Variational quantum solver employing the PDS energy functional

Abstract

Recently a new class of quantum algorithms that are based on the quantum computation of the connected moment expansion has been reported to find the ground and excited state energies. In particular, the Peeters-Devreese-Soldatov (PDS) formulation is found variational and bearing the potential for further combining with the existing variational quantum infrastructure. Here we find that the PDS formulation can be considered as a new energy functional of which the PDS energy gradient can be employed in a conventional variational quantum solver. In comparison with the usual variational quantum eigensolver (VQE) and the original static PDS approach, this new variational quantum solver offers an effective approach to navigate the dynamics to be free from getting trapped in the local minima that refer to different states, and achieve high accuracy at finding the ground state and its energy through the rotation of the trial wave function of modest quality, thus improves the accuracy and efficiency of the quantum simulation. We demonstrate the performance of the proposed variational quantum solver for toy models, H${}_2$ molecule, and strongly correlated planar H${}_4$ system in some challenging situations. In all the case studies, the proposed variational quantum approach outperforms the usual VQE and static PDS calculations even at the lowest order. We also discuss the limitations of the proposed approach and its preliminary execution for model Hamiltonian on the NISQ device.

References in corpus (40)

• Quantum Computing in the NISQ era and beyond
• A variational eigenvalue solver on a quantum processor
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• Barren plateaus in quantum neural network training landscapes
• The theory of variational hybrid quantum-classical algorithms
• Quantum computational chemistry
• Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuits
• Evaluating analytic gradients on quantum hardware
• An adaptive variational algorithm for exact molecular simulations on a quantum computer
• Extending the computational reach of a noisy superconducting quantum processor
• Simulating Hamiltonian dynamics with a truncated Taylor series
• Hartree-Fock on a superconducting qubit quantum computer
• Towards Practical Quantum Variational Algorithms
• Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution
• Efficient quantum algorithms for simulating sparse Hamiltonians
• Variational ansatz-based quantum simulation of imaginary time evolution
• The Bravyi-Kitaev transformation for quantum computation of electronic structure
• Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics
• Quantum Natural Gradient
• Robust determination of molecular spectra on a quantum processor
• Theory of variational quantum simulation
• Generalized Unitary Coupled Cluster Wavefunctions for Quantum Computation
• On the relationship between continuous- and discrete-time quantum walk
• Quantum Implementation of Unitary Coupled Cluster for Simulating Molecular Electronic Structure
• Low Depth Quantum Simulation of Electronic Structure
• Efficient and Noise Resilient Measurements for Quantum Chemistry on Near-Term Quantum Computers
• Exact Parameterization of Fermionic Wave Functions via Unitary Coupled Cluster Theory
• Avoiding local minima in variational quantum eigensolvers with the natural gradient optimizer
• A Non-Orthogonal Variational Quantum Eigensolver
• Application of fermionic marginal constraints to hybrid quantum algorithms
• Higher Order Derivatives of Quantum Neural Networks with Barren Plateaus
• On barren plateaus and cost function locality in variational quantum algorithms
• Hamiltonian Simulation Using Linear Combinations of Unitary Operations
• Quantum Algorithm for Spectral Measurement with Lower Gate Count
• Quantum Power Method by a Superposition of Time-Evolved States
• High Performance Emulation of Quantum Circuits
• Quantum inverse iteration algorithm for programmable quantum simulators
• Quantum computed moments correction to variational estimates
• Improving the accuracy and efficiency of quantum connected moments expansions
• Quantum simulations employing connected moments expansions

Cited by in corpus (11)

• A Quantum Computing View on Unitary Coupled Cluster Theory
• Improving the accuracy and efficiency of quantum connected moments expansions
• The Basics of Quantum Computing for Chemists
• Dual Exponential Coupled Cluster Theory: Unitary Adaptation, Implementation in the Variational Quantum Eigensolver Framework and Pilot Applications
• A backend-agnostic, quantum-classical framework for simulations of chemistry in C++
• Modeling singlet fission on a quantum computer
• Precision ground-state energy calculation for the water molecule on a superconducting quantum processor
• Flexibility of the factorized form of the unitary coupled cluster ansatz
• Quantum subspace expansion approach for simulating dynamical response functions of Kitaev spin liquids
• State preparation and evolution in quantum computing: a perspective from Hamiltonian moments
• Moments-based quantum computation of the electric dipole moment of molecular systems