DOCSLIB.ORG

A Photonic Cluster State Machine Gun

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
A Photonic Cluster State Machine Gun A photonic cluster state machine gun Netanel H. Lindner1 and Terry Rudolph2, 3 1Department of Physics, Technion|Israel Institute of Technology, 32000 Haifa, Israel 2Optics Section, Blackett Laboratory, Imperial College London, London SW7 2BZ, United Kingdom 3Institute for Mathematical Sciences, Imperial College London, London SW7 2BW, United Kingdom We present a method to convert certain single photon sources into devices capable of emitting large strings of photonic cluster state in a controlled and pulsed \on demand" manner. Such sources would greatly reduce the resources required to achieve linear optical quantum computation. Standard spin errors, such as dephasing, are shown to affect only 1 or 2 of the emitted photons at a time. This allows for the use of standard fault tolerance techniques, and shows that the photonic machine gun can be fired for arbitrarily long times. Using realistic parameters for current quantum dot sources, we conclude high entangled-photon emission rates are achievable, with Pauli-error rates per photon of less than 0:2%. For quantum dot sources the method has the added advantage of alleviating the problematic issues of obtaining identical photons from independent, non-identical quantum dots, and of exciton dephasing. PACS numbers: 03.67.-a, 03.67.Lx, 73.43.Nq The primary challenge facing optical quantum compu- charged-exciton decay [6]. We only consider the emitted tation is that of building suitable photon sources. The photons propagating along the z axis. Therefore, if the majority of effort has been directed at single photon initial state of the source is j"i (j#i), an excitation to sources. Four single photons can be used in an inter- the state j *i (j +i) followed by radiative decay, results ferometer to produce a maximally entangled Bell pair in the emission of a single right (left)-circularly polarized of photons [1], and given a source of Bell pairs it is in photon jRi (jLi) and leaves the source in the state j"i principle possible to fuse them [2] into larger so-called (j #i). Now, consider the initial state j "i + j #i, and a cluster states [3]. These somewhat magical quantum coherent excitation pulse with a linear polarization along states can be used for performing quantum computation the x direction. (The exciting pulse itself need not nec- via the simple procedure of making individual (single- essarily propagate along the z direction, which is useful qubit) measurements on the photons involved. Recently for separation of the coherent and emitted light). Such a promising new approach has been to produce Bell pairs a pulse couples equally to both transitions. Therefore, directly [4, 5] via a radiative cascade in quantum dots. the processes described above happen in superposition, However, even an ideal such source would only reduce and the emitted photon will be entangled with the elec- the overall resources required for a full optical quantum tron: the joint state of both systems would be the Bell computation by a small factor. pair j";Ri + j#;Li. Repeating such a procedure would We will show that with current technology it is possible produce GHZ-type entangled states, which are not use- to manipulate certain single photon sources, in particular ful for quantum computing, and for which disentangling quantum dots, so as to generate a continuous stream of the photons from the electron spin is difficult. Moreover, photons entangled in long strings of (various varieties of) the GHZ state is highly vulnerable to decoherence. By 1-dimensional cluster states. Using these strings, cluster contrast, the cluster states suffer none of these problems. states capable of running arbitrary quantum algorithms To see how to create cluster states, we now imagine can be very efficiently generated by fusion. We analyze that before the second excitation of the system, when the all error mechanisms and show that the error rates can be state of the spin and the first photon is j"ijR1i + j#ijL1i, very low - close to fault tolerant thresholds for quantum the spin undergoes a π=2-rotation about the y-axis. Un- computing - even if the source is operated for timescales der this operation, described by exp(−iY π=4) the state much longer than the typical decoherence times. evolves to (j"i+j#i)jR1i+(−|"i+j#i)jL1i. A second pulse We begin with a highly idealized description of the excitation, accompanied by a second photon emission, arXiv:0810.2587v2 [quant-ph] 23 Aug 2009 proposal. Consider a source with a degenerate spin 1=2 will now result in the two photons and the electron spin ground state manifold. The basis j"i, j#i denotes the spin