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- Title
On the Role of Hadamard Gates in Quantum Circuits.
- Authors
Shepherd, D.
- 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.
- Subjects
ALGORITHMS; MATHEMATICAL forms; COMBINATORICS; HADAMARD matrices; ALGEBRA; MATHEMATICS
- Publication
Quantum Information Processing, 2006, Vol 5, Issue 3, p161
- ISSN
1570-0755
- Publication type
Article
- DOI
10.1007/s11128-006-0023-4