Asymptotic Improvements to Quantum Circuits Via Qutrits
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Modern Quantum Technologies of Information Security
MODERN QUANTUM TECHNOLOGIES OF INFORMATION SECURITY Oleksandr Korchenko 1, Yevhen Vasiliu 2, Sergiy Gnatyuk 3 1,3 Dept of Information Security Technologies, National Aviation University, Kosmonavta Komarova Ave 1, 03680 Kyiv, Ukraine 2Dept of Information Technologies and Control Systems, Odesa National Academy of Telecommunications n.a. O.S. Popov, Koval`ska Str 1, 65029 Odesa, Ukraine E-mails: [email protected], [email protected], [email protected] In this paper, the systematisation and classification of modern quantum technologies of information security against cyber-terrorist attack are carried out. The characteristic of the basic directions of quantum cryptography from the viewpoint of the quantum technologies used is given. A qualitative analysis of the advantages and disadvantages of concrete quantum protocols is made. The current status of the problem of practical quantum cryptography use in telecommunication networks is considered. In particular, a short review of existing commercial systems of quantum key distribution is given. 1. Introduction Today there is virtually no area where information technology ( ІТ ) is not used in some way. Computers support banking systems, control the work of nuclear reactors, and control aircraft, satellites and spacecraft. The high level of automation therefore depends on the security level of IT. The latest achievements in communication systems are now applied in aviation. These achievements are public switched telephone network (PSTN), circuit switched public data network (CSPDN), packet switched public data network (PSPDN), local area network (LAN), and integrated services digital network (ISDN) [73]. These technologies provide data transmission systems of various types: surface-to-surface, surface-to-air, air-to-air, and space telecommunication. -
Quantum Information in the Posner Model of Quantum Cognition
Quantum information in quantum cognition Nicole Yunger Halpern1, 2 and Elizabeth Crosson1 1Institute for Quantum Information and Matter, Caltech, Pasadena, CA 91125, USA 2Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106, USA (Dated: November 15, 2017) Matthew Fisher recently postulated a mechanism by which quantum phenomena could influence cognition: Phosphorus nuclear spins may resist decoherence for long times. The spins would serve as biological qubits. The qubits may resist decoherence longer when in Posner molecules. We imagine that Fisher postulates correctly. How adroitly could biological systems process quantum information (QI)? We establish a framework for answering. Additionally, we apply biological qubits in quantum error correction, quantum communication, and quantum computation. First, we posit how the QI encoded by the spins transforms as Posner molecules form. The transformation points to a natural computational basis for qubits in Posner molecules. From the basis, we construct a quantum code that detects arbitrary single-qubit errors. Each molecule encodes one qutrit. Shifting from information storage to computation, we define the model of Posner quantum computation. To illustrate the model's quantum-communication ability, we show how it can teleport information in- coherently: A state's weights are teleported; the coherences are not. The dephasing results from the entangling operation's simulation of a coarse-grained Bell measurement. Whether Posner quantum computation is universal remains an open question. However, the model's operations can efficiently prepare a Posner state usable as a resource in universal measurement-based quantum computation. The state results from deforming the Affleck-Lieb-Kennedy-Tasaki (AKLT) state and is a projected entangled-pair state (PEPS). -
Parafermions in a Kagome Lattice of Qubits for Topological Quantum Computation
