Simulating Quantum Chaos with Quantum Computers

We study the effect of quantum non-integrability in quantum computation. A quantum Hamiltonian H = 1 2 (p 2 x + p 2 y + x 2 y 2 ) whose classical counterpart is known to be non-integrable is considered as a candidate of quantum non-integrable Hamiltonian using the Weyl rule. Our analysis illustrates a relation between quantum computability and quantum integrability, whose classical limit corresponds to the known fact that there is no symplectic integrators which preserves the total energy for autonomous non-integrable Hamiltonian systems