Simulated Quantum Computation of Molecular Energies

Abstract

The calculation time for the energy of atoms and molecules scales exponentially with system size on a classical computer but polynomially using quantum algorithms. We demonstrate that such algorithms can be applied to problems of chemical interest using modest numbers of quantum bits. Calculations of the water and lithium hydride molecular ground-state energies have been carried out on a quantum computer simulator using a recursive phase-estimation algorithm. The recursive algorithm reduces the number of quantum bits required for the readout register from about 20 to 4. Mappings of the molecular wave function to the quantum bits are described. An adiabatic method for the preparation of a good approximate ground-state wave function is described and demonstrated for a stretched hydrogen molecule. The number of quantum bits required scales linearly with the number of basis functions, and the number of gates required grows polynomially with the number of quantum bits.

20 pages, 3 figures

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• Engineering analog quantum chemistry Hamiltonians using cold atoms in optical lattices
• TFermion: A non-Clifford gate cost assessment library of quantum phase estimation algorithms for quantum chemistry
• Novel Trotter formulas for digital quantum simulation
• Scalable simulation of non-equilibrium quantum dynamics via classically optimised unitary circuits
• Expressive Quantum Supervised Machine Learning using Kerr-nonlinear Parametric Oscillators
• Cooper quartets in interacting hybrid superconducting systems
• Variational quantum computing for quantum simulation: principles, implementations, and challenges
• Message passing in fault tolerant quantum error correction
• Why should we care about quantum discord?
• Generalising quantum imaginary time evolution to solve linear partial differential equations
• Accelerating quantum imaginary-time evolution with random measurements
• Multiple Network Alignment on Quantum Computers
• Digital quantum simulation of the BCS model with a central-spin-like quantum processor
• Error estimation in current noisy quantum computers
• Efficient variational quantum circuit structure for correlated topological phases
• Implementation of a Quantum Algorithm to Estimate the Energy of a Particle in a Finite Square Well Potential on IBM Quantum Computer
• Statistical Approach to Quantum Phase Estimation
• An Iterative Method to Improve the Precision of Quantum Phase Estimation Algorithm
• Quantum simulation from the bottom up: the case of rebits
• Calculation of core-excited and core-ionized states using variational quantum deflation method and applications to photocatalyst modelling
• Non-adiabatic Quantum Wavepacket Dynamics Simulation Based on Electronic Structure Calculations using the Variational Quantum Eigensolver
• Classical Pre-optimization Approach for ADAPT-VQE: Maximizing the Potential of High-Performance Computing Resources to Improve Quantum Simulation of Chemical Applications
• Hybrid quantum-classical unsupervised data clustering based on the self-organizing feature map
• Coupled cluster method tailored with quantum computing
• Quantum algorithm for spectral projection by measuring an ancilla iteratively
• Shortcut to Chemically Accurate Quantum Computing via Density-based Basis-set Correction
• Quantum Information reveals that orbital-wise correlation is essentially classical in Natural Orbitals
• Quantum Computation of Electronic Structure with Projector Augmented-Wave Method and Plane Wave Basis Set
• The quest and hope of Majorana zero modes in topological superconductor for fault-tolerant quantum computing: an introductory overview
• A Hybrid Qubit Encoding: Splitting Fock Space into Fermionic and Bosonic Subspaces
• Practicality of quantum adiabatic algorithm for chemistry applications
• Fermionic Adaptive Sampling Theory for Variational Quantum Eigensolvers
• Quantum technologies for climate change: Preliminary assessment
• Simulated Quantum Computation of Global Minima
• Measuring Trotter error and its application to precision-guaranteed Hamiltonian simulations
• Projective Quantum Phase Difference Estimation Algorithm for the Direct Computation of Eigenenergy Gaps on a Quantum Computer
• Exploiting anticommutation in Hamiltonian simulation
• Quantum autoencoders using mixed reference states
• Robust Preparation of Many-body Ground States in Jaynes-Cummings Lattices
• SHARC-VQE: Simplified Hamiltonian Approach with Refinement and Correction enabled Variational Quantum Eigensolver for Molecular Simulation
• Ab initio extended Hubbard model of short polyenes for efficient quantum computing
• Size-consistency and orbital-invariance issues revealed by VQE-UCCSD calculations with the FMO scheme
