Fast simulation of fermions with reconfigurable qubits

Abstract: Performing large-scale, accurate quantum simulations of many-fermion systems is a central challenge in quantum science, with applications in chemistry, materials, and high-energy physics. Despite significant progress, realizing generic fermionic algorithms with qubit systems incurs significant space-time overhead, scaling as O(N) for N fermionic modes. Here we present a method for faster fermionic simulation with asymptotic space-time overhead of O(log(N)) in the worst case, and O(1) for circuits with additional structure, including important subroutines like the fermionic fast Fourier transform. This exponential reduction is achieved by using reconfigurable quantum systems with non-local connectivity, mid-circuit measurement, and classical feedforward, to generate dynamical fermion-to-qubit mappings. We apply this technique to achieve efficient compilation for key simulation tasks, including Hamiltonian simulation of the sparse Sachdev-Ye-Kitaev model and periodic materials, as well as free-fermion state-preparation. Moreover, we show that the algorithms themselves can be adapted to use only the O(1)-overhead structures to further reduce resource overhead. These techniques can lower gate counts by orders of magnitude for practical system sizes and are natively compatible with error corrected computation, making them ideal for early fault-tolerant quantum devices. Our results tightly bound the computational gap between fermionic and qubit models and open new directions in quantum simulation algorithm design and implementation.