being in the state (j"ijR2i + j#ijL2i)jR1i + (−|"ijR2i + j# projection along the z axis. Furthermore, imagine that ijL2i)jL1i. In terms of abstract (logical) qubit encodings optical transitions at frequency !0 are possible only to we will take jRi ≡ j0i; jLi ≡ −|1i. It can be readily a doubly degenerate excited state manifold. The excited verified that rotating the spin with another π=2 rota- states j *i, j +i have Jz = ±3=2~, thus only the (single tion, now leaves the spin and two photons in the state: photon) transitions j"i $ j *i and j#i $ j +i are allowed. j000i+j001i+j010i−j011i+j100i+j101i−j110i+j111i; Such transitions are well known to occur, for example, which is exactly the 3 qubit linear cluster state. Repeat- in quantum dots (QDs) which emit single photons via ing the process of excitation followed by π=2 rotation, 2 confinement. They correspond to trions containing two Y electrons in the singlet state and a light hole or heavy electron hole respectively. We can consider only the heavy trions spin H H H H H H and neglect the mixing between them. In other systems, while the transitions to Jz = ±1=2 may be energetically photon 5 split off by an external field, or may simply have differ- ent couplings, generically they will still lead to imper- fections equivalent to non-orthogonality of the emitted Z photons. Moreover processes in other systems tend to Y be slower, and temporally longer pulses may well also be photon 1 state linear Output cluster required because of nearby energy levels. Although these problems can be remedied somewhat by applying proper filtration protocols to the output cluster state (at the ex- FIG. 1: (Color online) A quantum circuit readily verified pense of larger loss rates) we focus on quantum dots for to output linear cluster state. For mapping to the clus- ter state machine gun, the top qubit line is the electron which the suppression is essentially perfect, the processes spin, the Hadamard gates are replaced by single qubit uni- are fast, and the energy levels well separated. taries exp(−iπY=4) (requiring the careful tracking of certain Although other options exist, we will consider from phases), and the physical process of creating a photon with now on the situation where the π=2 rotations on the spin left/right circular polarization conditioned on the state of the are performed by placing the quantum dot in a constant electron spin becomes the controlled not gate which leaves magnetic field of strength B which is directed along the the qubit (photon) in state j0i (i.e. jRi) if the electron spin is y-direction (i.e. in the plane of the dot). The spin preces- in state j0i (i.e. j"i), but otherwise flips it. Crucially, as de- picted, a Pauli Y error on the spin localizes; i.e it is equivalent sion at frequency !B = geµB=~ in the z-x plane therefore to Y and Z errors on the next two photons produced. implements the desired rotation every Tcycle = π=2!B. Suitably timed strobing of the dot by the excitation pulse, followed by the rapid exciton decay, will therefore enable will produce a third photon such that the electron and the machine-gun-like generation of 1d cluster state de- three photons are in a 4-qubit linear cluster state. The scribed above. procedure can, in principle, be repeated indefinitely, pro- The potential imperfections to be considered are as fol- ducing a continuous chain of photons in an entangled lin- lows: (i) The non-zero lifetime of the trion τdecay means ear cluster state. Note that one advantage of producing a that the magnetic field causes precession of the electrons cluster state is that the electron can be readily disentan- during the emission process. This leads to errors induced gled from the string of entangled photons, for example on the quantum circuit of Fig 1; however we shall find by making a computational (jRi; jLi) basis measurement that they can be understood as implementing an error on the most recently created photon. In fact, since in model on the final output cluster state which takes the general the initial state of the spin will be mixed, such a form of Pauli errors occurring with some independent detection of a photon in state jRi(jLi) polarization can probability on pairs of (photonic) qubits. (ii) Interaction also be used to project the spin to the j"i (j#i) state, of the electron spin with its environment results in a non- and initializes the cluster state (either outcome is ok). It unitary evolution of the spin. This evolution consists of can be readily verified that the whole idealized procedure two parts: decoherence (in which we include both de- just described is equivalent to the qubit quantum circuit phasing and spin flips) and spin relaxation. Decoherence depicted in Fig. 1. is characterized by a T2 time.
