The Cost of Improving the Precision of the Variational Quantum Eigensolver for Quantum Chemistry

Abstract

Quantum computing brings a promise of new approaches into computational quantum chemistry. While universal, fault-tolerant quantum computers are still not available, we want to utilize today's noisy quantum processors. One of their flagship applications is the variational quantum eigensolver (VQE) -- an algorithm to calculate the minimum energy of a physical Hamiltonian. In this study, we investigate how various types of errors affect the VQE, and how to efficiently use the available resources to produce precise computational results. We utilize a simulator of a noisy quantum device, an exact statevector simulator, as well as physical quantum hardware to study the VQE algorithm for molecular hydrogen. We find that the optimal way of running the hybrid classical-quantum optimization is to (i) allow some noise in intermediate energy evaluations, using fewer shots per step and fewer optimization iterations, but require high final readout precision, (ii) emphasize efficient problem encoding and ansatz parametrization, and (iii) run all experiments within a short time-frame, avoiding parameter drift with time. Nevertheless, current publicly available quantum resources are still very noisy and scarce/expensive, and even when using them efficiently it is quite difficult to obtain trustworthy calculations of molecular energies.

References in corpus (34)

• Quantum Computing in the NISQ era and beyond
• Quantum Cryptography
• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• A variational eigenvalue solver on a quantum processor
• Quantum sensing
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• Supervised learning with quantum enhanced feature spaces
• A Quantum Engineer's Guide to Superconducting Qubits
• Quantum computational chemistry
• Secure quantum key distribution with realistic devices
• Quantum Chemistry in the Age of Quantum Computing
• Error mitigation for short-depth quantum circuits
• Strong quantum computational advantage using a superconducting quantum processor
• Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuits
• Fermionic quantum computation
• Extending the computational reach of a noisy superconducting quantum processor
• Scalable Quantum Simulation of Molecular Energies
• Quantum Random Number Generators
• O(N) methods in electronic structure calculations
• Phase-Programmable Gaussian Boson Sampling Using Stimulated Squeezed Light
• A Tutorial on Bayesian Optimization
• Mitigating measurement errors in multi-qubit experiments
• Quantum speedup of Monte Carlo methods
• The Density Matrix Renormalization Group in Chemistry and Molecular Physics: Recent Developments and New Challenges
• Even more efficient quantum computations of chemistry through tensor hypercontraction
• Mitigation of readout noise in near-term quantum devices by classical post-processing based on detector tomography
• Tapering off qubits to simulate fermionic Hamiltonians
• Quantum Algorithm Implementations for Beginners
• A Compact Fermion to Qubit Mapping
• Expressibility of the alternating layered ansatz for quantum computation
• Efficient correction of multiqubit measurement errors
• Quantum Error Mitigation using Symmetry Expansion
• Dimensional Expressivity Analysis of Parametric Quantum Circuits
• Algorithmic Error Mitigation Scheme for Current Quantum Processors

Cited by in corpus (8)

• A Hybrid Quantum Computing Pipeline for Real World Drug Discovery
• TenCirChem: An Efficient Quantum Computational Chemistry Package for the NISQ Era
• Towards chemical accuracy with shallow quantum circuits: A Clifford-based Hamiltonian engineering approach
• Identification of topological phases using classically-optimized variational quantum eigensolver
• Resource-efficient utilization of quantum computers
• Harmonic Oscillator based Particle Swarm Optimization
• Best-practice aspects of quantum-computer calculations: A case study of hydrogen molecule
• Efficient implementation of single particle Hamiltonians in exponentially reduced qubit space