PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

A Single-shot Measurement of the Energy of Product States in a Translation Invariant Spin Chain Can Replace Any Quantum Computation
Dominik Janzing, Pawel Wocjan and Shenghui Zhang
New Journal of Physics Volume 10, Number 093004, pp. 1-18, 2008.

Abstract

In measurement-based quantum computation, quantum algorithms are implemented via sequences of measurements. We describe a translationally invariant finite-range interaction on a one-dimensional qudit chain and prove that a single-shot measurement of the energy of an appropriate computational basis state with respect to this Hamiltonian provides the output of any quantum circuit. The required measurement accuracy scales inverse polynomially with the size of the simulated quantum circuit. This shows that the implementation of energy measurements on generic qudit chains is as hard as the realization of quantum computation. Here, a ‘measurement‘ is any procedure that samples from the spectral measurement induced by the observable and the state under consideration. As opposed to measurement-based quantum computation, the post-measurement state is irrelevant.

PDF - Requires Adobe Acrobat Reader or other PDF viewer.
EPrint Type:Article
Additional Information:quantum complexity theory
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Theory & Algorithms
ID Code:5374
Deposited By:Dominik Janzing
Deposited On:31 March 2009