Quantum synthesis of arbitrary unitary operators

Abstract

Nature provides us with a restricted set of microscopic interactions. The question is whether we can synthesize out of these fundamental interactions an arbitrary unitary operator. In this paper we present a constructive algorithm for realization of any unitary operator which acts on a (truncated) Hilbert space of a single bosonic mode. In particular, we consider a physical implementation of unitary transformations acting on 1-dimensional vibrational states of a trapped ion. As an example we present an algorithm which realizes the discrete Fourier transform.

6 RevTeX pages with 3 figures, submitted to Phys.Rev.A, see also http://nic.savba.sk/sav/inst/fyzi/qo/

References in corpus (4)

• Quantum Computing
• Quantum computation over continuous variables
• Basics of Quantum Computation
• Quantum-state synthesis of multi-mode bosonic fields: Preparation of arbitrary states of 2-D vibrational motion of trapped ions

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• Implementation of quantum maps by programmable quantum processors
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• Conditional measurements on multimode pairwise entangled states from spontaneous parametric downconversion
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• Quantum state conversion by cross-Kerr interaction
• Generalized measurements via programmable quantum processor
• Linear optics substituting scheme for multi-mode operations