Load more

Recommended publications
  • Quantum Entanglement Concentration Based on Nonlinear Optics for Quantum Communications
    Entropy 2013, 15, 1776-1820; doi:10.3390/e15051776 OPEN ACCESS entropy ISSN 1099-4300 www.mdpi.com/journal/entropy Review Quantum Entanglement Concentration Based on Nonlinear Optics for Quantum Communications Yu-Bo Sheng 1;2;* and Lan Zhou 2;3 1 Institute of Signal Processing Transmission, Nanjing University of Posts and Telecommunications, Nanjing 210003, China 2 Key Lab of Broadband Wireless Communication and Sensor Network Technology, Nanjing University of Posts and Telecommunications, Ministry of Education, Nanjing 210003, China 3 College of Mathematics & Physics, Nanjing University of Posts and Telecommunications, Nanjing 210003, China; E-Mail: [email protected] (L.Z.) * Author to whom correspondence should be addressed; E-Mail: [email protected]; Tel./Fax: +86-025-83492417. Received: 14 March 2013; in revised form: 3 May 2013 / Accepted: 8 May 2013 / Published: 16 May 2013 Abstract: Entanglement concentration is of most importance in long distance quantum communication and quantum computation. It is to distill maximally entangled states from pure partially entangled states based on the local operation and classical communication. In this review, we will mainly describe two kinds of entanglement concentration protocols. One is to concentrate the partially entangled Bell-state, and the other is to concentrate the partially entangled W state. Some protocols are feasible in current experimental conditions and suitable for the optical, electric and quantum-dot and optical microcavity systems. Keywords: quantum entanglement; entanglement concentration; quantum communication 1. Introduction Quantum communication and quantum computation have attracted much attention over the last 20 years, due to the absolute safety in the information transmission for quantum communication and the super fast factoring for quantum computation [1,2].
    [Show full text]
  • Quantum Macroscopicity Versus Distillation of Macroscopic
    Quantum macroscopicity versus distillation of macroscopic superpositions Benjamin Yadin1 and Vlatko Vedral1, 2 1Atomic and Laser Physics, Clarendon Laboratory, University of Oxford, Parks Road, Oxford, OX1 3PU, UK 2Centre for Quantum Technologies, National University of Singapore, Singapore 117543 (Dated: October 7, 2018) We suggest a way to quantify a type of macroscopic entanglement via distillation of Greenberger- Horne-Zeilinger states by local operations and classical communication. We analyze how this relates to an existing measure of quantum macroscopicity based on the quantum Fisher information in sev- eral examples. Both cluster states and Kitaev surface code states are found to not be macroscopically quantum but can be distilled into macroscopic superpositions. We look at these distillation pro- tocols in more detail and ask whether they are robust to perturbations. One key result is that one-dimensional cluster states are not distilled robustly but higher-dimensional cluster states are. PACS numbers: 03.65.Ta, 03.67.Mn, 03.65.Ud I. INTRODUCTION noted here by N ∗. We will not impose any cut-off above which a value of N ∗ counts as macroscopic, but instead Despite the overwhelming successes of quantum me- consider families of states parameterized by some obvious chanics, one of its greatest remaining problems is to ex- size quantity N (e.g. the number of qubits). Then the plain why it appears to break down at the macroscopic relevant property of the family is the scaling of N ∗ with scale. In particular, macroscopic objects are never seen N. The case N ∗ = O(N) is ‘maximally macroscopic’ [9]. in quantum superpositions.
