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Physics Letters A

Deterministic linear optical quantum Toffoli gate

He-Liang Huang, Wan‐Su Bao, Tan Li, Feng‐Guang Li, Xiang-Qun Fu, Shuo Zhang, Hailong Zhang, Xiang Wang

Published Jun 23, 2017• 21 citations
Publisher
DOI
10.1016/j.physleta.2017.06.034

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A particular type of linear optical multiport, the Grover four-port, has previously been shown to couple the spatial symmetry of a photon to its direction of travel. It is shown here that use of a nonstandard choice of qubit, based on symmetry, allows Grover four ports to act as compact, low-resource deterministic linear optical controlledNOTgates, with no post-selection or ancilla measurements required. This approach allows programmable devices, made from Grover multiports in combination with other standard optical components, that can implement multiple different one-, two-, and three-qubit gates, including the Fredkin and Toffoli gates.
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.