Narrow Results

We design an efficient optical circuit to realize a Toffoli gate via weak cross-Kerr nonlinearity and classical feedback. To obtain a high-fidelity gate, we probe different path detectors to minimize the influence from the environmental noise. Compared to previous proposals, our scheme does not need external auxiliary photons and is easy to implement in experiment.

A thin-layer Belousov–Zhabotinsky (BZ) medium is a powerful computing device capable for implementing logical circuits, memory, image processors, robot controllers, and neuromorphic architectures. We design the reversible logical gates — Fredkin gate and Toffoli gate — in a BZ medium network of excitable channels with subexcitable junctions. Local control of the BZ medium excitability is an important feature of the gates’ design. An excitable thin-layer BZ medium responds to a localized perturbation with omnidirectional target or spiral excitation waves. A subexcitable BZ medium responds to an asymmetric perturbation by producing traveling localized excitation wave-fragments similar to dissipative solitons. We employ interactions between excitation wave-fragments to perform the computation. We interpret the wave-fragments as values of Boolean variables. The presence of a wave-fragment at a given site of a circuit represents the logical truth, absence of the wave-fragment — logically false. Fredkin gate consists of ten excitable channels intersecting at 11 junctions, eight of which are subexcitable. Toffoli gate consists of six excitable channels intersecting at six junctions, four of which are subexcitable. The designs of the gates are verified using numerical integration of two-variable Oregonator equations.

A scheme for realizing the non-local Toffoli gate among three spatially separated nodes through cavity quantum electrodynamics (C-QED) is presented. The scheme can obtain high fidelity in the current C-QED system. With entangled qubits as quantum channels, the operation is resistive to actual environment noise.

In the framework of quantum computation with mixed states, fuzzy representations based on continuous t-norms for Toffoli and Fredkin quantum gates are introduced. A comparison between both gates is also studied.