Abstract
Linear-optical passive (LOP) devices and photon counters are sufficient to implement universal quantum computation with single photons, and particular schemes have already been proposed. In this paper we discuss the link between the algebraic structure of LOP transformations and quantum computing. We first show how to decompose the Fock space of N optical modes in finite-dimensional subspaces that are suitable for encoding strings of qubits and invariant under LOP transformations (these subspaces are related to the spaces of irreducible unitary representations of U (N). Next we show how to design in algorithmic fashion LOP circuits which implement any quantum circuit deterministically. We also present some simple examples, such as the circuits implementing a cNOT gate and a Bell state generator/analyser.
Original language | English (US) |
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Pages (from-to) | S711-S720 |
Journal | Journal of Optics B: Quantum and Semiclassical Optics |
Volume | 7 |
Issue number | 12 |
DOIs | |
State | Published - Dec 1 2005 |
Externally published | Yes |
Keywords
- Jordan-Schwinger map
- Linear optics quantum computation
- Linear-optical passive device
- Single-photon multi-qubit encoding
ASJC Scopus subject areas
- Atomic and Molecular Physics, and Optics
- Physics and Astronomy (miscellaneous)