    [Show full text]
  • Bidirectional Quantum Controlled Teleportation by Using Five-Qubit Entangled State As a Quantum Channel
    Bidirectional Quantum Controlled Teleportation by Using Five-qubit Entangled State as a Quantum Channel Moein Sarvaghad-Moghaddam1,*, Ahmed Farouk2, Hussein Abulkasim3 to each other simultaneously. Unfortunately, the proposed Abstract— In this paper, a novel protocol is proposed for protocol required additional quantum and classical resources so implementing BQCT by using five-qubit entangled states as a that the users required two-qubit measurements and applying quantum channel which in the same time, the communicated users global unitary operations. There are many approaches and can teleport each one-qubit state to each other under permission prototypes for the exploitation of quantum principles to secure of controller. The proposed protocol depends on the Controlled- the communication between two parties and multi-parties [18, NOT operation, proper single-qubit unitary operations and single- 19, 20, 21, 22]. While these approaches used different qubit measurement in the Z-basis and X-basis. The results showed that the protocol is more efficient from the perspective such as techniques for achieving a private communication among lower shared qubits and, single qubit measurements compared to authorized users, but most of them depend on the generation of the previous work. Furthermore, the probability of obtaining secret random keys [23, 2]. In this paper, a novel protocol is Charlie’s qubit by eavesdropper is reduced, and supervisor can proposed for implementing BQCT by using five-qubit control one of the users or every two users. Also, we present a new entanglement state as a quantum channel. In this protocol, users method for transmitting n and m-qubits entangled states between may transmit an unknown one-qubit quantum state to each other Alice and Bob using proposed protocol.
    [Show full text]
  • G53NSC and G54NSC Non Standard Computation Research Presentations
    G53NSC and G54NSC Non Standard Computation Research Presentations March the 23rd and 30th, 2010 Tuesday the 23rd of March, 2010 11:00 - James Barratt • Quantum error correction 11:30 - Adam Christopher Dunkley and Domanic Nathan Curtis Smith- • Jones One-Way quantum computation and the Measurement calculus 12:00 - Jack Ewing and Dean Bowler • Physical realisations of quantum computers Tuesday the 30th of March, 2010 11:00 - Jiri Kremser and Ondrej Bozek Quantum cellular automaton • 11:30 - Andrew Paul Sharkey and Richard Stokes Entropy and Infor- • mation 12:00 - Daniel Nicholas Kiss Quantum cryptography • 1 QUANTUM ERROR CORRECTION JAMES BARRATT Abstract. Quantum error correction is currently considered to be an extremely impor- tant area of quantum computing as any physically realisable quantum computer will need to contend with the issues of decoherence and other quantum noise. A number of tech- niques have been developed that provide some protection against these problems, which will be discussed. 1. Introduction It has been realised that the quantum mechanical behaviour of matter at the atomic and subatomic scale may be used to speed up certain computations. This is mainly due to the fact that according to the laws of quantum mechanics particles can exist in a superposition of classical states. A single bit of information can be modelled in a number of ways by particles at this scale. This leads to the notion of a qubit (quantum bit), which is the quantum analogue of a classical bit, that can exist in the states 0, 1 or a superposition of the two. A number of quantum algorithms have been invented that provide considerable improvement on their best known classical counterparts, providing the impetus to build a quantum computer.
    [Show full text]
  • Quadratic Entanglement Criteria for Qutrits K
    Vol. 137 (2020) ACTA PHYSICA POLONICA A No. 3 Quadratic Entanglement Criteria for Qutrits K. Rosołeka, M. Wieśniaka;b;∗and L. Knipsc;d aInstitute of Theoretical Physics and Astrophysics, Faculty of Mathematics, Physics, and Informatics, University of Gdańsk, 80-308 Gdańsk, Poland bInternational Centre for Theories of Quantum Technologies, University of Gdańsk, Wita Swosza 57, 80-308 Gdańsk, Poland cMax-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, D-85748 Garching, Germany dDepartment für Physik, Ludwig-Maximilians-Universität, D-80797 München, Germany (Received September 10, 2019; revised version December 2, 2019; in final form December 5, 2019) The problem of detecting non-classical correlations of states of many qudits is incomparably more involved than in the case of qubits. One reason is that for qubits we have a convenient description of the system by the means of the well-studied correlation tensor allowing to encode the complete information about the state in mean values of dichotomic measurements. The other reason is the more complicated structure of the state space, where, for example, different Schmidt ranks or bound entanglement comes into play. We demonstrate that for three-dimensional quantum subsystems we are able to formulate nonlinear entanglement criteria of the state with existing formalisms. We also point out where the idea for constructing these criteria fails for higher-dimensional systems, which poses well-defined open questions. DOI: 10.12693/APhysPolA.137.374 PACS/topics: quantum information, quantum correlations, entanglements, qutrits 1. Introduction practical reasons. The task is very simple for pure states, which practically never occur in a real life. However, for For complex quantum systems, we distinguish between mixed states, it is still an open question.
