TY - JOUR

T1 - Efficient Toffoli gates using qudits

AU - Ralph, T. C.

AU - Resch, K. J.

AU - Gilchrist, A.

PY - 2007/2/16

Y1 - 2007/2/16

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=33847066783&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.75.022313

DO - 10.1103/PhysRevA.75.022313

M3 - Article

VL - 75

SP - 1

EP - 5

JO - Physical Review A: covering atomic, molecular, and optical physics and quantum information

JF - Physical Review A: covering atomic, molecular, and optical physics and quantum information

SN - 2469-9926

IS - 2

M1 - 022313

ER -