DOCSLIB.ORG

Quantum Inductive Learning and Quantum Logic Synthesis

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
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. However, despite its growth, there is no any unified aproach to QLS as Quantum Computing is still being discovered and novel applications are being identified. The intent of this study is to experimentally explore principles of Quantum Logic Synthesis and its applications to Inductive Machine Learning. Based on algorithmic approach, I first design a Genetic Algorithm for Quantum Logic Synthesis that is used to prove and verify the methods proposed in this work. Based on results obtained from the evolutionary experimentation, I propose a fast, structure and cost based exhausitve search that is used for the design of a novel, least expensive universal familly of quantum gates. The results form both the evolutionary and heuristic search are used to for­ mulate an Inductive Learning Approach based on Quantum Logic Synthesis wih the intended application being the humanoid behavioral robotics. The presented approach illustrates a succesful algorithmic approach, where the search algorithm was able to invent/discover novel quantum circuits as well as novel principles in Quantum Logic Synthesis. To my parents and family. ACKNOWLEDGMENTS My sincere thanks to my advisor prof. Marek Perkowski and to each member of my dissertation committee for their guidance and help. CONTENTS Acknowledgments ii List of Tables x List of Figures xii 1 Introduction 1 1.1 Dissertation Statement 3 1.2 Contributions 3 2 Quantum Computing Basics and Concepts 8 2.1 Why quantum computing? 8 2.2 Mathematical Preliminaries to Quantum Computing 10 2.2.1 Bra-Ket notation 12 2.2.2 Matrix Trace 12 2.3 Quantum Mechanics 13 2.3.1 Bohr Particle Model 13 2.3.2 Quantum Model of Elementary Particle 15 CONTENTS iv 2.3.3 Schrodinger equation 20 2.3.4 Superposition of quantum states 21 2.4 Prom Quantum Mechanics to Quantum Logic 24 2.4.1 Simple Projective Measurement 29 2.4.2 Density Matrix and POVM 37 2.5 Quantum Logic, Quantum Gates and Quantum Logic Circuits 46 2.5.1 Single-qubit Quantum Gates 46 2.5.2 Multi-qubit and Controlled Quantum Gates 49 2.5.3 Quantum Circuits and Representation 52 2.5.4 Quantum Circuits and Sequential Logic 60 3 Quantum Logic Synthesis and Algorithmic Search 68 3.1 Introduction 68 3.2 Previous research on automated synthesis of quantum circuits 69 3.3 Function Classification for Logic Synthesis 71 3.4 Representation 72 3.5 Quantum-Based Synthesis: useful quantum circuits synthesis problems 75 3.5.1 Cost of quantum circuits 77 3.5.2 The Size of Quantum circuits 80 CONTENTS v 3.5.3 Quantum Logic Synthesis 83 3.5.4 NMR-based Quantum Logic Gates 86 3.6 Principles of Synthesis for NMR technology 88 3.6.1 V/T Gate - 'Level-generalization' 88 3.6.2 Insertion principle 91 3.6.3 The Divide and Conquer Principle 91 3.6.4 The Gate-collapsing principle 92 3.7 Examples of circuits obtained automatically for NMR technol­ ogy using methods from sections 3.5 and 3.6 94 3.8 Chapter Conclusion 100 4 Genetic Algorithm for Logic Synthesis 101 4.1 Introduction 101 4.2 Genetic algorithm 105 4.2.1 Encoding/Representation 105 4.2.2 Initialization steps of GA 107 4.3 Evaluation of Synthesis Errors Ill 4.3.1 Element Error Evaluation method (EE) 112 4.3.2 Measurement Evaluation method (ME) 113 4.3.3 Comparison of EE and ME 116 CONTENTS vi 4.4 Fitness functions of the GA 122 4.4.1 Simple Fitness Functions 123 4.4.2 Cost Based Fitness Functions 124 4.5 The Selection Process 129 4.6 Crossover and Mutation 133 4.6.1 Mutation 135 4.6.2 Additional GA tuning strategies 138 4.7 Chapter Conclusion 142 5 Evolutionary Search for Logic synthesis 144 5.1 Evolutionary Search 146 5.2 Experimental setup of GA 147 5.2.1 Input Sets of Quantum Primitives 147 5.3 Discussion of the Results of the Evolutionary Quantum Logic Synthesis using ME evaluation 150 5.3.1 Toffoli Gate 150 5.3.2 Synthesis of Fredkin Gate 159 5.3.3 Synthesis of Majority Gate 166 5.4 Discussion of the Results of the Evolutionary Quantum Logic Synthesis using EE evaluation 173 CONTENTS vii 5.4.1 Toffoli Gate 173 5.4.2 Predkin Gate 176 5.4.3 Entanglement Circuit 177 5.5 Discussion of the results of the Evolutionary Synthesis .... 180 5.5.1 Results Comparison 180 5.5.2 Encountered problems during the Evolutionary QLS . 181 5.6 Conclusion of the Evolutionary QLS 186 6 Structure Based Search for Universal Quantum Circuits 188 6.1 Introduction 188 6.2 The EX algorithm 191 6.3 Heuristic Search for Lowest Cost Function Class using the EX algorithm 195 6.3.1 New Quantum Logic Family 197 6.4 Discussion and Conclusion to the Structure Based Exhaustive search 201 7 Learning Quantum Behaviors 206 7.1 Quantum Behaviors 208 7.2 The concept of learning robotic behaviors from examples. 218 CONTENTS viu 7.2.1 Symbolic Quantum Synthesis of Single Output Quan­ tum Circuits 233 7.3 Experiments and Results for learning Quantum Behaviors . 239 7.3.1 Symbolic synthesis - Single output functions 239 7.4 Discussion on learning Quantum Benchmarks 242 7.5 Measurement Synthesis 246 7.5.1 Conclusions on the Measurement Dependent Quantum Logic Synthesis 265 8 Dissertation conclusion and contributions 268 References 271 Appendices 287 A Glossary 288 B Models of Quantum Computing 290 B.0.2 Quantum Cellular Automata 290 B.0.3 Quantum Finite Automata and Quantum State Machines301 B.0.4 Quantum Turing machine 316 B.0.5 Quantum Robots 317 CONTENTS ix C Cynthea, an interactive robotic system 321 C.l Definitions 321 C.2 Cynthea - the social interactive robotic framework 322 C.3 Learning and Adaptation 323 C.4 Sensors 327 C.4.1 Video-Sensor 328 C.4.2 Audio-Sensor 331 C.4.3 Voltage/Power-Sensor 333 C.5 Actuators 334 C.5.1 Servo-Control 336 C.5.2 Speech-Control 337 C.5.3 Network Control 338 C.5.4 Speech and Dialogue generation 339 C.6 Control and Scripting 341 C.6.1 CRL - The language 344 C.6.2 Scripting 355 C.7 Artificial Emotions 357 LIST OF TABLES 1 a). - K-map , b) - LUT 52 2 K-map of an incompletely specified 3x1 reversible quantum function before measurement 56 3 K-map of an incompletely specified 3x3 reversible quantum function before measurement with don't cares within single minterms 58 4 K-map of the Feynman gate 64 1 Cost models 78 1 Structure of a Genetic Algorithm 105 2 Example of the Majority gate encoding for the GA. Observe that each input minterm with qubit |g3) = |1) is a don't care. 115 1 Fixed parameters during search for Toffoli gate 150 2 Example of a 3 x 3 quantum probabilistic and a 3 x 1 determin­ istic functions generated by the circuit from Figure 5.4c. 159 3 Fixed parameters during search for Fredkin gate 159 4 Comparison of various fitness functions for all illustrated bench­ mark functions 181 1 Pseudo Code of EX Algorithm 192 LIST OF TABLES xi 6.2 The Peres gate Truth Table 196 6.3 The family of Peres gates 198 7.1 Braitenberg vehicle behaviors: (a) afraid of light, (b) attracted to light 209 7.2 A K-map of a completely specified reversible function 224 7.3 Incompletely specified reversible function f 227 7.4 Single output Boolean functions R to be synthesized (learned) 233 7.5 Example of analysis on circuit from Figure 7.11 236 7.6 Example of analysis on circuit from Figure 7.12 238 7.7 GA benchmark functions 239 LIST OF FIGURES 2.1 Bohr model of the atom (nucleus, orbiting electrons). Shown are light colors respective to the electron orbit transitions.
Load more

