Classical and Quantum Tensor Product Expanders
| dc.creator | Hastings, M. B. | |
| dc.creator | Harrow, A. W. | |
| dc.date | 2008-04-01 | |
| dc.date | 2008-12-16 | |
| dc.date.accessioned | 2026-07-07T13:02:59Z | |
| dc.date.available | 2026-07-07T13:02:59Z | |
| dc.description | 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. | |
| dc.description | 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 | |
| dc.identifier | https://arxiv.org/abs/0804.0011 | |
| dc.identifier | http://arxiv.org/abs/0804.0011 | |
| dc.identifier | QIC 9, 336 (2009). | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/226638 | |
| dc.subject | Quantum Physics | |
| dc.title | Classical and Quantum Tensor Product Expanders | |
| dc.type | text |