On the Role of Hadamard Gates in Quantum Circuits

On the Role of Hadamard Gates in Quantum Circuits We study a reduced quantum circuit computation paradigm in which the only allowable gates either permute the computational basis states or else apply a “global Hadamard operation”, i.e. apply a Hadamard operation to every qubit simultaneously. In this model, we discuss complexity bounds (lower-bounding the number of global Hadamard operations) for common quantum algorithms: we illustrate upper bounds for Shor’s Algorithm, and prove lower bounds for Grover’s Algorithm. We also use our formalism to display a gate that is neither quantum-universal nor classically simulable, on the assumption that Integer Factoring is not in BPP. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

On the Role of Hadamard Gates in Quantum Circuits

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Publisher
Springer Journals
Copyright
Copyright © 2006 by Springer Science+Business Media, Inc.
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-006-0023-4
Publisher site
See Article on Publisher Site

Abstract

We study a reduced quantum circuit computation paradigm in which the only allowable gates either permute the computational basis states or else apply a “global Hadamard operation”, i.e. apply a Hadamard operation to every qubit simultaneously. In this model, we discuss complexity bounds (lower-bounding the number of global Hadamard operations) for common quantum algorithms: we illustrate upper bounds for Shor’s Algorithm, and prove lower bounds for Grover’s Algorithm. We also use our formalism to display a gate that is neither quantum-universal nor classically simulable, on the assumption that Integer Factoring is not in BPP.

Journal

Quantum Information ProcessingSpringer Journals

Published: May 27, 2006

References

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