Quantum Orbital-Optimized Unitary Coupled Cluster Methods in the Strongly Correlated Regime: Can Quantum Algorithms Outperform their Classical Equivalents?

Abstract

The Coupled Cluster (CC) method is used to compute the electronic correlation energy in atoms and molecules and often leads to highly accurate results. However, due to its single-reference nature, standard CC in its projected form fails to describe quantum states characterized by strong electronic correlations and multi-reference projective methods become necessary. On the other hand, quantum algorithms for the solution of many-electron problems have also emerged recently. The quantum UCC with singles and doubles (q-UCCSD) is a popular wavefunction Ansatz for the Variational Quantum Eigensolver (VQE) algorithm. The variational nature of this approach can lead to significant advantages compared to its classical equivalent in the projected form, in particular for the description of strong electronic correlation. However, due to the large number of gate operations required in q-UCCSD, approximations need to be introduced in order to make this approach implementable in a state-of-the-art quantum computer. In this work, we evaluate several variants of the standard q-UCCSD Ansatz in which only a subset of excitations is included. In particular, we investigate the singlet and pair q-UCCD approaches combined with orbital optimization. We show that these approaches can capture the dissociation/distortion profiles of challenging systems such as H${}_4$, H${}_2$O and N${}_2$ molecules, as well as the one-dimensional periodic Fermi-Hubbard chain. These results promote the future use of q-UCC methods for the solution of challenging electronic structure problems in quantum chemistry.

References in corpus (28)

• A variational eigenvalue solver on a quantum processor
• The theory of variational hybrid quantum-classical algorithms
• An adaptive variational algorithm for exact molecular simulations on a quantum computer
• Fermionic quantum computation
• Scalable Quantum Simulation of Molecular Energies
• Elucidating Reaction Mechanisms on Quantum Computers
• Quantum optimization using variational algorithms on near-term quantum devices
• Generalized Unitary Coupled Cluster Wavefunctions for Quantum Computation
• Quantum algorithms for electronic structure calculations: particle/hole Hamiltonian and optimized wavefunction expansions
• Digital quantum simulation of fermionic models with a superconducting circuit
• Accelerated Variational Quantum Eigensolver
• From transistor to trapped-ion computers for quantum chemistry
• Exact Parameterization of Fermionic Wave Functions via Unitary Coupled Cluster Theory
• Tapering off qubits to simulate fermionic Hamiltonians
• Increasing the representation accuracy of quantum simulations of chemistry without extra quantum resources
• Is the Trotterized UCCSD Ansatz chemically well-defined?
• Seniority-based coupled cluster theory
• Can single-reference coupled cluster theory describe static correlation?
• Gate-efficient simulation of molecular eigenstates on a quantum computer
• Orbital optimized unitary coupled cluster theory for quantum computer
• On the difference between variational and unitary coupled cluster theories
• Downfolding of many-body Hamiltonians using active-space models: extension of the sub-system embedding sub-algebras approach to unitary coupled cluster formalisms
• Bravyi-Kitaev Superfast simulation of fermions on a quantum computer
• Accuracy and Resource Estimations for Quantum Chemistry on a Near-term Quantum Computer
• Pair extended coupled cluster doubles
• Optimizing qubit resources for quantum chemistry simulations in second quantization on a quantum computer
• Quantum simulations of excited states with active-space downfolded Hamiltonians
• Assessing the Accuracy of the Jastrow Antisymmetrized Geminal Power in the H4 Model System

Cited by in corpus (82)