    [Show full text]
  • Quantum Computing Cluster State Model
    Quantum Computing Cluster State Model Phillip Blakey, Alex Karapetyan, Thomas Ma December 2019 1 Introduction The traditional circuit-based model of quantum computation is strictly based on unitary evolution. Especially in view of the Principle of Deferred Measurement in the context of implementation of algorithms with the circuit model, the role of measurement is secondary to unitary quantum gates - a quantum circuit, sans the final measurements, is the application of a carefully crafted unitary transformation to a carefully chosen initial quantum state. Measurement is a non-unitary operation and thereby ruins quantum states. The cluster state model of quantum computing, also known as a \one-way quantum computer", is based on the idea of performing a sequence of single-qubit measurements on some large initial state, resulting in an output in the form of a several-qubit state. In particular, measurement is essential to the entirety of any computation, in contrast to the circuit model. This model was first introduced in [1] (see also [2]), and it has been studied from both the theoretical and experimental implementation points of view. The initial state of a computation in this model, called a cluster state, is a specially prepared entangled state associated to a particularly chosen graph. To perform a quantum computation on a cluster state, the rules of the game are: (a) the allowed operations are single-qubit measurements in any basis on any of the nodes of the graph, (b) the basis in which to measure at every stage of the sequence is conditioned on the outcome of the previous measurement, and (c) efficient classical processing is allowed on the measurement outcomes.
    [Show full text]
  • Logical Measurement-Based Quantum Computation in Circuit-QED
    www.nature.com/scientificreports OPEN Logical measurement-based quantum computation in circuit- QED Jaewoo Joo1,2*, Chang-Woo Lee 1,3, Shingo Kono4 & Jaewan Kim1 We propose a new scheme of measurement-based quantum computation (MBQC) using an error- correcting code against photon-loss in circuit quantum electrodynamics. We describe a specifc protocol of logical single-qubit gates given by sequential cavity measurements for logical MBQC and a generalised Schrödinger cat state is used for a continuous-variable (CV) logical qubit captured in a microwave cavity. To apply an error-correcting scheme on the logical qubit, we utilise a d-dimensional quantum system called a qudit. It is assumed that a three CV-qudit entangled state is initially prepared in three jointed cavities and the microwave qudit states are individually controlled, operated, and measured through a readout resonator coupled with an ancillary superconducting qubit. We then examine a practical approach of how to create the CV-qudit cluster state via a cross-Kerr interaction induced by intermediary superconducting qubits between neighbouring cavities under the Jaynes- Cummings Hamiltonian. This approach could be scalable for building 2D logical cluster states and therefore will pave a new pathway of logical MBQC in superconducting circuits toward fault-tolerant quantum computing. Measurement-based quantum computation (MBQC) ofers a new platform of quantum information (QI) pro- cessing. Quantum algorithms are performed by sequential single-qubit measurements in multipartite entangled states initially (e.g., cluster states1) instead of massive controls of individual qubits during the whole information processing2,3. Tis advantage is, however, only benefcial for QI processing if the specifc multipartite entangled state can be initially well-prepared and the capability of fast and precise single-qubit measurements are viable.
