Quantum supremacy regime for compressed fermionic models

TL;DR

This paper demonstrates that certain quadratic fermionic Hamiltonians can be efficiently simulated in compressed quantum space, revealing a regime where quantum supremacy is achievable for sampling these models.

Contribution

It introduces a class of compressible matchgate circuits for quadratic fermionic Hamiltonians and provides methods for efficient ground state energy evaluation and variational state preparation.

Findings

Ground state energy can be evaluated with O(log n) measurements.

A logarithmic qubit circuit ansatz for variational ground state search.

Identifies a quantum supremacy regime for sampling compressed Gaussian fermionic models.

Abstract

Compressible models extend the domain of simulable systems in quantum computers, but little is known about their precise limits of applicability. Using the theory of compressible matchgate circuits, we identify a class of quadratic fermionic Hamiltonians that can be simulated in compressed space. In particular, for systems of $n$ orbitals encoded to 2-local qubit models with nearest neighbour interactions, the ground state energy can be evaluated with $O\left(\log n\right)$ sets of measurements, independently of the number of dimensions in which the $n$ sites are arranged. We also provide an expressible circuit ansatz in a logarithmic number of qubits for finding the compressed ground state with a variational quantum eigensolver. From the complexity analysis of the compressed circuits, we find a regime of quantum supremacy for sampling compressed Gaussian fermionic models.