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IEEE International Conference on Solid-State and Integrated Circuit Technology

Extended Toffoli gate implementation with photons

Jialin Chen, Xiao-Ying Zhang, Lingli Wang, Xinyuan Wei, Wenqing Zhao

Published Oct 1, 2008• 13 citations
Publisher

Abstract

The Toffoli gate is an especially important case of the quantum gates. In this paper, we show how to construct Toffoli gates using several additional (ancilla) photons, linear optical instruments and cross-Kerr nonlinearities. Then they are expanded to implement Extended Toffoli gates (ETOF). Our work shows only one n-IPC (n-input parity check) gate plus at most 2m CNOT or NCNOT gates can implement arbitrary ETOF (n, m), indicating the feasibility and advantage of modularizing quantum gates with photons.

DOI
10.1109/icsict.2008.4734595

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The Toffoli gate is an especially important case of the quantum gates. In this paper, we show how to construct Toffoli gates using several additional (ancilla) photons, linear optical instruments and cross-Kerr nonlinearities. Then they are expanded to implement Extended Toffoli gates (ETOF). Our work shows only one n-IPC (n-input parity check) gate plus at most 2m CNOT or NCNOT gates can implement arbitrary ETOF (n, m), indicating the feasibility and advantage of modularizing quantum gates with photons.
Toffoli gate is an especially important case of the quantum gates. In this paper, we show how to construct Toffoli gates using several additional (ancilla) photons, linear optical instruments and cross-Kerr nonlinearities. Then they are expanded to implement Extended Toffoli gates (ETOF). Our work shows only one n-IPC (w-input parity check) gate plus at most 2 m CNOT or NCNOT gates can implement arbitrary ETOF (n, m), indicating the feasibility and advantage of modularizing quantum gates with photons.
Minimizing the number of necessary two-qubit gates is an important task in quantum information processing. By introducing non-computational quantum states in auxiliary spaces, we construct effective circuits for the controlled-NOT (CNOT) gate and the n-control-qubit Toffoli gate with (2n-1) qubit-qudit gates and (2n-2) single-qudit gates. We propose the polarization CNOT and Toffoli gates based on the designed quantum circuits in linear optics by operating on the spatial-mode degree of freedom of photons. Our optical schemes can be achieved with a higher success probability and no extra auxiliary photons are needed.
We design linear-optics multiqubit quantum logic gates. We assume the traditional encoding of a qubit onto the state of a single photon in two modes (e.g., spatial or polarization). We suggest schemes allowing direct probabilistic realization of the fundamental Toffoli and Fredkin gates without resorting to a sequence of single- and two-qubit gates. This yields more compact schemes and potentially reduces the number of ancilla photons. The proposed setups involve passive linear optics, sources of auxiliary single photons or maximally entangled pairs of photons, and single-photon detectors. In particular, we propose an interferometric implementation of the Toffoli gate in the coincidence basis, which does not require any ancilla photons and is experimentally feasible with current technology.
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.
Abstract Universal quantum entangling gates are a crucial building block in the large‐scale quantum computation and quantum communication, and it is an important task to find simple ways to implement them. Here an effective quantum circuit for the implementation of a controlled‐NOT (CNOT) gate is constructed by introducing a non‐computational quantum state in the auxiliary space. Furthermore, the method is extended to the construction of a general n ‐control‐qubit Toffoli gate with qubit–qudit gates and single‐qudit gates. Based on the presented quantum circuits, the polarization CNOT and Toffoli gates with linear optics are designed by operating on the spatial‐mode degree of freedom of photons. The proposed optical schemes can be achieved with a higher success probability and no extra auxiliary photons are needed.