    [Show full text]
  • Large-Scale Cluster-State Entanglement in the Quantum Optical Frequency Comb
    Large-Scale Cluster-State Entanglement in the Quantum Optical Frequency Comb Moran Chen Nanchong, Sichuan, China B.S. Physics, Beijing Normal University, 2009 A Dissertation presented to the Graduate Faculty of the University of Virginia in Candidacy for the degree of Doctor of Philosophy Department of Physics University of Virginia May 2015 c Copyright All Rights Reserved Moran Chen Ph.D., May 2015 i Acknowledgments First of all, I would like to thank my adviser, Prof. Olivier Pfister. Without his help and guidance, all of the research and work described in this thesis would have been impossible. I am wholeheartedly grateful to have him as my adviser. He gave me enough freedom and trust to allow me to conduct research and independent thinking on my own, and his incredible patience and knowledge in both the theory and in the experiments also gave me confidence and reassurance when I came across obstacles and difficulties. He is also always encouraging and kind, and is the best adviser I could have hoped for. He has led me into the amazing field of quantum optics, and I am truly blessed to have him as my adviser. I want to give special thanks to our theoretical collaborator Nick Menicucci. Nick is an outstanding theorist and a very smart, quick and straightforward person, and it has always been a pleasure talking with him about research topics or other general issues. We had many good and interesting discussions and his genius ideas and simplified theoretical proposals helped make our experiment easier and more feasible. I am truly thankful to have him as our theoretical collaborator and friend.
    [Show full text]
  • Continuous-Variable Gaussian Analog of Cluster States
    PHYSICAL REVIEW A 73, 032318 ͑2006͒ Continuous-variable Gaussian analog of cluster states Jing Zhang1,* and Samuel L. Braunstein2 1State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan 030006, People’s Republic of China 2Computer Science, University of York, York YO10 5DD, United Kingdom ͑Received 21 October 2005; published 16 March 2006͒ We present a continuous-variable ͑CV͒ Gaussian analog of cluster states, a new class of CV multipartite entangled states that can be generated from squeezing and quantum nondemolition coupling HI = ប␹XAXB. The entanglement properties of these states are studied in terms of classical communication and local operations. The graph states as general forms of the cluster states are presented. A chain for a one-dimensional example of cluster states can be readily experimentally produced only with squeezed light and beam splitters. DOI: 10.1103/PhysRevA.73.032318 PACS number͑s͒: 03.67.Hk, 03.65.Ta I. INTRODUCTION ment. The study of entanglement properties of the harmonic chain has aroused great interest ͓12͔, which is in direct anal- Entanglement is one of the most fascinating features of ogy to a spin chain with an Ising interaction. To date, the quantum mechanics and plays a central role in quantum- study and application of CV multipartite entangled states has information processing. In recent years, there has been an mainly focused on CV GHZ-type states. However, a richer ongoing effort to characterize qualitatively and quantitatively understanding and more definite classification of CV multi- the entanglement properties of multiparticle systems and ap- partite entangled states are needed for developing a CV ply them in quantum communication and information.
    [Show full text]
  • Aqis'07 Program
    AQIS’07 PROGRAM Reception desk will be open for registration at 8:30 on September 3. September 2, 2007 (Sunday) 19:00 - 21:00 [Welcome Reception at Shirankaikan (Conference Venue)] September 3, 2007 (Monday) 8:50 - 9:00 [Opening] 9:00 - 10:30 [Invited Talks] 9:00 - 9:45 Complementarity, distillable key, and distillable entanglement Masato Koashi (Osaka University) 9:45 - 10:30 Quantum algorithms for formula evaluation Ben W. Reichardt (Caltech) 11:00 - 12:30 [Long Talks] NONLOCALITY 11:00 - 11:30 All bipartite entangled states display some hidden nonlocality Lluis Masanes (University of Bristol), Yeong-Cherng Liang (University of Queensland), and Andrew C. Doherty (University of Queensland) 11:30 - 12:00 Detection loophole in asymmetric Bell experiments Nicolas Brunner (Group of Applied physics / Uni. of Geneva), Nicolas Gisin (Group of Applied physics / Uni. of Geneva), Christoph Simon (Group of Applied physics / Uni. of Geneva), and Valerio Scarani (Department of Physics, Faculty of Science, National University of Singapore) 12:00 - 12:30 No nonlocal box is universal Fr´ed´eric Dupuis (Universit´ede Montr´eal), Nicolas Gisin (Universit´ede Gen`eve), Avinatan Hasidim (He- brew University), Andr´eAllan M´ethot (Universit´ede Gen`eve), and Haran Pilpel (Hebrew University) 14:30 - 16:10 [Parallel session A] QUANTUM CIRCUITS & QUANTUM ALGS 14:30 - 14:50 The Quantum Fourier Transform on a Linear Nearest Neighbor Architecture Yasuhiro Takahashi (NTT Communication Science Laboratories), Noboru Kunihiro (The University of Electro-Communications), and Kazuo Ohta (The University of Electro-Communications) 14:50 - 15:10 Shor’s algorithm on a nearest-neighbor machine Samuel A.
