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Journal of Contemporary Physics (Armenian Academy of Sciences)

Implementation of all-optical Toffoli gate in Λ-systems

E. A. Gazazyan, G. G. Grigoryan, V. O. Chaltykyan, Daniel Schraft

Published Sep 1, 2012• 11 citations
Publisher

Abstract

An optical Toffoli gate is the essential logical element, which permits the implementation of a reversible optical processor. We propose a simple realization of such a gate in films of crystals doped with rare-earth ions. The proposed scheme is based on adiabatic population transfer in a Λ-system by means of counterintuitive and intuitive sequences of short laser pulses. We also discuss possibilities for experimental realization of the proposed gate.

DOI
10.3103/s1068337212050040

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An optical Toffoli gate is the essential logical element, which permits the implementation of a reversible optical processor. We propose a simple realization of such a gate in films of crystals doped with rare-earth ions. The proposed scheme is based on adiabatic population transfer in a Λ-system by means of counterintuitive and intuitive sequences of short laser pulses. We also discuss possibilities for experimental realization of the proposed gate.
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.
We consider a multiqubit system of atoms or ions with two computational ground states and an interacting excited state in the so-called blockade regime, such that only one qubit can be excited at any one time. Examples of such systems are rare-earth-ion-doped crystals and neutral atoms trapped in tweezer arrays. We present a simple laser excitation protocol that yields a complex phase factor on any desired multiqubit product state, and which can be used to implement multiqubit gates such as the nnn-bit Toffoli gates. The operation is performed using only two pulses, where each pulse simultaneously address all qubits involved in the operation. By relying on the well-established complex hyperbolic secant pulse shape, our scheme is also robust and permits complete transfers to and from the excited states despite variations in Rabi frequencies and transition frequencies. A detailed analysis of the multiqubit gate performance is provided.
The paper reports on the experimental realization on the possibility of isolating ions in a selected frequency channel. In the scheme, this interaction is mediated by the change in permanent dipole moment experienced by the rare-earth ions when they are optically excited from the ground state to an excited state. The change in dipole moment changes the electric field experienced by ions situated close to the excited ion, thus their absorption frequencies are changed. The important aspect, in order to use this frequency shift for controlled logic, is that the shift is large enough for ions, originally resonant with a certain laser frequency, to be shifted out of resonance with this laser field. Excitation induced frequency shifts are experimentally observed, which opens the way for the realisation of the first quantum gate in this type of solid state materials.
We present a robust construction of a set of logic gates operating on a system of qubits encoded in the rovibrational eigenstates of an Na2{\mathrm{Na}}_{2}Na2​ molecule using the optical adiabatic population transfer (APT) phenomenon. We demonstrate the operation of a complete universal gate set for quantum computation on a two-qubit system with gate fidelities approaching 99.99%. Like other APT-based processes, the method is robust against substantial fluctuations in the intensity of the laser pulse. Our construction is easily scalable to deal with a larger number of qubits. With the aid of the set of gates thus shown we may construct pulse sequences for a wide class of quantum logic operations. We also show how to produce a representation of Bell states from a representation of product states with essentially perfect fidelity. Our scheme can be realized in all diatomic and polyatomic molecules that possess easily accessible and well characterized excited electronic states.