[QIP-Sem] QIP seminar, Thu 2/24, 11:00, 6-310, Sanders,Barry

[Peter Shor]

MIT Quantum Information Processing seminar
Thursday 2/24 at 11:00 in 6-310
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 Sanders,Barry (University of Calgary)

Simulating Time-Dependent Quantum Dynamics On A Quantum Computer

Abstract:

Since 1982, when Feynman first proposed efficiently simulating  Hamiltonian dynamics on a quantum computer as a way around classical- computer intractability, great advances have been achieved in  developing general-purpose quantum-simulation algorithms for bounded- error solutions that fully account for all consumed computational  resources. The primary focus has been on time-independent Hamiltonian  evolution, but time-dependent Hamiltonian evolution is also important  as it is central to quantum control and adiabatic processes. I report  our efficient quantum algorithm for simulating time-dependent  Hamiltonian evolution of general input states on a quantum computer  provided that the Hamiltonian is sufficiently smooth. The time cost of  our algorithm is close to linear in the evolution time, hence  comparable to algorithms for simulating time-independent Hamiltonian  evolution. Our algorithm is based on queries to an oracle holding the  Hamiltonian, and we assign unit cos
 t per bit or qubit for oracle calls  in contrast to previous work wherein an oracle query yields an  arbitrary number of bits or qubits at constant cost. Our per-bit or  per-qubit costing of oracle calls reveals hitherto unnoticed  simulation costs even for the case of simulating time-independent  Hamiltonian evolution. We also account for discretization errors in  the time and the representation of the Hamiltonian. Consequently our  algorithm not only enables simulation of time-dependent quantum  dynamics on a quantum computer but also reduces to the time- independent evolution case and with a fair assessment of oracle-query  cost.

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