    [Show full text]
  • One-Way Quantum Computer Simulation
    One-Way Quantum Computer Simulation Eesa Nikahd, Mahboobeh Houshmand, Morteza Saheb Zamani, Mehdi Sedighi Quantum Design Automation Lab Department of Computer Engineering and Information Technology Amirkabir University of Technology Tehran, Iran {e.nikahd, houshmand, szamani, msedighi}@aut.ac.ir Abstract— In one-way quantum computation (1WQC) model, universal quantum computations are performed using measurements to designated qubits in a highly entangled state. The choices of bases for these measurements as well as the structure of the entanglements specify a quantum algorithm. As scalable and reliable quantum computers have not been implemented yet, quantum computation simulators are the only widely available tools to design and test quantum algorithms. However, simulating the quantum computations on a standard classical computer in most cases requires exponential memory and time. In this paper, a general direct simulator for 1WQC, called OWQS, is presented. Some techniques such as qubit elimination, pattern reordering and implicit simulation of actions are used to considerably reduce the time and memory needed for the simulations. Moreover, our simulator is adjusted to simulate the measurement patterns with a generalized flow without calculating the measurement probabilities which is called extended one-way quantum computation simulator (EOWQS). Experimental results validate the feasibility of the proposed simulators and that OWQS and EOWQS are faster as compared with the well-known quantum circuit simulators, i.e., QuIDDPro and libquantum for simulating 1WQC model1. Keywords-Quantum Computing, 1WQC, Simulation 1 INTRODUCTION Quantum information [2] is an interdisciplinary field which combines quantum physics, mathematics and computer science. Quantum computers have some advantages over the classical ones, e.g., they give dramatic speedups for tasks such as integer factorization [3] and database search [4].
    [Show full text]
  • Entanglement Distribution in Quantum Networks
    Technische Universitat¨ Munchen¨ Max-Planck–Institut f¨ur Quantenoptik Entanglement Distribution in Quantum Networks S´ebastien Perseguers Vollst¨andiger Abdruck der von der Fakult¨at f¨ur Physik der Technischen Universit¨at M¨unchen zur Erlangung des akademischen Grades eines Doktors der Naturwissenschaften (Dr. rer. nat.) genehmigten Dissertation. Vorsitzender : Univ.-Prof. J. J. Finley, Ph.D. Pr¨ufer der Dissertation : 1. Hon.-Prof. I. Cirac, Ph.D. 2. Univ.-Prof. Dr. P. Vogl Die Dissertation wurde am 25.02.2010 bei der Technischen Universit¨at M¨unchen eingereicht und durch die Fakult¨at f¨ur Physik am 15.04.2010 angenommen. Every great and deep difficulty bears in itself its own “ solution. It forces us to change our thinking in order to find it. ” – Niels Bohr Abstract This Thesis contributes to the theory of entanglement distribution in quantum networks, analyzing the generation of long-distance entangle- ment in particular. We consider that neighboring stations share one par- tially entangled pair of qubits, which emphasizes the difficulty of creating remote entanglement in realistic settings. The task is then to design local quantum operations at the stations, such that the entanglement present in the links of the whole network gets concentrated between few parties only, regardless of their spatial arrangement. First, we study quantum networks with a two-dimensional lattice struc- ture, where quantum connections between the stations (nodes) are de- scribed by non-maximally entangled pure states (links). We show that the generation of a perfectly entangled pair of qubits over an arbitrarily long distance is possible if the initial entanglement of the links is larger than a threshold.
    [Show full text]