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Kothari: Exponential improvement in precision for simulating sparse HamiltoniansExport this event to calendar

Thursday, April 17, 2014 — 12:00 PM to 1:00 PM EDT

Robin Kothari

We provide a quantum algorithm for simulating the
dynamics of sparse Hamiltonians with complexity sublogarithmic in
the inverse error, an exponential improvement over previous methods.
Unlike previous approaches based on product formulas, the query
complexity is independent of the number of qubits acted on, and for
time-varying Hamiltonians, the gate complexity is logarithmic in the
norm of the derivative of the Hamiltonian. Our algorithm is based on
a significantly improved simulation of the continuous- and
fractional-query models using discrete quantum queries, showing that
the former models are not much more powerful than the discrete model
even for very small error. We also significantly simplify the
analysis of this conversion, avoiding the need for a complex fault
correction procedure. Our simplification relies on a new form of
"oblivious amplitude amplification" that can be applied even though
the reflection about the input state is unavailable. Finally, we
prove new lower bounds showing that our algorithms are optimal as a
function of the error.

This is joint work with Dominic W. Berry, Andrew M. Childs, Richard
Cleve, and Rolando D. Somma.

Location 
QNC - Quantum Nano Centre
1102
200 University Avenue West

Waterloo, ON N2L 3G1
Canada

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