Dear Quanta
Barry Sanders will give a talk in a special group meeting on Thursday at 11 in 6-310. I
hope the room is available. If not we will find another spot.
Eddie
Title: Simulating Time-Dependent Quantum Dynamics On A Quantum Computer
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 cost 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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Edward Farhi
Cecil and Ida Green Professor of Physics
Director
Center for Theoretical Physics
6-300
Massachusetts Institute of Technology
Cambridge MA 02139
617 253 4871
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