Classical and Quantum Tensor Product Expanders

M. B. Hastings; A. W. Harrow

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arXiv · 0804.0011

Classical and Quantum Tensor Product Expanders

M. B. Hastings·A. W. Harrow

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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.

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M. B. Hastings, A. W. Harrow. 2008-12-16. Classical and Quantum Tensor Product Expanders. https://arxiv.org/abs/0804.0011

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