Photonic Implementation of the One-Way Model of Quantum Computation

Le calcul quantique par consommation d'intrication requiert comme ressource initiale un type particulier d'état intriqué, les  "états graphesÂ". Il s'effectue en mesurant des bits quantiques (qubits) uniques dans differentes bases. Ces bases dépendent de l'algorithme utilisé et des résultats des mesures précédentes. Ainsi, on doit pouvoir stocker les nouveaux qubits d'une certaine façon pendant qu'on traite les résultats des mesures précédentes. Pour la mise en application de ce modèle (le calcul par consommation d'intrication) en photonique, les fibres optiques constituent la manière la plus pratique de stocker des qubits. Le temps d'arrivée de chaque photon au détecteur, que l'on nomme qubit temporel, est le degré de liberté le plus robuste associé aux photons se propageant dans les fibres optiques. Pour créer la ressource intriquée initiale, on doit d'abord produire des paires de photons EPR, photons qui sont totalement indifférenciables les uns des autres dans tous leurs degrés de liberté, sauf celui qui permettra d'encoder les qubits logiques. Ces paires de photons sont combinées au moyen de portes fusion pour produire des états graphes plus grands. Les portes fusion ne sont pas déterministes et elles présentent une probabilité limitée de succès. De plus, il faut pouvoir stocker les photons. Pour la réalisation de ce modèle basé sur les qubits temporels, on utilise une combinaison particulière de coupleurs 50/50 tout-fibre et de modulateurs électro-optiques pour constituer les portes fusion, ainsi que les portes à qubit unique arbitraires, qui sont nécessaires au calcul en soi. Ces deux étapes, soit la production de graphes au moyen des portes fusion et l'exécution du calcul quantique, exigent le stockage de qubits temporels, ce que la méthode proposée utilisant la fibre optique permet de faire tout naturellement. L'une des questions auxquelles se sont intéressés les mathématiciens qui travaillent sur le calcul par consommation d'intrication est la détermination des calculs possibles à partir d'un état graphe donné, ainsi que les possibilités de qubits d'entrée et de sortie pour cet état graphe. Les études qu'ils ont faites ont permis d'établir un algorithme utilisé pour élaborer une séquence de mesures et de corrections menant à un calcul déterministe à partir d'un état graphe. Cette séquence est ce qu'on appelle un ot simple tracé sur un graphe. Récemment, on a modifié cet algorithme de manière à trouver le ot généralisé, soit une séquence de calculs sur des graphes présentant des géométries particulières, comme des graphes contenant des structures en boucle. Dans le cadre de cette thèse, nous avons expérimentalement réalisé un graphe en boucle à 4 qubits comportant un qubit d'entrée, c'est-à-dire le plus petit graphe admettant un flot généralisé mais pas de flot simple. Les graphes de ce type à structure en boucle conduisent à une boucle temporelle, donc un circuit non exécutable. Toutefois,----------Abstract The one-way model of quantum computation (QC) uses a particular type of entangled state as its initial resource, which are called graph states. The computation is then performed by measuring single qubits in various bases. These bases depend on the algorithm that is being implemented and the results of the previous measurements. Hence, the qubits need to be stored in some way, while the results of the previous measurements are being processed. For the photonic implementation of this model, optical fibers are the most practical choice for storing the qubits. The arrival time of each photon at the detector, referred to as the time-bin qubit, is the most robust physical degree of freedom of photons in optical fibers. In order to make the initial entangled resource, one first produces EPR-type entangled pairs of photons, which are fully indistinguishable in all their degrees of freedom, but the one that is encoding the logical qubits. Using fusion gates, these photon pairs are combined to produce larger graph states. Fusion gates are not deterministic and have a finite probability of success. For them to be scalable, one further requires storage of photons. For the implementation of this model by time-bin qubits, one uses a special combination of all-fiber 50 : 50 couplers and electro-optical modulators to perform the fusion gates, in addition to the arbitrary single qubit gates necessary for performing the computation itself. Both these steps, namely the production of graphs using fusion gates and performing the quantum computation, require storage of time-bin qubits, which is implemented naturally in the proposed scheme that takes advantage of optical fibers. One of the questions that has been addressed by the mathematicians working on the oneway model is how to figure out what computations are possible, if any, by a given graph state and the choices of input and output qubits on this graph state. These studies have led to the development of an algorithm for finding a proper pattern of measurements and corrections that leads to deterministic quantum computation on the graph state. This pattern is said to be a flow on the graph. Recently this algorithm is generalized to finding the generalized flow, which are computation patterns on graphs with interesting geometries, such as graphs that contain loop structures. We experimentally realize a 4-qubit loop graph with an input qubit that renders it to be the smallest graph with a generalized flow and no flow. Such graphs with a loop structure result into a time-like loop and thus a circuit that is not runnable. Using generalized flow, however, allows us to find an equivalent to the loop graph that respects the ordinary time line and is runnable. Bennett, Schumacher and Svetlichny (BSS) have proposed using quantum teleportation and post-selection to simulate time-like loops. It is shown that time-like loops arise naturall

