An adaptive variational algorithm for exact molecular simulations on a quantum computer

Abstract

Quantum simulation of chemical systems is one of the most promising near-term applications of quantum computers. The variational quantum eigensolver, a leading algorithm for molecular simulations on quantum hardware, has a serious limitation in that it typically relies on a pre-selected wavefunction ansatz that results in approximate wavefunctions and energies. Here we present an arbitrarily accurate variational algorithm that instead of fixing an ansatz upfront, this algorithm grows it systematically one operator at a time in a way dictated by the molecule being simulated. This generates an ansatz with a small number of parameters, leading to shallow-depth circuits. We present numerical simulations, including for a prototypical strongly correlated molecule, which show that our algorithm performs much better than a unitary coupled cluster approach, in terms of both circuit depth and chemical accuracy. Our results highlight the potential of our adaptive algorithm for exact simulations with present-day and near-term quantum hardware.

11 pages, 3 figures; published version

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• Multi-target quantum compilation algorithm
• Low variance estimations of many observables with tensor networks and informationally-complete measurements
• Stabilizer configuration interaction: Finding molecular subspaces with error detection properties
• Expressivity of deterministic quantum computation with one qubit
• Simulating methylamine using symmetry adapted qubit-excitation-based variational quantum eigensolver
• Quantum implicit representation of vortex filaments in turbulence
• Exploring new variational quantum circuit ansatzes for solving $SU(2)$ matrix models
• Multi-set variational quantum dynamics algorithm for simulating nonadiabatic dynamics on quantum computers
• Pathfinding Quantum Simulations of Neutrinoless Double-Beta Decay
• Limitations of Quantum Hardware for Molecular Energy Estimation Using VQE
• Bridging Quantum Computing and Nuclear Structure: Atomic Nuclei on a Trapped-Ion Quantum Computer
• Quantum Computing Beyond Ground State Electronic Structure: A Review of Progress Toward Quantum Chemistry Out of the Ground State
• Constraint-Aware Quantum Optimization via Hamming Weight Operators
• Efficient Fermi-Hubbard model ground-state preparation by coupling to a classical reservoir in the instantaneous-response limit
• Encoding strongly-correlated many-boson wavefunctions on a photonic quantum computer: application to the attractive Bose-Hubbard model
• Orbital Expansion Variational Quantum Eigensolver: Enabling Efficient Simulation of Molecules with Shallow Quantum Circuit
• ORQVIZ: Visualizing High-Dimensional Landscapes in Variational Quantum Algorithms
• Quantum Simulations of Chemical Reactions: Achieving Accuracy with NISQ Devices
• Freedom of mixer rotation-axis improves performance in the quantum approximate optimization algorithm
• Counterdiabatic ADAPT-VQE for molecular simulation
• Efficient Online Quantum Circuit Learning with No Upfront Training
• Mitigating the measurement overhead of ADAPT-VQE with optimised informationally complete generalised measurements
• A Quantum-Inspired Algorithm for the Factorized Form of Unitary Coupled Cluster Theory
• A Cyclic Layerwise QAOA Training
• Determining the ensemble N-representability of Reduced Density Matrices
• Generative flow-based warm start of the variational quantum eigensolver
• Feasibility of performing quantum chemistry calculations on quantum computers
• Parallelized Givens Ansatz for Molecular ground-states: Bridging Accuracy and Efficiency on NISQ Platforms
• Improved Strategies for Fermionic Quantum Simulation with Global Interactions
• Accelerating Quantum Eigensolver Algorithms With Machine Learning
• Quantum natural gradient with thermal-state initialization
• Efficient 2D Tensor Network Simulation of Quantum Systems
• Electronic Structure Theory with Molecular Point Group Symmetries on Quantum Annealers
