Designing Quantum Circuits for Efficient Many-Body Quantum Simulation

We construct an efficient autonomous quantum-circuit design algorithm for creating efficient quantum circuits to simulate Hamiltonian many-body quantum dynamics for arbitrary input states. The resultant quantum circuits have optimal space complexity and employ a sequence of gates that is close to optimal with respect to time complexity. We also devise an algorithm that exploits commutativity to optimize the circuits for parallel execution. As examples, we show how our autonomous algorithm constructs circuits for simulating the dynamics of Kitaev's honeycomb model and the Bardeen-Cooper-Schrieffer model of superconductivity.