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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Digital optical adders based on the photon echo effect

A. N. Yashin

Published Sep 26, 1997• 0 citations
Publisher

Abstract

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.

DOI
10.1117/12.287707

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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.
Photon echoes have been studied both experimentally and theoretically, with the main part of the work centred around the concept of using photon echoes for all-optical data storage and processing. The four basic Boolean operators, AND, OR, NOT and XOR have been experimentally demonstrated using photon echoes. These constitute a complete set of Boolean operators. Selective erasure of digital data bits stored using photon echoes have been performed experimentally using three different laser systems with increasing frequency stabilities spanning three orders of magnitude, and the demands put on laser phase- and frequency stability using the suggested erasure method, have been studied. The effects of laser phase- and frequency fluctuations on both ordinary stimulated echoes and on coherently added echoes, have been analysed theoretically using the theory of stochastic processes. The resulting bit error rates in digital optical data processing systems due to such fluctuations have been considered. It has been shown possible experimentally to amplify photon echoes using fibre amplifiers, and to regenerate echoes from echoes amplified with this method. The advantages and limitations of this method for regeneration of photon echoes have been studied.
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.
Word-by-word logical AND and OR operation with photon-echo processing is demonstrated for what is to our knowledge the first time. The photon-echo process can store sequences of optical data before processing. The present logical operations on 8- and 4-bit words are performed by using single-shot frequency-chirped photon echoes. Data rates of approximately 1 MHz, input energies of 1-10 nJ/bit, and output energies in the picojouleper-bit range are demonstrated by using a transition with a transition probability of only 20 s(-1).
In this study, we construct the quantum reversible counterparts of the logical AND, OR, XOR, NOR, and NAND gates. We utilize a quantum Fourier transform (QFT)-based adder circuit that replicates the functionality of a digital half-adder, which computes the sum and carry of two input bits using XOR and AND gates, respectively. To realize different logic gate operations, we apply pre- and post-processing to the QFT-adder using quantum gates, leveraging Boolean algebra properties to enable conversions between various logical functions. Although the number of elementary quantum logic gates increases for a small number of inputs-making the approach appear inefficient at first glance-the overall required qubit count is reduced compared to non-QFT-based designs as the number of inputs increases.
In recent years possible applications of the photon echo process in optical processing, data storage systems, bit-rate conversion of optical pulses, time compression of optical pulses etc. have been investigated.Much of this research aim at replacing electrical components in the framework of today's information networks with components that are entirely based on optics.It is likely that we in the future will see more and more of the electrical components linked to a fibre network being replaced by all optical components, e.g.routers and bit-rate converters.The concept of temporal compression of optical pulses, which is the subject of this thesis, could be used to increase the transmission rate through optical fibres and thereby use the full capacity of today's fibres.It should also be mentioned that more basic components, e.g.XOR gates, are studied in this research field and these components could possibly be used in future concepts of a "light-computer".In this thesis a theoretical model of time compression of both single optical pulses and optical pulse sequences using photon echoes is presented.A full analytical treatment was done for gaussian shaped pulses as a first step of building a numerical model.An analytic approximate approach was also used for both square pulses and pulse sequences.A theoretical understanding of the duration, the intensity spectrum and peak intensity of the compressed signals was reached.It is shown that the intensity spectrum of a compressed pulse sequence containing N bits is completely analogous to the pattern observed in the well-known Fraunhofer diffraction experiment with N slits.A numerical model was built and used to evaluate how non-linearities and noise affect the degree of compression.In addition theoretical models were developed to explain the effects of non-linearities and noise and the hope is that these might be used as guidelines on how to design future experiments in order to achieve highest possible degree of compression.Some of the results presented in this thesis is compared with experimental data obtained in the research group during the time this work was going on.
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.