An Algebraic Quantum Circuit Compression Algorithm for Hamiltonian Simulation

Quantum computing is a promising technology that harnesses the peculiarities of quantum mechanics to deliver computational speedups for some problems are intractable solve on classical computer. Current generation noisy intermediate-scale (NISQ) computers severely limited in terms chip size and error rates. Shallow circuits with uncomplicated topologies essential successful applications NISQ era. Based matrix analysis, we derive localized circuit transformations efficiently compress simulation certain spin Hamiltonians known as free fermions. The depth compressed independent time grows linearly number spins. proposed numerical compression algorithm behaves backward stable scales cubically spins enabling synthesis beyond $\mathcal{O}(10^3)$ resulting have simple nearest-neighbor topology, which makes them ideally suited devices.