swapping for partially entangled qudits and the role of quantum complementarity
• Hybrid Quantum-Classical Clustering for Preparing a Prior Distribution of Eigenspectrum
• The Quantum Ensemble Variational Optimization Algorithm: Applications to Molecular Inverse Design
• Power and limitations of distributed quantum state purification
• Noise-resilient and resource-efficient hybrid algorithm for robust quantum gap estimation
• Numerical investigation of the quantum inverse algorithm on small molecules
• Analog quantum simulation of non-Condon effects in molecular spectroscopy
• Molecular resonance identification in complex absorbing potentials via integrated quantum computing and high-throughput computing
• Improving shadow estimation with locally-optimal dual frames
• Evolutionary reduction of the laser noise impact on quantum gates
• Resource Estimation for VQE on Small Molecules: Impact of Fermion Mappings and Hamiltonian Reductions
• Size-Consistent Quantum Chemistry on Quantum Computers
• Topology-Aware Block Coordinate Descent for Qubit Frequency Allocation of Superconducting Quantum Processors
• Quantum phase estimation with optimal confidence interval using three control qubits
• QuaSiMo: A Composable Library to Program Hybrid Workflows for Quantum Simulation
• Quantum State Preparation and Non-Unitary Evolution with Diagonal Operators
• Resource-efficient Quantum Algorithms for Selected Hamiltonian Subspace Diagonalization
• Distributed variational quantum computing with deterministic entanglement tuning
• Velocity Verlet-based optimization for variational quantum eigensolvers
• IBM quantum platforms: a quantum battery perspective
• Toward Density Functional Theory on Quantum Computers?
• Extension of the Jordan-Wigner mapping to nonorthogonal spin orbitals for quantum computing application to valence bond approaches
• Perturbational Decomposition Analysis for Quantum Ising Model with Weak Transverse Fields
• Non-destructively probing the thermodynamics of quantum systems with qumodes
• Improving the performance of fermionic neural networks with the Slater exponential Ansatz
• The Effect of Noise on the Performance of Variational Algorithms for Quantum Chemistry
• Spin vs. position conjugation in quantum simulations with atoms: application to quantum chemistry
• iSwitch: QEC on Demand via In-Situ Encoding of Bare Qubits for Ion Trap Architectures
• Fast-forwardability of Qubit-mapped Fermion models based on Cartan decomposition
• Matrix Product State on a Quantum Computer