# On the Role of Hadamard Gates in Quantum Circuits

Shepherd Daniel

Research output: Contribution to journalArticle (Academic Journal)peer-review

9 Citations (Scopus)

## 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'', \emph{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 \textbf{BPP}.
Translated title of the contribution On the Role of Hadamard Gates in Quantum Circuits English 161-177 Quantum Information Processing 5(3) Published - 2006

### Bibliographical note

Other identifier: 2000588

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