An algebraic approach to linear-optical schemes for deterministic quantum computing

Paolo Aniello, Ruben Coen Cagli

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


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 languageEnglish (US)
Pages (from-to)S711-S720
JournalJournal of Optics B: Quantum and Semiclassical Optics
Issue number12
StatePublished - Dec 1 2005
Externally publishedYes


  • 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)


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