PHYSICAL REVIEW X 5, 041040 (2015) Parafermions in a Kagome Lattice of Qubits for Topological Quantum Computation Adrian Hutter, James R. Wootton, and Daniel Loss Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland (Received 3 June 2015; revised manuscript received 16 September 2015; published 14 December 2015) Engineering complex non-Abelian anyon models with simple physical systems is crucial for topological quantum computation. Unfortunately, the simplest systems are typically restricted to Majorana zero modes (Ising anyons). Here, we go beyond this barrier, showing that the Z4 parafermion model of non-Abelian anyons can be realized on a qubit lattice. Our system additionally contains the Abelian DðZ4Þ anyons as low-energetic excitations. We show that braiding of these parafermions with each other and with the DðZ4Þ anyons allows the entire d ¼ 4 Clifford group to be generated. The error-correction problem for our model is also studied in detail, guaranteeing fault tolerance of the topological operations. Crucially, since the non- Abelian anyons are engineered through defect lines rather than as excitations, non-Abelian error correction is not required. Instead, the error-correction problem is performed on the underlying Abelian model, allowing high noise thresholds to be realized. DOI: 10.1103/PhysRevX.5.041040 Subject Areas: Condensed Matter Physics, Quantum Physics, Quantum Information I. INTRODUCTION Non-Abelian anyons supported by a qubit system Non-Abelian anyons exhibit exotic physics that would typically are Majorana zero modes, also known as Ising – make them an ideal basis for topological quantum compu- anyons [12 15]. A variety of proposals for experimental tation [1–3]. -
Arxiv:1807.01863V1 [Quant-Ph] 5 Jul 2018 Β 2| +I Γ 2 =| I 1
Quantum Error Correcting Code for Ternary Logic Ritajit Majumdar1,∗ Saikat Basu2, Shibashis Ghosh2, and Susmita Sur-Kolay1y 1Advanced Computing & Microelectronics Unit, Indian Statistical Institute, India 2A. K. Choudhury School of Information Technology, University of Calcutta, India Ternary quantum systems are being studied because these provide more computational state space per unit of information, known as qutrit. A qutrit has three basis states, thus a qubit may be considered as a special case of a qutrit where the coefficient of one of the basis states is zero. Hence both (2 × 2)-dimensional as well as (3 × 3)-dimensional Pauli errors can occur on qutrits. In this paper, we (i) explore the possible (2 × 2)-dimensional as well as (3 × 3)-dimensional Pauli errors in qutrits and show that any pairwise bit swap error can be expressed as a linear combination of shift errors and phase errors, (ii) propose a new type of error called quantum superposition error and show its equivalence to arbitrary rotation, (iii) formulate a nine qutrit code which can correct a single error in a qutrit, and (iv) provide its stabilizer and circuit realization. I. INTRODUCTION errors or (d d)-dimensional errors only and no explicit circuit has been× presented. Quantum computers hold the promise of reducing the Main Contributions: In this paper, we study error cor- computational complexity of certain problems. However, rection in qutrits considering both (2 2)-dimensional × quantum systems are highly sensitive to errors; even in- as well as (3 3)-dimensional errors. We have intro- × teraction with environment can cause a change of state. -
Quantum Inductive Learning and Quantum Logic Synthesis
Portland State University PDXScholar Dissertations and Theses Dissertations and Theses 2009 Quantum Inductive Learning and Quantum Logic Synthesis Martin Lukac Portland State University Follow this and additional works at: https://pdxscholar.library.pdx.edu/open_access_etds Part of the Electrical and Computer Engineering Commons Let us know how access to this document benefits ou.y Recommended Citation Lukac, Martin, "Quantum Inductive Learning and Quantum Logic Synthesis" (2009). Dissertations and Theses. Paper 2319. https://doi.org/10.15760/etd.2316 This Dissertation is brought to you for free and open access. It has been accepted for inclusion in Dissertations and Theses by an authorized administrator of PDXScholar. For more information, please contact [email protected]. QUANTUM INDUCTIVE LEARNING AND QUANTUM LOGIC SYNTHESIS by MARTIN LUKAC A dissertation submitted in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY in ELECTRICAL AND COMPUTER ENGINEERING. Portland State University 2009 DISSERTATION APPROVAL The abstract and dissertation of Martin Lukac for the Doctor of Philosophy in Electrical and Computer Engineering were presented January 9, 2009, and accepted by the dissertation committee and the doctoral program. COMMITTEE APPROVALS: Irek Perkowski, Chair GarrisoH-Xireenwood -George ^Lendaris 5artM ?teven Bleiler Representative of the Office of Graduate Studies DOCTORAL PROGRAM APPROVAL: Malgorza /ska-Jeske7~Director Electrical Computer Engineering Ph.D. Program ABSTRACT An abstract of the dissertation of Martin Lukac for the Doctor of Philosophy in Electrical and Computer Engineering presented January 9, 2009. Title: Quantum Inductive Learning and Quantum Logic Synhesis Since Quantum Computer is almost realizable on large scale and Quantum Technology is one of the main solutions to the Moore Limit, Quantum Logic Synthesis (QLS) has become a required theory and tool for designing Quantum Logic Circuits. -
