Quantum Simulation of Electronic Structure with Linear Depth and Connectivity

TL;DR

This paper introduces a linear-depth quantum algorithm for simulating electronic structures using a fermionic swap network, optimizing for minimal connectivity and reducing gate complexity for practical quantum architectures.

Contribution

It presents a novel fermionic swap network approach enabling electronic structure simulation with linear depth and minimal connectivity, improving efficiency over previous methods.

Findings

Simulation of a Trotter step in exactly N depth

Preparation of arbitrary Slater determinants in at most N/2 depth

Reduction in entangling gates compared to prior algorithms

Abstract

As physical implementations of quantum architectures emerge, it is increasingly important to consider the cost of algorithms for practical connectivities between qubits. We show that by using an arrangement of gates that we term the fermionic swap network, we can simulate a Trotter step of the electronic structure Hamiltonian in exactly $N$ depth and with $N^2/2$ two-qubit entangling gates, and prepare arbitrary Slater determinants in at most $N/2$ depth, all assuming only a minimal, linearly connected architecture. We conjecture that no explicit Trotter step of the electronic structure Hamiltonian is possible with fewer entangling gates, even with arbitrary connectivities. These results represent significant practical improvements on the cost of most Trotter based algorithms for both variational and phase estimation based simulation of quantum chemistry.