Parallel and Distributed Fermionic Simulation via Dynamic Encoding

We demonstrate a simple and efficient method to parallelize and distribute Trotterized Hamiltonian simulation of fermionic systems across multiple QPUs. Using combinatorial covering designs to define a minimal set of fermion-qubit encodings, we demonstrate communication cost scaling as $\mathcal{O}(Mr)$ for a system of $M$ fermionic modes and Trotter number $r$, improving on the static encoding bound for $q$ QPUs, $\mathcal{O}(M^{4}qr)$. We compare this approach to dynamic encoding using a randomised method, Pauli-weight based optimisation and hypergraph partitioning. Applying this to the Hamiltonians of a range of molecular systems, we find the combinatorial covering approach results in the lowest communication cost in all but the sparsest Hamiltonians.