[quantum-info] IQC Seminar Thursday, June 6th, Ish Dhand

[Bronwyn Greavette]

IQC Seminar

Thursday, 6 June 2013 at 12:00 PM
QNC 0101

Speaker: Ish Dhand
University of Calgary 

Title:
Finite-precision computation of ordered operator-exponential decomposition

Abstract:
Trotter-Suzuki ordered operator-exponential decomposition finds use in
quantum control, simulation of physical systems and in algorithms for
finding the ground state of quantum many-body systems. The decomposition
has well-defined error bounds in theory but is unstable in practice;
higher-order approximations should provide exponentially exact solutions
but yield approximations with error that grows exponentially beyond a
certain order. We investigate the stability of the Trotter-Suzuki
decomposition scheme for ordered operator exponentials in the context of
finite-precision computation. Finite precision is a result of finite
computational space on a classical Turing machine and of finiteness of
gate set on a quantum circuit. We show that that numerical error in
computation causes instabilities in the Lie-Trotter-Suzuki product
formulae for operator exponentials for approximation of exp(iHλ) for λ
large as compared to 1/|H|, where |*| is the operator norm. To address
the problem of approximating an operator exponential to within a
specified error, we present an algorithm to decide whether a
Trotter-Suzuki expansion is possible on a computer with given numerical
precision and then find the corresponding optimal decomposition. This
algorithm would enable the simulation, control and analysis of more
complex physical systems using the same computational resources.

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