• Variational Quantum Algorithms
• The Variational Quantum Eigensolver: a review of methods and best practices
• A Quantum Computing View on Unitary Coupled Cluster Theory
• Quantum equation of motion for computing molecular excitation energies on a noisy quantum processor
• Emerging quantum computing algorithms for quantum chemistry
• Qubit-excitation-based adaptive variational quantum eigensolver
• Orbital optimized unitary coupled cluster theory for quantum computer
• Learning to Measure: Adaptive Informationally Complete Generalized Measurements for Quantum Algorithms
• Hardware Efficient Quantum Algorithms for Vibrational Structure Calculations
• Simulating Quantum Materials with Digital Quantum Computers
• Quantum-optimal-control-inspired ansatz for variational quantum algorithms
• Efficient step-merged quantum imaginary time evolution algorithm for quantum chemistry
• Orbital-optimized pair-correlated electron simulations on trapped-ion quantum computers
• A state-averaged orbital-optimized hybrid quantum-classical algorithm for a democratic description of ground and excited states
• Tequila: A platform for rapid development of quantum algorithms
• Quantum HF/DFT-Embedding Algorithms for Electronic Structure Calculations: Scaling up to Complex Molecular Systems
• Quantum Embedding Method for the Simulation of Strongly Correlated Systems on Quantum Computers
• Adaptive pruning-based optimization of parameterized quantum circuits
• Analytic gradients in variational quantum algorithms: Algebraic extensions of the parameter-shift rule to general unitary transformations
• Reducing qubit requirements while maintaining numerical precision for the Variational Quantum Eigensolver: A Basis-Set-Free Approach
• Simulating quantum chemistry in the seniority-zero space on qubit-based quantum computers
• Chemistry on quantum computers with virtual quantum subspace expansion
• Quantum chemistry simulation of ground- and excited-state properties of the sulfonium cation on a superconducting quantum processor
• Optimized Low-Depth Quantum Circuits for Molecular Electronic Structure using a Separable Pair Approximation
• Ancilla-free implementation of generalized measurements for qubits embedded in a qudit space
• Microcanonical and finite temperature ab initio molecular dynamics simulations on quantum computers
• Quantum Simulations in Effective Model Spaces (I): Hamiltonian Learning-VQE using Digital Quantum Computers and Application to the Lipkin-Meshkov-Glick Model
• Spin-projection for quantum computation: A low-depth approach to strong correlation
• Analytical energy gradient for state-averaged orbital-optimized variational quantum eigensolvers and its application to a photochemical reaction
• Quantum Computation of Reactions on Surfaces Using Local Embedding
• Molecular Excited State Calculations with Adaptive Wavefunctions on a Quantum Eigensolver Emulation: Reducing Circuit Depth and Separating Spin States
• Tight and Efficient Gradient Bounds for Parameterized Quantum Circuits
• Molecular Quantum Circuit Design: A Graph-Based Approach
• Dual Exponential Coupled Cluster Theory: Unitary Adaptation, Implementation in the Variational Quantum Eigensolver Framework and Pilot Applications
• AGP-based unitary coupled cluster theory for quantum computers
• Adaptive construction of shallower quantum circuits with quantum spin projection for fermionic systems
• TenCirChem: An Efficient Quantum Computational Chemistry Package for the NISQ Era
• A self-consistent field approach for the variational quantum eigensolver: orbital optimization goes adaptive
• Unitary coupled-cluster based self-consistent polarization propagator theory: a quadratic unitary coupled-cluster singles and doubles scheme
• Calculating the ground state energy of benzene under spatial deformations with noisy quantum computing
• Which options exist for NISQ-friendly linear response formulations?
• Quantum algorithms for scientific computing
• Quantum Equation of Motion with Orbital Optimization for Computing Molecular Properties in Near-Term Quantum Computing
• Extension of the Trotterized Unitary Coupled Cluster to Triple Excitations
• Unraveling correlated material properties with noisy quantum computers: Natural orbitalized variational quantum eigensolving of extended impurity models within a slave-boson approach
• Benchmarking the Variational Quantum Eigensolver through Simulation of the Ground State Energy of Prebiotic Molecules on High-Performance Computers
• Partitioning Quantum Chemistry Simulations with Clifford Circuits
• Reducing Entanglement With Physically-Inspired Fermion-To-Qubit Mappings
• A Quantum Computing Implementation of Nuclear-Electronic Orbital (NEO) Theory: Towards an Exact pre-Born-Oppenheimer Formulation of Molecular Quantum Systems
• Towards chemical accuracy with shallow quantum circuits: A Clifford-based Hamiltonian engineering approach
• Efficient and Robust Parameter Optimization of the Unitary Coupled-Cluster Ansatz
• Analytical formulation of the second-order derivative of energy for orbital-optimized variational quantum eigensolver: application to polarizability
• Towards Efficient Quantum Computing for Quantum Chemistry: Reducing Circuit Complexity with Transcorrelated and Adaptive Ansatz Techniques
• Reduced density matrix formulation of quantum linear response
• Implementing Jastrow--Gutzwiller operators on a quantum computer using the cascaded variational quantum eigensolver algorithm
• Coupled cluster method tailored with quantum computing
• Precision ground-state energy calculation for the water molecule on a superconducting quantum processor
• Quantum Information reveals that orbital-wise correlation is essentially classical in Natural Orbitals
• Understanding and mitigating noise in molecular quantum linear response for spectroscopic properties on quantum computers
• Assessing the Orbital-Optimized Unitary Ansatz for Density Cumulant Theory
• Divergences in classical and quantum linear response and equation of motion formulations
• SHARC-VQE: Simplified Hamiltonian Approach with Refinement and Correction enabled Variational Quantum Eigensolver for Molecular Simulation
• Distinguishing homolytic versus heterolytic bond dissociation of phenyl sulfonium cations with localized active space methods
• Optimization strategies in WAHTOR algorithm for quantum computing empirical ansatz: a comparative study
• Mantra: Rewriting Quantum Programs to Minimize Trap-Movements for Zoned Rydberg Atom Arrays
• Estimating molecular thermal averages with the quantum equation of motion and informationally complete measurements
• Cascaded variational quantum eigensolver algorithm
• Calculation of the moscovium ground-state energy by quantum algorithms
• Non-Iterative Disentangled Unitary Coupled-Cluster based on Lie-algebraic structure
• Decomposition of high-rank factorized unitary coupled-cluster operators using ancilla and multi-qubit controlled low-rank counterparts
• Quantum Machine Learning of Molecular Energies with Hybrid Quantum-Neural Wavefunction
• Simulating the Fermi-Hubbard model with long-range hopping on a quantum computer
• Almost optimal measurement scheduling of molecular Hamiltonian via finite projective plane
• Optimal Particle-Conserved Linear Encoding for Practical Fermionic Simulation
• Quantum-Classical Auxiliary Field Quantum Monte Carlo with Matchgate Shadows on Trapped Ion Quantum Computers
• Hyperfine Coupling Constants on Quantum Computers: Performance, Errors, and Future Prospects
• Parallelized Givens Ansatz for Molecular ground-states: Bridging Accuracy and Efficiency on NISQ Platforms
• Encoding strongly-correlated many-boson wavefunctions on a photonic quantum computer: application to the attractive Bose-Hubbard model
• Quantum neural network autoencoder and classifier applied to an industrial case study
• Quantum-Enhanced Neural Exchange-Correlation Functionals
• Capabilities and Limits of the Unitary Coupled-cluster Approach with Generalized Two-body Cluster Operators
• Variational Quantum Subspace Construction via Symmetry-Preserving Cost Functions