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Days on Diffraction

Toffoli gate in twisted anisotropic and multihelical optical fibers

Constantine N. Alexeyev, Баршак Елена Владимировна, Dmitriy Vikulin, Boris P. Lapin, M. A. Yavorsky

Published May 25, 2020• 4 citations
Publisher

Abstract

We demonstrate the ability to use multihelical and twisted anisotropic fibers to implement the all-fiber stable logical element controlled-controlled-NOT gate (Toffoli gate). In twisted anisotropic fibers, we imply the radial number and the topological charge of input optical vortex as the control bits and the circular polarization carries the target bit. In multihelical fiber, the circular polarization and the radial number carry the control bits, while the topological charge carries the target one.

DOI
10.1109/dd49902.2020.9274577

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We demonstrate the ability to use multihelical and twisted anisotropic fibers to implement the all-fiber stable logical element controlled-controlled-NOT gate (Toffoli gate). In twisted anisotropic fibers, we imply the radial number and the topological charge of input optical vortex as the control bits and the circular polarization carries the target bit. In multihelical fiber, the circular polarization and the radial number carry the control bits, while the topological charge carries the target one.
We study the propagation of optical vortices in a system which consists of a tandem of a multi-helical and twisted anisotropic fiber. We show that at certain resonance regimes of the optical fibers such a system allows one to control sign flipping of the topological charge and the circular polarization of the input optical vortex. Moreover, parameters of the multihelical and the twisted anisotropic fibers are established for the implementation of a logical operation that corresponds to the sequential executing of two fundamental SWAP and CNOT gates over the states of circularly polarized optical vortices.
We study the propagation of circularly-polarized optical vortices of higher order topological charges ℓ ≥ 2 in a sandwich of multihelical - anisotropic - multihelical fibers on the basis of the Jones formalism for modes with orbital angular momentum. We demonstrate that such a system can operate as the all - fiber two - bit SWAP as well as universal tree - bit controlled-SWAP (Fredkin) gates over states of optical vortices, in which the mode radial number carries the control bit, while circular polarization and topological charge are the controlled bits.
The Toffoli gate is an essential logic element, which permits implementation of a reversible processor. It is of relevance both for classical as well as quantum logics. We propose and theoretically study all-optical implementations of three-bit and four-bit Toffoli gates by application of adiabatic population transfer techniques. For a three-bit Toffoli gate we use variants of stimulated Raman adiabatic passage (STIRAP) processes in a ΛΛΛ-type level scheme, driven by two laser pulses at sufficiently large detunings. For the implementation of a four-bit Toffoli gate, we apply reversible adiabatic population transfer in five-level quantum systems, interacting with three laser pulses. We demonstrate correct all-optical implementation of the truth table of three-bit and four-bit Toffoli gates. Moreover, we derive conditions for adiabatic evolution of the population dynamics and robust operation of the gates.
Quantum computation offers potential advantages in solving a number of interesting and difficult problems. Several controlled logic gates, the elemental building blocks of quantum computer, have been realized with various physical systems. A general technique was recently proposed that significantly reduces the realization complexity of multiple-control logic gates by harnessing multi-level information carriers. We present implementations of a key quantum circuit: the three-qubit Toffoli gate. By exploring the optical selection rules of one-sided optical microcavities, a Toffoli gate may be realized on all combinations of photon and quantum spins in the QD-cavity. The three general controlled-NOT gates are involved using an auxiliary photon with two degrees of freedom. Our results show that photons and quantum spins may be used alternatively in quantum information processing.