Quantum simulation of bosons with the contracted quantum eigensolver

Abstract

Quantum computers are promising tools for simulating many-body quantum systems due to their potential scaling advantage over classical computers. While significant effort has been expended on many-fermion systems, here we simulate a model entangled many-boson system with the contracted quantum eigensolver (CQE). We generalize the CQE to many-boson systems by encoding the bosonic wavefunction on qubits. The CQE provides a compact ansatz for the bosonic wave function whose gradient is proportional to the residual of a contracted Schrödinger equation. We apply the CQE to a bosonic system, where N quantum harmonic oscillators are coupled through a pairwise quadratic repulsion. The model is relevant to the study of coupled vibrations in molecular systems on quantum devices. Results demonstrate the potential efficiency of the CQE in simulating bosonic processes such as molecular vibrations with good accuracy and convergence even in the presence of noise.

Quantum simulation of excited states from parallel contracted quantum eigensolvers

“…gives accurate results both for ground bosonic [28] and ground and excited electronic [20,21] states. Although the ACSE, unlike the CSE, does not rigorously imply the SE [19], it contains roughly half of the degrees of freedom in the CSE, and hence, provides a stringent necessary condition for satisfaction of the SE.…”

Machine learning assisted construction of a shallow depth dynamic ansatz for noisy quantum hardware

“…42 The CSE and its anti-hermitian variant (ACSE) leads to the direct determination of energy and two-electron reduced density matrices of many-electron molecules 45,46 and is shown to be more expressive and efficient than the UCC ansatz. The ACSE has been implemented for quantum simulations, both on simulators and devices 47–51 at the cost of shallow quantum circuits.…”

Quantum simulation of conical intersections

“…42–50 To address some of the concerns in the last paragraph, we observe first that the gate operations are unitary, which makes it convenient to implement a unitary ansatz of wavefunctions ( e.g. , the unitary coupled cluster (UCC) ansatz 51,52 or the anti-Hermitian contracted Schrödinger equation (ACSE) ansatz 53–61 ). They offer robust and accurate solutions to the electronic structure data near CIs.…”