Classical and Quantum Tensor Product Expanders
Abstract
We introduce the concept of quantum tensor product expanders. These are expanders that act on several copies of a given system, where the Kraus operators are tensor products of the Kraus operator on a single system. We begin with the classical case, and show that a classical two-copy expander can be used to produce a quantum expander. We then discuss the quantum case and give applications to the Solovay-Kitaev problem. We give probabilistic constructions in both classical and quantum cases, giving tight bounds on the expectation value of the largest nontrivial eigenvalue in the quantum case.
Keywords
Cite
@article{arxiv.0804.0011,
title = {Classical and Quantum Tensor Product Expanders},
author = {M. B. Hastings and A. W. Harrow},
journal= {arXiv preprint arXiv:0804.0011},
year = {2009}
}
Comments
18 pages. v2 fixed proof and slightly changed statement of Lemma 1. v3 clarified discussion of state randomization, non-Hermitian expanders, and various proof details. Journal version