• Consensus-based qubit configuration optimization for variational algorithms on neutral atom quantum systems
• Qiskit-Torch-Module: Fast Prototyping of Quantum Neural Networks
• Expressiveness of Commutative Quantum Circuits: A Probabilistic Approach
• Multi-channel convolutional neural quantum embedding
• Adaptive Quantum Generative Training using an Unbounded Loss Function
• Hyperfine Coupling Constants on Quantum Computers: Performance, Errors, and Future Prospects
• Molecular resonance identification in complex absorbing potentials via integrated quantum computing and high-throughput computing
• Improving shadow estimation with locally-optimal dual frames
• Exploring fixed points and eigenstates of quantum systems with reinforcement learning
• Resource-efficient Quantum Algorithms for Selected Hamiltonian Subspace Diagonalization
• A Quantum Variational Approach to Prototypical Recurrent Unit
• Extension of the Jordan-Wigner mapping to nonorthogonal spin orbitals for quantum computing application to valence bond approaches
• Efficacious qubit mappings for quantum simulations of the ${}^{12}$C rotational band
• Ancillary entangling Floquet kicks for accelerating quantum algorithms
• Quantum information theory on sparse wavefunctions and applications for Quantum Chemistry
• Double-bracket quantum algorithms for high-fidelity ground state preparation
• Optimizing Unitary Coupled Cluster Wave Functions on Quantum Hardware: Error Bound and Resource-Efficient Optimizer
• Gate Efficient Composition of Hamiltonian Simulation and Block-Encoding with its Application on HUBO, Chemistry and Finite Difference Method
• Hidden local adiabatic ramp in the modulated time evolution and the quantum approximate optimization algorithm
• Variational Quantum Subspace Construction via Symmetry-Preserving Cost Functions
• Using optimal control to guide neural-network interpolation of continuously-parameterized gates
• On Assessing the Quantum Advantage for MaxCut Provided by Quantum Neural Network Ansätze
• QuaSiMo: A Composable Library to Program Hybrid Workflows for Quantum Simulation
• Feedback-Based Quantum Algorithm for Constrained Optimization Problems
• The Virtual Quantum Device (VQD): A tool for detailed emulation of quantum computers
• Universal Euler-Cartan Circuits for Quantum Field Theories
• Qubit frugal entanglement determination with the deep multi-scale entanglement renormalization ansatz
• EVA: a quantum Exponential Value Approximation algorithm
• Interpolation-based coordinate descent method for parameterized quantum circuits
• Performance evaluation of variational quantum eigensolver and quantum dynamics algorithms on the advection-diffusion equation
• A quantum eigenvalue solver based on tensor networks
• Mapping quantum chemical dynamics problems onto spin-lattice simulators
• Unbiased observable estimation with approximate channels in fault-tolerant quantum computation
• Hamiltonian-reconstruction distance as a success metric for the Variational Quantum Eigensolver
• Chemistry beyond the Hartree-Fock limit via quantum computed moments
• Quantum Imaginary-Time Evolution with Polynomial Resources in Evolution Time
• Hamiltonian Expressibility for Ansatz Selection in Variational Quantum Algorithms
• Evaluating Ground State Energies of Chemical Systems with Low-Depth Quantum Circuits and High Accuracy
• Shot-Efficient ADAPT-VQE via Reused Pauli Measurements and Variance-Based Shot Allocation
• Extended parameter shift rules with minimal derivative variance for parameterized quantum circuits
• When to Build Quantum Software?
• Perturbation theory, irrep truncations, and state preparation methods for quantum simulations of SU(3) lattice gauge theory
• Slice-Wise Initial State Optimization to Improve Cost and Accuracy of the VQE on Lattice Models
• The Effect of Noise on the Performance of Variational Algorithms for Quantum Chemistry
• Utility-Scale Quantum State Preparation: Classical Training using Pauli Path Simulation
• Quantum feature-map learning with reduced resource overhead
• Benchmarking Quantum Simulation of Chemical Hamiltonians using the Sorted-List Encoding