• Exploring Many-body Interactions Through Quantum Fisher Information
• Adaptive variational ground state preparation for spin-1 models on qubit-based architectures
• First-quantized adiabatic time evolution for the ground state of a many-electron system and the optimal nuclear configuration
• Demonstrating Quantum Computation for Quasiparticle Band Structures
• Error mitigation, optimization, and extrapolation on a trapped ion testbed
• Greedy Gradient-free Adaptive Variational Quantum Algorithms on a Noisy Intermediate Scale Quantum Computer
• Adiabatic time evolution of highly excited states
• Efficient ground-state energy estimation and certification on early fault-tolerant quantum computers
• Determination of Molecular Energies via Quantum Imaginary Time Evolution in a Superconducting Qubit System
• Routing in Quantum Networks with End-to-End Knowledge
• Variational Phase Estimation with Variational Fast Forwarding
• Adaptive variational quantum dynamics simulations with compressed circuits and fewer measurements
• Quantum computational study of chloride ion attack on chloromethane for chemical accuracy and quantum noise effects with UCCSD and k-UpCCGSD ansatzes
• Toward a quantum computing algorithm to quantify classical and quantum correlation of system states
• ChemiQ: A Chemistry Simulator for Quantum Computer
• Characterizing conical intersections of nucleobases on quantum computers
• MISTIQS: An open-source software for performing quantum dynamics simulations on quantum computers
• Efficient Bayesian phase estimation using mixed priors
• Roadmap for quantum simulation of the fractional quantum Hall effect
• Digital-analog quantum genetic algorithm using Rydberg-atom arrays
• Quantum Emulation of Molecular Force Fields: A Blueprint for a Superconducting Architecture
• Quantum Simulation of Simple Many-Body Dynamics
• Trotterization is substantially efficient for low-energy states
• A Quantum Algorithm for Dynamic Mode Decomposition Integrated with a Quantum Differential Equation Solver
• Leveraging Zero-Level Distillation to Generate High-Fidelity Magic States
• Estimating molecular thermal averages with the quantum equation of motion and informationally complete measurements
• One-dimensional quantum walks driven by two-entangled-qubit coins
• Critical Limitations in Quantum-Selected Configuration Interaction Methods
• Quantum computing of the pairing Hamiltonian at finite temperatures
• Quantum computing quantum Monte Carlo algorithm
• Kernel-Function Based Quantum Algorithms for Finite Temperature Quantum Simulation
• Shallow quantum circuits for efficient preparation of Slater determinants and correlated states on a quantum computer
• A quantum Monte Carlo algorithm for arbitrary spin-1/2 Hamiltonians
• A Full Quantum Eigensolver for Quantum Chemistry Simulations
• ArsoNISQ: Analyzing Quantum Algorithms on Near-Term Architectures
• Geometric quantum adiabatic methods for quantum chemistry
• Non-Iterative Disentangled Unitary Coupled-Cluster based on Lie-algebraic structure
• Composable Programming of Hybrid Workflows for Quantum Simulation
• Decomposition of high-rank factorized unitary coupled-cluster operators using ancilla and multi-qubit controlled low-rank counterparts
• Refining resource estimation for the quantum computation of vibrational molecular spectra through Trotter error analysis
• Synchronization for Fault-Tolerant Quantum Computers
• Encoded probabilistic imaginary-time evolution on a trapped-ion quantum computer for ground and excited states of spin qubits
• Practical sampling schemes for quantum phase estimation
• Multireference error mitigation for quantum computation of chemistry
• Quantum Circuit Distillation and Compression
• Large-scale Efficient Molecule Geometry Optimization with Hybrid Quantum-Classical Computing
• Decoherence and Quantum Error Correction for Quantum Computing and Communications
• Efficient Quantum Cooling Algorithm for Fermionic Systems
• A Partially Random Trotter Algorithm for Quantum Hamiltonian Simulations
• Ladder Operator Block-Encoding
• Efficient state initialization by a quantum spectral filtering algorithm
• Quantum Zeno approach for molecular energies with maximum commuting initialHamiltonians
• Computing Electronic Correlation Energies using Linear Depth Quantum Circuits
• Inverse iteration quantum eigensolvers assisted with a continuous variable
• Self-consistent Quantum Linear Response with a Polarizable Embedding environment
• Simulation of the elementary evolution operator with the motional states of an ion in an anharmonic trap
• Efficient application of the factorized form of the unitary coupled-cluster ansatz for the variational quantum eigensolver algorithm by using linear combination of unitaries
• Quantum computing hardware in the cloud: Should a computational chemist care?