Quantum Algorithms for Classical Lattice Models
Home Search Collections Journals About Contact us My IOPscience Quantum algorithms for classical lattice models This content has been downloaded from IOPscience. Please scroll down to see the full text. 2011 New J. Phys. 13 093021 (http://iopscience.iop.org/1367-2630/13/9/093021) View the table of contents for this issue, or go to the journal homepage for more Download details: IP Address: 147.96.14.15 This content was downloaded on 16/12/2014 at 15:54 Please note that terms and conditions apply. New Journal of Physics The open–access journal for physics Quantum algorithms for classical lattice models G De las Cuevas1,2,5, W Dür1, M Van den Nest3 and M A Martin-Delgado4 1 Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 25, A-6020 Innsbruck, Austria 2 Institut für Quantenoptik und Quanteninformation der Österreichischen Akademie der Wissenschaften, Innsbruck, Austria 3 Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Strasse 1, D-85748 Garching, Germany 4 Departamento de Física Teórica I, Universidad Complutense, 28040 Madrid, Spain E-mail: [email protected] New Journal of Physics 13 (2011) 093021 (35pp) Received 15 April 2011 Published 9 September 2011 Online at http://www.njp.org/ doi:10.1088/1367-2630/13/9/093021 Abstract. We give efficient quantum algorithms to estimate the partition function of (i) the six-vertex model on a two-dimensional (2D) square lattice, (ii) the Ising model with magnetic fields on a planar graph, (iii) the Potts model on a quasi-2D square lattice and (iv) the Z2 lattice gauge theory on a 3D square lattice. -
Reversible Logic Synthesis with Minimal Usage of Ancilla Bits Siyao
Reversible Logic Synthesis with Minimal Usage of Ancilla Bits by Siyao Xu Submitted to the Department of Electrical Engineering and Computer Science in partial fulfillment of the requirements for the degree of Master of Engineering in Electrical Engineering and Computer Science at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY June 2015 ○c Massachusetts Institute of Technology 2015. All rights reserved. Author................................................................ Department of Electrical Engineering and Computer Science May 20, 2015 Certified by. Prof. Scott Aaronson Associate Professor Thesis Supervisor Accepted by . Prof. Albert R. Meyer Chairman, Masters of Engineering Thesis Committee 2 Reversible Logic Synthesis with Minimal Usage of Ancilla Bits by Siyao Xu Submitted to the Department of Electrical Engineering and Computer Science on May 20, 2015, in partial fulfillment of the requirements for the degree of Master of Engineering in Electrical Engineering and Computer Science Abstract Reversible logic has attracted much research interest over the last few decades, espe- cially due to its application in quantum computing. In the construction of reversible gates from basic gates, ancilla bits are commonly used to remove restrictions on the type of gates that a certain set of basic gates generates. With unlimited ancilla bits, many gates (such as Toffoli and Fredkin) become universal reversible gates. However, ancilla bits can be expensive to implement, thus making the problem of minimizing necessary ancilla bits a practical topic. This thesis explores the problem of reversible logic synthesis using a single base gate and a few ancilla bits. Two base gates are discussed: a variation of the 3- bit Toffoli gate and the original 3-bit Fredkin gate. -
In Situ Quantum Control Over Superconducting Qubits
