Grid-based methods for chemistry simulations on a quantum computer

Abstract

First-quantized, grid-based methods for chemistry modeling are a natural and elegant fit for quantum computers. However, it is infeasible to use today’s quantum prototypes to explore the power of this approach because it requires a substantial number of near-perfect qubits. Here, we use exactly emulated quantum computers with up to 36 qubits to execute deep yet resource-frugal algorithms that model 2D and 3D atoms with single and paired particles. A range of tasks is explored, from ground state preparation and energy estimation to the dynamics of scattering and ionization; we evaluate various methods within the split-operator QFT (SO-QFT) Hamiltonian simulation paradigm, including protocols previously described in theoretical papers and our own techniques. While we identify certain restrictions and caveats, generally, the grid-based method is found to perform very well; our results are consistent with the view that first-quantized paradigms will be dominant from the early fault-tolerant quantum computing era onward.

Exploiting subspace constraints and ab initio variational methods for quantum chemistry

“…The advantage is even more significant for reactions that preserve the number of particles. Finally, it possesses a potential in first-quantised simulations [54][55][56]. For instance, Chan et al [56] have successfully predicted oscillations in the Helium dimer using the first-quantised method.…”

“…Finally, it possesses a potential in first-quantised simulations [54][55][56]. For instance, Chan et al [56] have successfully predicted oscillations in the Helium dimer using the first-quantised method. Their simulation extensively employs propagators for each potential term, spatial grid, and time grid; thus, maintaining shallow circuits of the propagators can significantly improve the efficiency, which are expected to assist in the prediction of the behaviour of larger molecules in the future.…”

First-quantized eigensolver for ground and excited states of electrons under a uniform magnetic field

“…Although chemical shifts depend on the electronic environment and are smaller than the reference energy splittings in general, they are not negligible for realizing precise quantum information processing based on NMR techniques. [7][8][9][10][11][12][13] Although the second-quantized formalism is widely adopted in the quantum computation community to determine the ground state of electronic systems, the first-quantized formalism [14][15][16][17][18][19] (or equivalently the grid-based formalism) has attracted recent attention as a promising alternative. In particular, first-quantized eigensolver (FQE), 18) which is a framework of quantum chemistry based on the probabilistic imaginary-time evolution (PITE), provides nonvariational energy minimization with favorable scaling of computational resources compared to the second-quantized ones.…”

“…In addition, we provide a generic construction of the derivative circuits, together with measurement-based formulae to extract the electric-current density that helps reveal the microscopic magnetic response of the target system. We also propose filtration circuits for eliminating undesired energy eigenstates based on the idea of Chan et al 19) Our new techniques are validated by performing FQE simulations for confined electronic systems under external magnetic fields.…”

A Quantum Algorithm from Response Theory: Digital Quantum Simulation of Two-Dimensional Electronic Spectroscopy

“…An early demonstration of quantum speed-up in the simulation of unitary quantum dynamics was proposed by Lloyd . More recently, several sophisticated protocols have been developed for simulating the dynamics of molecular systems. − In this work, we build on the established advantage of quantum simulation of field-free many-body Hamiltonian dynamics and focus on the algorithm connecting such dynamics to the simulation of spectral features in linear and nonlinear optical techniques. To this aim, we leverage the structure of the response function as a linear combination of Time Correlation Functions (TCFs) of the dipole moment operator of the system.…”