Increasing the representation accuracy of quantum simulations of chemistry without extra quantum resources

Abstract

Proposals for near-term experiments in quantum chemistry on quantum computers leverage the ability to target a subset of degrees of freedom containing the essential quantum behavior, sometimes called the active space. This approximation allows one to treat more difficult problems using fewer qubits and lower gate depths than would otherwise be possible. However, while this approximation captures many important qualitative features, it may leave the results wanting in terms of absolute accuracy (basis error) of the representation. In traditional approaches, increasing this accuracy requires increasing the number of qubits and an appropriate increase in circuit depth as well. Here we introduce a technique requiring no additional qubits or circuit depth that is able to remove much of this approximation in favor of additional measurements. The technique is constructed and analyzed theoretically, and some numerical proof of concept calculations are shown. As an example, we show how to achieve the accuracy of a 20 qubit representation using only 4 qubits and a modest number of additional measurements for a simple hydrogen molecule. We close with an outlook on the impact this technique may have on both near-term and fault-tolerant quantum simulations.

References in corpus (31)

• A variational eigenvalue solver on a quantum processor
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• The theory of variational hybrid quantum-classical algorithms
• A Quantum Approximate Optimization Algorithm
• Quantum Circuit Learning
• Simulated Quantum Computation of Molecular Energies
• Characterizing Quantum Supremacy in Near-Term Devices
• Scalable Quantum Simulation of Molecular Energies
• Elucidating Reaction Mechanisms on Quantum Computers
• Hybrid Quantum-Classical Hierarchy for Mitigation of Decoherence and Determination of Excited States
• Simulation of Electronic Structure Hamiltonians Using Quantum Computers
• Robust determination of molecular spectra on a quantum processor
• Quantum chemistry calculations on a trapped-ion quantum simulator
• Quantum Simulation of Electronic Structure with Linear Depth and Connectivity
• Encoding Electronic Spectra in Quantum Circuits with Linear T Complexity
• A random compiler for fast Hamiltonian simulation
• Quantum Computation of Electronic Transitions using a Variational Quantum Eigensolver
• Gate count estimates for performing quantum chemistry on small quantum computers
• Low Depth Quantum Simulation of Electronic Structure
• Low-cost error mitigation by symmetry verification
• Qubitization of Arbitrary Basis Quantum Chemistry Leveraging Sparsity and Low Rank Factorization
• Witnessing eigenstates for quantum simulation of Hamiltonian spectra
• Chemical Basis of Trotter-Suzuki Errors in Quantum Chemistry Simulation
• Low rank representations for quantum simulation of electronic structure
• Improved Fault-Tolerant Quantum Simulation of Condensed-Phase Correlated Electrons via Trotterization
• Quantum algorithms to simulate many-body physics of correlated fermions
• Application of fermionic marginal constraints to hybrid quantum algorithms
• Exponentially more precise quantum simulation of fermions I: Quantum chemistry in second quantization
• Exploiting locality in quantum computation for quantum chemistry
• Quantum Simulation of Chemistry with Sublinear Scaling in Basis Size
• Hamiltonian Simulation in the Interaction Picture

Cited by in corpus (104)

