Efficient Toffoli gates using qudits

T. C. Ralph*, K. J. Resch, A. Gilchrist

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

177 Citations (Scopus)


The simplest decomposition of a Toffoli gate acting on 3 qubits requires five 2-qubit gates. If we restrict ourselves to controlled-sign (or controlled-NOT) gates this number climbs to 6. We show that the number of controlled-sign gates required to implement a Toffoli gate can be reduced to just 3 if one of the three quantum systems has a third state that is accessible during the computation-i.e., is actually a qutrit. Such a requirement is not unreasonable or even atypical since we often artificially enforce a qubit structure on multilevel quantums systems (e.g., atoms, photonic polarization plus spatial modes). We explore the implementation of these techniques in optical quantum processing and show that linear optical circuits could operate with much higher probabilities of success.

Original languageEnglish
Article number022313
Pages (from-to)1-5
Number of pages5
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Issue number2
Publication statusPublished - 16 Feb 2007
Externally publishedYes


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