• Efficient explicit circuit for quantum state preparation of piecewise continuous functions
• Quantum computation of a quasiparticle band structure with the quantum-selected configuration interaction
• Comparative study on compact quantum circuits of hybrid quantum-classical algorithms for quantum impurity models
• Efficient Quantum Simulation of Non-Adiabatic Molecular Dynamics with Precise Electronic Structure
• Quantum Phase Estimation Algorithm for Finding Polynomial Roots
• Optimizing Electronic Structure Simulations on a Trapped-ion Quantum Computer using Problem Decomposition
• Heisenberg-limited adaptive gradient estimation for multiple observables
• Leveraging commuting groups for an efficient variational Hamiltonian ansatz
• Equation-of-motion internally contracted multireference unitary coupled-cluster theory
• Simulating polaritonic ground states on noisy quantum devices
• Parent Hamiltonian as a benchmark problem for variational quantum eigensolvers
• Stable many-body resonances in open quantum systems
• Improved performance of the Bacon-Shor code with Steane's syndrome extraction method
• Gauged cooling of topological excitations and emergent fermions on quantum simulators
• Quantum Technology for Military Applications
• Quantum nuclear dynamics on a distributed set of ion-trap quantum computing systems
• Quantum simulation and ground state preparation for the honeycomb Kitaev model
• Full-Dimensional Schrödinger Wavefunction Calculations using Tensors and Quantum Computers: the Cartesian component-separated approach
• Basis set generation and optimization in the NISQ era with Quiqbox.jl
• Simple digital quantum algorithm for symmetric first order linear hyperbolic systems
• Development of research network on Quantum Annealing Computation and Information using Google Scholar data
• Coherence as a resource for phase estimation
• Stabilizer configuration interaction: Finding molecular subspaces with error detection properties
• Quantum Simulation of Molecules without Fermionic Encoding of the Wave Function
• State Specific Measurement Protocols for the Variational Quantum Eigensolver
• A measurement driven analog of adiabatic quantum computation for frustration-free Hamiltonians
• Fault-tolerant quantum simulation of generalized Hubbard models
• Classically-Boosted Variational Quantum Eigensolver
• Discontinuous Galerkin discretization for quantum simulation of chemistry
• Chemically Motivated Simulation Problems are Efficiently Solvable by a Quantum Computer
• Coupled-cluster pairing models for radicals with strong correlations
• Practical Quantum Computing: The value of local computation
• On the Trotter Error in Many-body Quantum Dynamics with Coulomb Potentials
• Topics in Estimation of Quantum Channels
• Faster Algorithmic Quantum and Classical Simulations by Corrected Product Formulas
• Photonic variational quantum eigensolver for NISQ-compatible quantum technology
• Quantum state preparation via piecewise QSVT
• Accelerating quantum adiabatic evolution with $\pi$-pulse sequences
• Limitations of Quantum Hardware for Molecular Energy Estimation Using VQE
• The impacts of optimization algorithm and basis size on the accuracy and efficiency of variational quantum eigensolver
• Does the full configuration interaction method based on quantum phase estimation with Trotter decomposition satisfy the size consistency condition?
• Error Analysis of the Variational Quantum Eigensolver Algorithm
• Quantum circuit and mapping algorithms for wavepacket dynamics: case study of anharmonic hydrogen bonds in protonated and hydroxide water clusters
• Quantum-inspired dynamical models on quantum and classical annealers
• Adiabatic state preparation from general initial states
• Spin-Boson Model to Demonstrate Quantum Tunneling in Biomolecules using IBM Quantum Computer
• Towards Practical Quantum Phase Estimation: A Modular, Scalable, and Adaptive Approach
• Rovibrational energy levels of H${}_2$O by quantum computing
• Quantum-Classical Auxiliary Field Quantum Monte Carlo with Matchgate Shadows on Trapped Ion Quantum Computers
• Efficient Berry Phase Calculation via Adaptive Variational Quantum Computing Approach
• Adaptive random compiler for Hamiltonian simulation
• Weighted Approximate Quantum Natural Gradient for Variational Quantum Eigensolver
• Parallelized Givens Ansatz for Molecular ground-states: Bridging Accuracy and Efficiency on NISQ Platforms
• Hardware-efficient quantum annealing with error mitigation via classical shadow
• Blockwise Optimization for Projective Variational Quantum Dynamics (BLOP-VQD): Algorithm and Implementation for Lattice Systems
• Quantum Simulations of Chemical Reactions: Achieving Accuracy with NISQ Devices
• Hidden $sl(2)-$Symmetry of the Generalized Landau-Zener Vibronic Model
• Qubit coupled cluster singles and doubles variational quantum eigensolver ansatz for electronic structure calculations
• Dissipative ground state preparation in ab initio electronic structure theory
• State preparation and evolution in quantum computing: a perspective from Hamiltonian moments
• Excited state calculations using variational quantum eigensolver with spin-restricted ansätze and automatically-adjusted constraints
• Two-dimensional quantum central limit theorem by quantum walks
• Linear-optical generation of eigenstates of the two-site XY model
• A Synthesis of Hidden Subgroup Quantum Algorithms and Quantum Chemical Dynamics
• Feasibility of performing quantum chemistry calculations on quantum computers
• Enhancing Scalability of Quantum Eigenvalue Transformation of Unitary Matrices for Ground State Preparation through Adaptive Finer Filtering
• Error Crafting in Mixed Quantum Gate Synthesis
• Variational Quantum Subspace Construction via Symmetry-Preserving Cost Functions
• Quantum Eigenvalue Estimation for Irreducible Non-negative Matrices
• Quantum Algorithm for a Convergent Series of Approximations towards the Exact Solution of the Lowest Eigenstates of a Hamiltonian
• Toward Density Functional Theory on Quantum Computers?
