Simulating electronic structure on bosonic quantum computers

TL;DR

This paper introduces a method to simulate molecular electronic structures using bosonic quantum computers, specifically qumodes, by mapping electronic Hamiltonians and employing variational algorithms on cQED platforms.

Contribution

It presents a novel approach to simulate electronic structure problems on bosonic quantum devices using qumodes and variational algorithms, expanding quantum computational chemistry capabilities.

Findings

Successfully computed ground state energies for H2 and H4 molecules.

Demonstrated compatibility with circuit QED hardware platforms.

Established a new pathway for simulating many-fermion systems.

Abstract

Quantum harmonic oscillators, or qumodes, provide a promising and versatile framework for quantum computing. Unlike qubits, which are limited to two discrete levels, qumodes have an infinite-dimensional Hilbert space, making them well-suited for a wide range of quantum simulations. In this work, we focus on the molecular electronic structure problem. We propose an approach to map the electronic Hamiltonian into a qumode bosonic problem that can be solved on bosonic quantum devices using the variational quantum eigensolver (VQE). Our approach is demonstrated through the computation of ground potential energy surfaces for benchmark model systems, including H$_2$ and the linear H$_4$ molecule. The preparation of trial qumode states and the computation of expectation values leverage universal ansatzes based on the echoed conditional displacement (ECD), or the selective number-dependent arbitrary phase (SNAP) operations. These techniques are compatible with circuit quantum electrodynamics (cQED) platforms, where microwave resonators coupled to superconducting transmon qubits can offer an efficient hardware realization. This work establishes a new pathway for simulating many-fermion systems, highlighting the potential of hybrid qubit-qumode quantum devices in advancing quantum computational chemistry.