! In situ quantum control over superconducting qubits Anatoly Kulikov M.Sc. A thesis submitted for the degree of Doctor of Philosophy at The University of Queensland in 2020 School of Mathematics and Physics ARC Centre of Excellence for Engineered Quantum Systems (EQuS) ABSTRACT In the last decade, quantum information processing has transformed from a field of mostly academic research to an applied engineering subfield with many commercial companies an- nouncing strategies to achieve quantum advantage and construct a useful universal quantum computer. Continuing efforts to improve qubit lifetime, control techniques, materials and fab- rication methods together with exploring ways to scale up the architecture have culminated in the recent achievement of quantum supremacy using a programmable superconducting proces- sor { a major milestone in quantum computing en route to useful devices. Marking the point when for the first time a quantum processor can outperform the best classical supercomputer, it heralds a new era in computer science, technology and information processing. One of the key developments enabling this transition to happen is the ability to exert more precise control over quantum bits and the ability to detect and mitigate control errors and imperfections. In this thesis, ways to efficiently control superconducting qubits are explored from the experimental viewpoint. We introduce a state-of-the-art experimental machinery enabling one to perform one- and two-qubit gates focusing on the technical aspect and outlining some guidelines for its efficient operation. We describe the software stack from the time alignment of control pulses and triggers to the data processing organisation. We then bring in the standard qubit manipulation and readout methods and proceed to describe some of the more advanced optimal control and calibration techniques. -
Reliably Distinguishing States in Qutrit Channels Using One-Way LOCC
Reliably distinguishing states in qutrit channels using one-way LOCC Christopher King Department of Mathematics, Northeastern University, Boston MA 02115 Daniel Matysiak College of Computer and Information Science, Northeastern University, Boston MA 02115 July 15, 2018 Abstract We present numerical evidence showing that any three-dimensional subspace of C3 ⊗ Cn has an orthonormal basis which can be reliably dis- tinguished using one-way LOCC, where a measurement is made first on the 3-dimensional part and the result used to select an optimal measure- ment on the n-dimensional part. This conjecture has implications for the LOCC-assisted capacity of certain quantum channels, where coordinated measurements are made on the system and environment. By measuring first in the environment, the conjecture would imply that the environment- arXiv:quant-ph/0510004v1 1 Oct 2005 assisted classical capacity of any rank three channel is at least log 3. Sim- ilarly by measuring first on the system side, the conjecture would imply that the environment-assisting classical capacity of any qutrit channel is log 3. We also show that one-way LOCC is not symmetric, by providing an example of a qutrit channel whose environment-assisted classical capacity is less than log 3. 1 1 Introduction and statement of results The noise in a quantum channel arises from its interaction with the environment. This viewpoint is expressed concisely in the Lindblad-Stinespring representation [6, 8]: Φ(|ψihψ|)= Tr U(|ψihψ|⊗|ǫihǫ|)U ∗ (1) E Here E is the state space of the environment, which is assumed to be initially prepared in a pure state |ǫi. -
Controlled Not (Cnot) Gate for Two Qutrit Systems
IOSR Journal of Applied Physics (IOSR-JAP) e-ISSN: 2278-4861.Volume 10, Issue 6 Ver. II (Nov. – Dec. 2018), 16-19 www.iosrjournals.org Controlled Not (Cnot) Gate For Two Qutrit Systems Mehpeyker KOCAKOÇ1, Recep TAPRAMAZ 2 1(Department of Computer Technologies, Vocational School of İmamoğlu / Çukurova University, Turkey)) 2(Department of Physics, Faculty of Science / Ondokuz Mayıs University, Turkey) Corresponding Author: Mehpeyker KOCAKOÇ Abstract: Quantum computation applications utilize basically the structures having two definite states named as QuBit (Quantum Bit). In spin based quantum computation applications like NMR and EPR techniques, besides the Spin-1/2 systems (electron and proton spins), there are many systems having spins greater than 1/2. For instance, in some structures, coupled two electrons can form triplet states with total spin of 1, and 14N nucleus has, one of the widely encountered nuclei, also spin of 1. In quantum computation, such systems are called Qutrit systems and have the potential of use in spin based quantum computation applications. Besides the well-known CNOT gates in QuBit system, we suggest some CNOT gates for Qutrit systems composed of two Spin-1 systems, forming control and target