Nathan Wiebe: Quantum Computer Simulations of Time Dependent Hamiltonians

Tuesday, October 19, 2010 12:00 pm - 1:00 pm EDT (GMT -04:00)

Nathan Wiebe, University of Calgary

We introduce an efficient quantum algorithm for simulating time-dependent Hamiltonian quantum dynamics on a quantum computer and accounts fully for all computational resources, especially the per-qubit oracle query cost, which has been previously regarded as constant cost per query regardless of the number of qubits accessed.

Our algorithm works for any time-dependent Hamiltonian that satisfies specified smoothness conditions. Furthermore, our Hamiltonian need not be sparse but rather can be a sum of Hamiltonians that can be
efficiently converted to sparse Hamiltonians in the computational basis. Our other algorithmic innovations include enhancement of the ordered-exponential decomposition procedure by adaptively choosing the integration step size and by accounting for errors due to discretization of Hamiltonian matrix elements and of time.