• Variational Quantum Algorithms
• Noisy intermediate-scale quantum (NISQ) algorithms
• Quantum computational chemistry
• The Variational Quantum Eigensolver: a review of methods and best practices
• Quantum algorithms for quantum chemistry and quantum materials science
• Hartree-Fock on a superconducting qubit quantum computer
• Quantum Error Mitigation
• A compact ion-trap quantum computing demonstrator
• Layerwise learning for quantum neural networks
• Unbiasing Fermionic Quantum Monte Carlo with a Quantum Computer
• Emerging quantum computing algorithms for quantum chemistry
• Fermionic partial tomography via classical shadows
• Quantum Orbital-Optimized Unitary Coupled Cluster Methods in the Strongly Correlated Regime: Can Quantum Algorithms Outperform their Classical Equivalents?
• Orbital optimized unitary coupled cluster theory for quantum computer
• Fault-Tolerant Quantum Simulations of Chemistry in First Quantization
• A Jastrow-type decomposition in quantum chemistry for low-depth quantum circuits
• Fault-tolerant resource estimate for quantum chemical simulations: Case study on Li-ion battery electrolyte molecules
• Nearly Optimal Measurement Scheduling for Partial Tomography of Quantum States
• Hardware Efficient Quantum Algorithms for Vibrational Structure Calculations
• Real time evolution for ultracompact Hamiltonian eigenstates on quantum hardware
• Quantum-centric Supercomputing for Materials Science: A Perspective on Challenges and Future Directions
• Simulating Quantum Materials with Digital Quantum Computers
• Quantum simulation with hybrid tensor networks
• Generalized quantum subspace expansion
• Orbital-optimized pair-correlated electron simulations on trapped-ion quantum computers
• Exact and efficient Lanczos method on a quantum computer
• A state-averaged orbital-optimized hybrid quantum-classical algorithm for a democratic description of ground and excited states
• Correlation-Informed Permutation of Qubits for Reducing Ansatz Depth in VQE
• Towards a Larger Molecular Simulation on the Quantum Computer: Up to 28 Qubits Systems Accelerated by Point Group Symmetry
• Quantum Chemistry Simulations of Dominant Products in Lithium-Sulfur Batteries
• Variational Quantum Eigensolver for Frustrated Quantum Systems
• Optimal fermion-to-qubit mapping via ternary trees with applications to reduced quantum states learning
• Quantum HF/DFT-Embedding Algorithms for Electronic Structure Calculations: Scaling up to Complex Molecular Systems
• Reduced Density Matrix Sampling: Self-consistent Embedding and Multiscale Electronic Structure on Current Generation Quantum Computers
• Subspace Variational Quantum Simulator
• Iterative Quantum Assisted Eigensolver
• Reducing qubit requirements while maintaining numerical precision for the Variational Quantum Eigensolver: A Basis-Set-Free Approach
• Chemistry on quantum computers with virtual quantum subspace expansion
• Quantum Machine-Learning for Eigenstate Filtration in Two-Dimensional Materials
• Analytical nonadiabatic couplings and gradients within the state-averaged orbital-optimized variational quantum eigensolver
• A variational quantum eigensolver for dynamic correlation functions
• Dimensionality reduction of many-body problem using coupled-cluster sub-system flow equations: classical and quantum computing perspective
• Quantum-Classical Hybrid Algorithm for the Simulation of All-Electron Correlation
• Real-Time Krylov Theory for Quantum Computing Algorithms
• Perturbative quantum simulation
• Preserving Symmetries for Variational Quantum Eigensolvers in the Presence of Noise
• N-electron valence perturbation theory with reference wavefunctions from quantum computing: application to the relative stability of hydroxide anion and hydroxyl radical
• Noisy intermediate-scale quantum algorithm for semidefinite programming
• Analytical energy gradient for state-averaged orbital-optimized variational quantum eigensolvers and its application to a photochemical reaction
• Quantum-Selected Configuration Interaction: classical diagonalization of Hamiltonians in subspaces selected by quantum computers
• Nearly-optimal state preparation for quantum simulations of lattice gauge theories
• Diagonalization of large many-body Hamiltonians on a quantum processor
• Collective optimization for variational quantum eigensolvers
• Error-mitigated fermionic classical shadows on noisy quantum devices
• AGP-based unitary coupled cluster theory for quantum computers
• Adaptive construction of shallower quantum circuits with quantum spin projection for fermionic systems
• Quantum computing quantum Monte Carlo with hybrid tensor network for electronic structure calculations
• A self-consistent field approach for the variational quantum eigensolver: orbital optimization goes adaptive
• Quantum algorithms for scientific computing
• Triply efficient shadow tomography
• Discretized quantum adiabatic process for free fermions and comparison with the imaginary-time evolution
• Quantum simulations of molecular systems with intrinsic atomic orbitals
• A stochastic quantum Krylov protocol with double factorized Hamiltonians
• Accurate and Efficient Quantum Computations of Molecular Properties Using Daubechies Wavelet Molecular Orbitals: A Benchmark Study against Experimental Data
• Analysis of quantum Krylov algorithms with errors
• VQE Method: A Short Survey and Recent Developments
• Tailored and Externally Corrected Coupled Cluster with Quantum Inputs
• Hybrid Tree Tensor Networks for quantum simulation
• Analytical formulation of the second-order derivative of energy for orbital-optimized variational quantum eigensolver: application to polarizability
• Quantum subspace expansion in the presence of hardware noise
• A Hybrid Quantum-Classical Method for Electron-Phonon Systems
• Accelerating quantum imaginary-time evolution with random measurements
• Coupled cluster method tailored with quantum computing
• A Quantum Algorithmic Approach to Multiconfigurational Valence Bond Theory: Insights from Interpretable Circuit Design
• Error-Mitigated Quantum Simulation of Interacting Fermions with Trapped Ions
• Exponential Qubit Reduction in Optimization for Financial Transaction Settlement
• Precision ground-state energy calculation for the water molecule on a superconducting quantum processor
• Unleashed from Constrained Optimization: Quantum Computing for Quantum Chemistry Employing Generator Coordinate Inspired Method
• Noise reduction using past causal cones in variational quantum algorithms
• Quantum computational study of chloride ion attack on chloromethane for chemical accuracy and quantum noise effects with UCCSD and k-UpCCGSD ansatzes
• A Classically Efficient Quantum Scalable Fermi-Hubbard Benchmark
• Adaptive variational ground state preparation for spin-1 models on qubit-based architectures
• Solving lattice gauge theories using the quantum Krylov algorithm and qubitization
• Quantum algorithm for calculation of transition amplitudes in hybrid tensor networks
• A Simple and Efficient Joint Measurement Strategy for Estimating Fermionic Observables and Hamiltonians
• State-Averaged Orbital-Optimized VQE: A quantum algorithm for the democratic description of ground and excited electronic states
• Calculation of the moscovium ground-state energy by quantum algorithms
• Sequence of penalties method to study excited states using VQE
• Digital simulation of convex mixtures of Markovian and non-Markovian single qubit Pauli channels on NISQ devices
• Optimizing Electronic Structure Simulations on a Trapped-ion Quantum Computer using Problem Decomposition
• Resource-efficient Generalized Quantum Subspace Expansion
• Almost optimal measurement scheduling of molecular Hamiltonian via finite projective plane
• Density matrix representation of hybrid tensor networks for noisy quantum devices
• Classically-Boosted Variational Quantum Eigensolver
• NISQ algorithm for the matrix elements of a generic observable
• High-Quality Protein Force Fields with Noisy Quantum Processors
• Geometric Constraints on Two-electron Reduced Density Matrices
• Excited state calculations using variational quantum eigensolver with spin-restricted ansätze and automatically-adjusted constraints
• Optimal Fermionic Joint Measurements for Estimating Non-Commuting Majorana Observables
• A penalty-free quantum algorithm to find energy eigenstates
• Chemistry beyond the Hartree-Fock limit via quantum computed moments
• Numerical investigation of the quantum inverse algorithm on small molecules
• Quantum Computation
• Variational Quantum Subspace Construction via Symmetry-Preserving Cost Functions