Qutrits. Keywords: Qutrit, spin, quantum computing, CNOT --------------------------------------------------------------------------------------------------------------------------------------- Date of Submission: 13-12-2018 Date of acceptance: 28-12-2018 ----------------------------------------------------------------------------------------------------------------------------- ---------- I. Introduction In quantum computation systems, the basic gates like Hadamard, Pauli X, Y and Z, CNOT, phase shift, SWAP, Toffoli and Fredkin have been constructed for two-state systems. Quantum logical gate such as the SWAP gate, controlled phase gate [1–2], and CNOT gate [3-5], one of the essential building block quantum computers [5-6]. -
Verified Compilation of Space-Efficient Reversible Circuits
Verified compilation of space-efficient reversible circuits Matthew Amy1;2, Martin Roetteler3, and Krysta M. Svore3 1 Institute for Quantum Computing, Waterloo, Canada 2 David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, Canada 3 Microsoft Research, Redmond, USA Abstract. The generation of reversible circuits from high-level code is an important problem in several application domains, including low- power electronics and quantum computing. Existing tools compile and optimize reversible circuits for various metrics, such as the overall cir- cuit size or the total amount of space required to implement a given function reversibly. However, little effort has been spent on verifying the correctness of the results, an issue of particular importance in quantum computing. There, compilation allows not only mapping to hardware, but also the estimation of resources required to implement a given quantum algorithm, a process that is crucial for identifying which algorithms will outperform their classical counterparts. We present a reversible circuit compiler called ReVerC, which has been formally verified in F? and compiles circuits that operate correctly with respect to the input pro- gram. Our compiler compiles the Revs language [21] to combinational reversible circuits with as few ancillary bits as possible, and provably cleans temporary values. 1 Introduction The ability to evaluate classical functions coherently and in superposition as part of a larger quantum computation is essential for many quantum algorithms. For example, Shor's quantum algorithm [26] uses classical modular arithmetic and Grover's quantum algorithm [11] uses classical predicates to implicitly define the underlying search problem. There is a resulting need for tools to help a programmer translate classical, irreversible programs into a form which a quan- tum computer can understand and carry out, namely into reversible circuits, arXiv:1603.01635v2 [quant-ph] 20 Apr 2018 which are a special case of quantum transformations [19]. -
High Energy Physics Quantum Information Science Awards Abstracts
High Energy Physics Quantum Information Science Awards Abstracts Towards Directional Detection of WIMP Dark Matter using Spectroscopy of Quantum Defects in Diamond Ronald Walsworth, David Phillips, and Alexander Sushkov Challenges and Opportunities in Noise‐Aware Implementations of Quantum Field Theories on Near‐Term Quantum Computing Hardware Raphael Pooser, Patrick Dreher, and Lex Kemper Quantum Sensors for Wide Band Axion Dark Matter Detection Peter S Barry, Andrew Sonnenschein, Clarence Chang, Jiansong Gao, Steve Kuhlmann, Noah Kurinsky, and Joel Ullom The Dark Matter Radio‐: A Quantum‐Enhanced Dark Matter Search Kent Irwin and Peter Graham Quantum Sensors for Light-field Dark Matter Searches Kent Irwin, Peter Graham, Alexander Sushkov, Dmitry Budke, and Derek Kimball The Geometry and Flow of Quantum Information: From Quantum Gravity to Quantum Technology Raphael Bousso1, Ehud Altman1, Ning Bao1, Patrick Hayden, Christopher Monroe, Yasunori Nomura1, Xiao‐Liang Qi, Monika Schleier‐Smith, Brian Swingle3, Norman Yao1, and Michael Zaletel Algebraic Approach Towards Quantum Information in Quantum Field Theory and Holography Daniel Harlow, Aram Harrow and Hong Liu Interplay of Quantum Information, Thermodynamics, and Gravity in the Early Universe Nishant Agarwal, Adolfo del Campo, Archana Kamal, and Sarah Shandera Quantum Computing for Neutrino‐nucleus Dynamics Joseph Carlson, Rajan Gupta, Andy C.N. Li, Gabriel Perdue, and Alessandro Roggero Quantum‐Enhanced Metrology with Trapped Ions for Fundamental Physics Salman Habib, Kaifeng Cui1,