# Algebraic Compression of Free Fermionic Quantum Circuits: Particle Creation, Arbitrary Lattices and Controlled Evolution

2023 IEEE International Conference on Quantum Computing and Engineering (QCE)（2023）

Abstract

In this work [1], we extend our recently introduced algebraic circuit compression algorithms [2], [3] that can compress time evolution circuits of free fermionic Hamiltonians on an n-site 1D chain, \begin{equation*} \mathcal{H}(t)=\sum\limits_{i=1}^{n-1}\left(h_{i}(t)c_{i}^{\dagger}c_{i+1}+p_{i}(t)c_{i}c_{i+1}\right)+\mathrm{h}.\mathrm{c}., \tag{1} \end{equation*} in three significant ways: (1) we allow for compression of free fermionic Hamiltonians on arbitrary lattices, (2) we incorporate particle creation/annihilation operators into the compression schemes, and (3) we extend the compression scheme to controlled time-evolution operators. We illustrate the effectiveness of our approach by simulating the dynamics of a fermion on a
$4\times 4\ 2\mathrm{D}$
square lattice on ibmq_washington, both in the presence and absence of disorder. Our quantum simulations show a remarkably high fidelity which is enabled through the compressed circuits.

MoreTranslated text

Key words

Quantum Circuit,Particle Creation,Free Fermions,Arbitrary Lattice,Time Evolution,Square Lattice,Absence Of Disorders,Compression Algorithm,Evolution Operator,Compression Scheme,Quantum Simulation

AI Read Science

Must-Reading Tree

Example

Generate MRT to find the research sequence of this paper

Chat Paper

Summary is being generated by the instructions you defined