Application of equivalence classes to the efficient construction of cluster states

Gerald Gilbert; Michael Hamrick; Yaakov S. Weinstein

doi:10.1117/12.666118

12 May 2006 Application of equivalence classes to the efficient construction of cluster states

Gerald Gilbert, Michael Hamrick, Yaakov S. Weinstein

Proceedings Volume 6244, Quantum Information and Computation IV; 62440U (2006) https://doi.org/10.1117/12.666118
Event: Defense and Security Symposium, 2006, Orlando (Kissimmee), Florida, United States

Abstract

We demonstrate a method of constructing L-shape cluster states by exploiting equivalence class properties of graph states. The L-shape cluster state is a primitive which can be used to construct cluster states capable of supporting universal quantum computation. The method is device independent but is shown to be considerably more efficient than previously proposed approaches for photonic cluster construction. Two-dimensional photonic cluster states can be efficiently built via local unitaries and type-I fusion only. To allow for a complete calculation of the cost of two-dimensional photonic cluster-state construction, we also provide a recursion relation relating the length of a photonic cluster chain to the average resources required.

Citation Download Citation

Gerald Gilbert, Michael Hamrick, and Yaakov S. Weinstein "Application of equivalence classes to the efficient construction of cluster states", Proc. SPIE 6244, Quantum Information and Computation IV, 62440U (12 May 2006); https://doi.org/10.1117/12.666118

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