Optimization strategies in WAHTOR algorithm for quantum computing empirical ansatz: a comparative study

Abstract

By exploiting the invariance of the molecular Hamiltonian by a unitary transformation of the orbitals it is possible to significantly shorter the depth of the variational circuit in the Variational Quantum Eigensolver (VQE) algorithm by using the Wavefunction Adapted Hamiltonian Through Orbital Rotation (WAHTOR) algorithm. This work introduces a non-adiabatic version of the WAHTOR algorithm and compares its efficiency with three implementations by estimating Quantum Processing Unit (QPU) resources in prototypical benchmarking systems. Calculating first and second-order derivatives of the Hamiltonian at fixed VQE parameters does not introduce a significant QPU overload, leading to results on small molecules that indicate the non-adiabatic Newton-Raphson method as the more convenient choice. On the contrary, we find out that in the case of Hubbard model systems the trust region non-adiabatic optimization is more efficient. The preset work therefore clearly indicates the best optimization strategies for empirical variational ansatzes, facilitating the optimization of larger variational wavefunctions for quantum computing.

References in corpus (34)

• Quantum Computing in the NISQ era and beyond
• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
• A variational eigenvalue solver on a quantum processor
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• Probing many-body dynamics on a 51-atom quantum simulator
• The theory of variational hybrid quantum-classical algorithms
• Quantum computational chemistry
• Quantum Chemistry in the Age of Quantum Computing
• The Variational Quantum Eigensolver: a review of methods and best practices
• An adaptive variational algorithm for exact molecular simulations on a quantum computer
• A quantum algorithm providing exponential speed increase for finding eigenvalues and eigenvectors
• Quantum algorithms for quantum chemistry and quantum materials science
• Variational ansatz-based quantum simulation of imaginary time evolution
• Simulating Lattice Gauge Theories within Quantum Technologies
• Quantum algorithms for electronic structure calculations: particle/hole Hamiltonian and optimized wavefunction expansions
• Warm-starting quantum optimization
• Strategies for solving the Fermi-Hubbard model on near-term quantum computers
• Quantum Orbital-Optimized Unitary Coupled Cluster Methods in the Strongly Correlated Regime: Can Quantum Algorithms Outperform their Classical Equivalents?
• Qubit-excitation-based adaptive variational quantum eigensolver
• Gate-efficient simulation of molecular eigenstates on a quantum computer
• Orbital optimized unitary coupled cluster theory for quantum computer
• Quantum Solver of Contracted Eigenvalue Equations for Scalable Molecular Simulations on Quantum Computing Devices
• An efficient quantum algorithm for the time evolution of parameterized circuits
• 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
• Quantum-classical hybrid algorithm using an error-mitigating $N$-representability condition to compute the Mott metal-insulator transition
• Optimal Control of Traffic Signals using Quantum Annealing
• Simulating Many-Body Systems with a Projective Quantum Eigensolver
• Pulse variational quantum eigensolver on cross-resonance based hardware
• Quantum simulation of molecules in solution
• Variational Quantum Eigensolver for SU($N$) Fermions
• Simulating a ring-like Hubbard system with a quantum computer
• NAPA: Intermediate-level Variational Native-pulse Ansatz for Variational Quantum Algorithms

Cited by in corpus (5)

• Natural orbitals and sparsity of quantum mutual information
• Quantum Information Driven Ansatz (QIDA): shallow-depth empirical quantum circuits from Quantum Chemistry
• Compact Multi-Threshold Quantum Information Driven Ansatz For Strongly Interactive Lattice Spin Models
• Optimizing Unitary Coupled Cluster Wave Functions on Quantum Hardware: Error Bound and Resource-Efficient Optimizer
• Quantum information theory on sparse wavefunctions and applications for Quantum Chemistry