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

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.