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Journal of the Optical Society of America B

All-optical logic operations by means of two interlinked χ^(2) interactions in a single crystal

Emiliano Puddu, Alessia Allevi, Alessandra Andreoni, Maria Bondani

Published Oct 1, 2004• 7 citations
Publisher

Abstract

The possibility of realizing the fundamental logic gates AND, OR, and NOT, which operate in parallel through two interlinked χ(2) interactions of sum- and difference-frequency generations in a single type I β-BaB2O4 crystal, is presented both theoretically and experimentally. Optical bits are encoded and read as amplitude modulation of the harmonics of a Nd:YAG laser. Owing to the excellent optical resolution of the system, data can be encoded at high density. The implementation of an all-optical parallel half-adder is also shown. The output fields can be frequency converted to implement an all-optical looping circuit.

DOI
10.1364/josab.21.001839

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The possibility of realizing the fundamental logic gates AND, OR, and NOT, which operate in parallel through two interlinked χ(2) interactions of sum- and difference-frequency generations in a single type I β-BaB2O4 crystal, is presented both theoretically and experimentally. Optical bits are encoded and read as amplitude modulation of the harmonics of a Nd:YAG laser. Owing to the excellent optical resolution of the system, data can be encoded at high density. The implementation of an all-optical parallel half-adder is also shown. The output fields can be frequency converted to implement an all-optical looping circuit.
The techniques which allow the stimulated photon echo to be used for digital addition are proposed. Time encoding is used to represent the input multibit numbers by laser pulse sequences. The on- and off-bits are encoded by the pulse intensities. The implementation of the logical operations AND, OR, XOR, and EQV is fulfilled in one setup. The setup includes an interferometer of the Mach-Zehnder type. To process the different bits in parallel a technique of frequency scanning within specimen inhomogeneous linewidth is invoked. Various adders are considered. An operation of both the half adder and full adder devices is based on cyclic repetition of the procedures SUM and CARRY. A carry-free adder with time data encoding based on the residue arithmetic is also considered.
The scope of this paper is to revisit the use of quadratic crystals cut for second harmonic generation (SHG) with type II phase-matching in view of all-optical processing of light signal. The investigations on this topic mainly focused in the past years on the possibilities opened by cascading of quadratic nonlinearities in phase-mismatched conditions [1]. The goal of this paper is to remind the reader that various types of optical processing are achievable with sum and difference frequency generation in phase-matched position without the requirement for cascaded nonlinearities. In a first part we will report few examples of the use of difference frequency generation (or down conversion) for signal processing. In a second part we will show that type II SHG with unbalanced fundamental inputs may lead to coherent amplification or transistor like operation.
Unlike classical digital computers in which a bit can represent either 1 or 0 at any time, quantum computers use a two-level system, i.e., a qubit, to implement logical operations based on quantum mechanical laws, which can represent both values at once. Owing to the superposition property of qubits, quantum computers have natural parallel processing advantages and thus have potential to exceed the computational efficiency of classical computers for particular tasks. Quantum logic gates are the generalization of classical logic gates in computational networks. It has been proved that two-qubit quantum gates together with one-qubit quantum gates are adequate for constructing networks with any possible quantum computational property. Directional couplers are the most critical elementsfor constructing the quantum gates. In recent years, photonic quantum technologies have emerged as a promising experimental platform for quantum computing. Single photons have robust noise resistance, long coherence time, high transmission speed and great compatibility with other systems. They can be easily manipulated and encoded in any of several degrees of freedom, for example, polarization, path, spatial mode or time bin. Optical waveguide technology enables the realizing of complex optical schemes comprised of many elements with desired scalability, stability and miniaturization. Femtosecond laser direct writing of waveguide has been adopted as a powerful tool for integrated quantum photonics with characteristics of rapidness, cost-effectiveness, mask-less and single-step process. In particular, it has the ability to build arbitrary three-dimensional circuits directly inside bulk materials, which is impossible to achieve with conventional lithography. In this article we review the femtosecond laser writing and quantum characterization of directional coupler and important one-qubit and two-qubit optical quantum logic gates, such as Hadamard gate, Pauli-X gate, controlled-NOT gate, and controlled-Phase gate. The qubits in these gates are usually encoded through optical paths or polarizations of photons. The key to the realization of polarization-encoded one-qubit gates is to achieve flexible wave-plate operations, which is described in detail. Controlled-NOT gate and controlled-phase gate are the most crucial two-qubit gates in the linear optics computation and sometimes they can be converted into each other by adding some one-qubit gates or special superposition states. Many different kinds of waveguide circuits have been used to implement these two-qubit gates. The outlook and challenges for the femtosecond laser writing of three-qubit gates, such as Toffoli gate and Fredkin gate, are briefly introduced.
Implementation of a linear optics quantum multibit half-adder that could show potential scalability is discussed. Parametric down-conversion sources are assumed that are pumped by a mode carrying orbital angular momentum lll. A single photon from a pair is prepared by detection of its twin. This preparation of a single photon defines two bits to be summed and the starting carry control bit. This hyperentangled single photon enters a sequence of optical gates that acts on this photon and ancilla photons. At the adder output, each single photon detected gives the sum operation plus carry. The photons belong to a hyperentangled system with a 23{2}^{3}23 Hilbert space describing each photon. Conditions to have a scalable system for quantum computation define the requirements for construction of this photon source.
In this article, we report, to the best of our knowledge, for the first time, the design and simulation of half-adder and full-adder circuits implemented using continuous variable (CV) quantum gates within the framework of quantum photonics. Our approach supports the high-dimensional nature of CV and offers an alternative to the commonly used discrete variable (DV) systems for scalable and noise-resilient quantum computing architectures. We utilize Gaussian operations, displacement gates, and beamsplitter-based interferometric circuits to perform quantum arithmetic operations, utilizing CV systems' entanglement and superposition principles. Carefully engineered gate sequences and phase-space manipulations allow us to realize logic operations corresponding to classical addition, with each optical mode representing a computational basis state. We present two distinct circuit designs, one for a half adder and one for a full adder, each verified using a CV simulation environment. Our results highlight the potential of continuous platforms to implement arithmetic logic for hybrid classical-quantum processors. This work opens a new pathway towards optical quantum computing with compact, noise-tolerant logic modules using CV quantum information processing.