Quantum search with modular variables

We give a dimension independent formulation of the quantum search algorithm introduced in [L. K. Grover, Phys. Rev. Lett. {\bf 79}, 325 (1997)]. This algorithm provides a quadratic gain when compared to its classical counterpart by manipulating quantum two--level systems, qubits. We show that this g...

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Bibliographic Details
Published in:arXiv.org 2014-07
Main Authors: Ketterer, A, Douce, T, Keller, A, Coudreau, T, Milman, P
Format: Article
Language:English
Subjects:
Coding
Continuity (mathematics)
Hilbert space
Logic circuits
Quantum computing
Quantum phenomena
Quantum theory
Qubits (quantum computing)
Search algorithms
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Summary:We give a dimension independent formulation of the quantum search algorithm introduced in [L. K. Grover, Phys. Rev. Lett. {\bf 79}, 325 (1997)]. This algorithm provides a quadratic gain when compared to its classical counterpart by manipulating quantum two--level systems, qubits. We show that this gain, already known to be optimal, is preserved, irrespectively of the dimension of the system used to encode quantum information. This is shown by adapting the protocol to Hilbert spaces of any dimension using the same sequence of operations/logical gates as its original qubit formulation. Our results are detailed and illustrated for a system described by continuous variables, where qubits can be encoded in infinitely many distinct states using the modular variable formalism.
ISSN:2331-8422