• Fluctuation-guided adaptive random compiler for Hamiltonian simulation
• Quantum Phase Estimation Algorithm with Gaussian Spin States
• Approximating Ground and Excited State Energies on a Quantum Computer
• Managing Classical Processing Requirements for Quantum Error Correction
• Quantum adiabaticity in many-body systems and almost-orthogonality in complementary subspace
• Towards Compact Wavefunctions from Quantum-Selected Configuration Interaction
• Resonant Coupling Parameter Estimation with Superconducting Qubits
• Optical Quantum Computing
• Enhancing quantum computations with the synergy of auxiliary field quantum Monte Carlo and computational basis tomography
• Quantum Simulation via Stochastic Combination of Unitaries
• Fast-forwardability of Qubit-mapped Fermion models based on Cartan decomposition
• Resource Estimation for VQE on Small Molecules: Impact of Fermion Mappings and Hamiltonian Reductions
• Quantum Circuits in Additive Hilbert Space
• Quantum Mechanical Model for Information Transfer from DNA to Protein
• Hybrid Quantum-Classical Clustering for Preparing a Prior Distribution of Eigenspectrum
• Low-Depth Unitary Coupled Cluster Theory for Quantum Computation
• A Useful Metric for the NISQ Era: Qubit Error Probability and Its Role in Zero Noise Extrapolation
• Building intuition for Quantum Algorithms using the Aharonov-Bohm effect
• Determining Molecular Ground State with Quantum Imaginary Time Evolution using Broken-Symmetry Wave Function
• Capabilities and Limits of the Unitary Coupled-cluster Approach with Generalized Two-body Cluster Operators
• Comprehensive Study on Heisenberg-limited Quantum Algorithms for Multiple Observables Estimation
• Comparison of spin-qubit architectures for quantum error-correcting codes
• Efficacious qubit mappings for quantum simulations of the ${}^{12}$C rotational band
• A combined quantum-classical method applied to material design: optimization and discovery of photochromic materials for photopharmacology applications
• Extension of the Jordan-Wigner mapping to nonorthogonal spin orbitals for quantum computing application to valence bond approaches
• Energy Spectra of Compressed Quantum States
• Correction scheme for molecular total energies from quantum phase estimation under limited qubit resources
• Fault-Tolerant Encoding of Logical Qudits in Spin Systems
• Quantum phase estimation with optimal confidence interval using three control qubits
• Nonadiabatic Self-Healing of Trotter Errors in Digitized Counterdiabatic Dynamics
• Fast collisional $\sqrt{\mathrm{SWAP}}$ gate for fermionic atoms in an optical superlattice
• A quantum eigenvalue solver based on tensor networks
• Efficiently preparing chiral states via fermionic cooling on bosonic quantum hardware
• QuaSiMo: A Composable Library to Program Hybrid Workflows for Quantum Simulation
• Numerical investigation of the quantum inverse algorithm on small molecules
• Two Variations of Quantum Phase Estimation for Reducing Circuit Error Rates: Application to the Harrow--Hassidim--Lloyd Algorithm
• Quantum Chaos and Universal Trotterisation Behaviours in Digital Quantum Simulations
• Quantum information theory on sparse wavefunctions and applications for Quantum Chemistry
• Hamiltonian Engineering in Quantum Spin Networks
• Resource-efficient encoding algorithm for variational bosonic quantum simulations