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Efficient Toffoli gates using qudits

2007; American Physical Society; Volume: 75; Issue: 2 Linguagem: Inglês

10.1103/physreva.75.022313

1538-4446

Timothy C. Ralph, Katharina Resch, Alexei Gilchrist,

Neural Networks and Reservoir Computing

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.