2007/02/16 by Timothy C. Ralph, T. C. Ralph, Katharina Resch +3 · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Arithmetic #Computer science #Controlled NOT gate #Mathematics #Neural Networks and Reservoir Computing #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum circuit #Quantum computer #Quantum error correction #Quantum gate #Quantum mechanics #Qubit #Qutrit #Toffoli gate #Topology (electrical circuits) #quant-ph
paper · pdf · doi:10.1103/physreva.75.022313
published as Phys.Rev.A 75 022313 (2007)
openalex publication_date 2007/02/16 · arxiv created 2008/06/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.