Exhaustive search for optimal molecular geometries using imaginary-time evolution on a quantum computer

Abstract

We propose a nonvariational scheme for geometry optimization of molecules for the first-quantized eigensolver, a recently proposed framework for quantum chemistry using the probabilistic imaginary-time evolution (PITE) on a quantum computer. While the electrons in a molecule are treated in the scheme as quantum mechanical particles, the nuclei are treated as classical point charges. We encode both electronic states and candidate molecular geometries as a superposition of many-qubit states, leading to quantum advantage. The histogram formed by outcomes of repeated measurements gives the global minimum of the energy surface. We demonstrate that the circuit depth scales as O (n_e^2 poly(log n_e)) for the electron number n_e, which can be reduced to O (n_e poly(log n_e)) if extra O (n_e log n_e) qubits are available. We corroborate the scheme via numerical simulations. The new efficient scheme will be helpful for achieving scalability of practical quantum chemistry on quantum computers. As a special case of the scheme, a classical system composed only of charged particles is admitted. We also examine the scheme adapted to variational calculations that prioritize saving circuit depths for noisy intermediate-scale quantum (NISQ) devices.

arXiv comment19 figures

References in corpus (25)

• 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
• Simulation of Many-Body Fermi Systems on a Universal Quantum Computer
• Variational ansatz-based quantum simulation of imaginary time evolution
• Theory of variational quantum simulation
• Polynomial-time quantum algorithm for the simulation of chemical dynamics
• Efficient Simulation of Quantum Systems by Quantum Computers
• A new quantum ripple-carry addition circuit
• Qulacs: a fast and versatile quantum circuit simulator for research purpose
• Variational quantum algorithms for discovering Hamiltonian spectra
• An Exact Quantum Polynomial-Time Algorithm for Simon's Problem
• Simulating chemistry efficiently on fault-tolerant quantum computers
• Improved Techniques for Preparing Eigenstates of Fermionic Hamiltonians
• Quantum simulation of the single-particle Schrodinger equation
• Non-adiabatic molecular quantum dynamics with quantum computers
• Reference electronic structure calculations in one dimension
• Quantum Algorithm for Molecular Properties and Geometry Optimization
• Grid-based methods for chemistry simulations on a quantum computer
• Construction of Green's functions on a quantum computer: applications to molecular systems
• Quantum Circuits for Toom-Cook Multiplication
• Charge and spin response functions on a quantum computer: applications to molecules
• Optimal scheduling in probabilistic imaginary-time evolution on a quantum computer
• Improved reversible and quantum circuits for Karatsuba-based integer multiplication
• Molecular Structure Optimization based on Electrons-Nuclei Quantum Dynamics Computation

Cited by in corpus (7)

• Grid-based methods for chemistry simulations on a quantum computer
• First-quantized eigensolver for ground and excited states of electrons under a uniform magnetic field
• First-quantized adiabatic time evolution for the ground state of a many-electron system and the optimal nuclear configuration
• Annealing for prediction of grand canonical crystal structures: Efficient implementation of n-body atomic interactions
• Optimized synthesis of circuits for diagonal unitary matrices with reflection symmetry
• Calculating potential energy surfaces with quantum computers by measuring only the density along adiabatic transitions
• Accelerated spin-adapted ground-state preparation with nonvariational quantum algorithms