Manipulating time-bin qubits with fiber optics components

We propose two experimental schemes to implement arbitrary unitary single qubit operations on single photons encoded in time-bin qubits. Both schemes require fiber optics components that are available with current technology.Comment: 2 pages, 3 figures, to be published in the proceedings of the IEEE LEOS 2006 topical meeting, Quebec city, Canada, July 200

Cluster state quantum computing in optical fibers

A scheme for the implementation of the cluster state model of quantum computing in optical fibers, which enables the feedforward feature, is proposed. This scheme uses the time-bin encoding of qubits. Following previously suggested methods of applying arbitrary one-qubit gates in optical fibers, two different ways for the realization of fusion gate types I and II for cluster production are proposed: a fully time-bin based encoding scheme and a combination of time-bin and polarization based encoding scheme. Also the methods of measurement in any desired bases for the purpose of the processing of cluster state computing for both these encodings are explained.Comment: 6 pages, 11 figures, submitted to the Optical Quantum-Information Science focus issue of JOSA

Violation of Heisenberg's Measurement-Disturbance Relationship by Weak Measurements

While there is a rigorously proven relationship about uncertainties intrinsic to any quantum system, often referred to as "Heisenberg's Uncertainty Principle," Heisenberg originally formulated his ideas in terms of a relationship between the precision of a measurement and the disturbance it must create. Although this latter relationship is not rigorously proven, it is commonly believed (and taught) as an aspect of the broader uncertainty principle. Here, we experimentally observe a violation of Heisenberg's "measurement-disturbance relationship", using weak measurements to characterize a quantum system before and after it interacts with a measurement apparatus. Our experiment implements a 2010 proposal of Lund and Wiseman to confirm a revised measurement-disturbance relationship derived by Ozawa in 2003. Its results have broad implications for the foundations of quantum mechanics and for practical issues in quantum mechanics.Comment: 5 pages, 4 figure

Closed timelike curves via post-selection: theory and experimental demonstration

Closed timelike curves (CTCs) are trajectories in spacetime that effectively travel backwards in time: a test particle following a CTC can in principle interact with its former self in the past. CTCs appear in many solutions of Einstein's field equations and any future quantum version of general relativity will have to reconcile them with the requirements of quantum mechanics and of quantum field theory. A widely accepted quantum theory of CTCs was proposed by Deutsch. Here we explore an alternative quantum formulation of CTCs and show that it is physically inequivalent to Deutsch's. Because it is based on combining quantum teleportation with post-selection, the predictions/retrodictions of our theory are experimentally testable: we report the results of an experiment demonstrating our theory's resolution of the well-known `grandfather paradox.Comment: 5 pages, 4 figure