Recommended publications
  • Simulating Quantum Field Theory with a Quantum Computer
    Simulating quantum field theory with a quantum computer John Preskill Lattice 2018 28 July 2018 This talk has two parts (1) Near-term prospects for quantum computing. (2) Opportunities in quantum simulation of quantum field theory. Exascale digital computers will advance our knowledge of QCD, but some challenges will remain, especially concerning real-time evolution and properties of nuclear matter and quark-gluon plasma at nonzero temperature and chemical potential. Digital computers may never be able to address these (and other) problems; quantum computers will solve them eventually, though I’m not sure when. The physics payoff may still be far away, but today’s research can hasten the arrival of a new era in which quantum simulation fuels progress in fundamental physics. Frontiers of Physics short distance long distance complexity Higgs boson Large scale structure “More is different” Neutrino masses Cosmic microwave Many-body entanglement background Supersymmetry Phases of quantum Dark matter matter Quantum gravity Dark energy Quantum computing String theory Gravitational waves Quantum spacetime particle collision molecular chemistry entangled electrons A quantum computer can simulate efficiently any physical process that occurs in Nature. (Maybe. We don’t actually know for sure.) superconductor black hole early universe Two fundamental ideas (1) Quantum complexity Why we think quantum computing is powerful. (2) Quantum error correction Why we think quantum computing is scalable. A complete description of a typical quantum state of just 300 qubits requires more bits than the number of atoms in the visible universe. Why we think quantum computing is powerful We know examples of problems that can be solved efficiently by a quantum computer, where we believe the problems are hard for classical computers.
    [Show full text]
  • Quantum Machine Learning: Benefits and Practical Examples
    Quantum Machine Learning: Benefits and Practical Examples Frank Phillipson1[0000-0003-4580-7521] 1 TNO, Anna van Buerenplein 1, 2595 DA Den Haag, The Netherlands [email protected] Abstract. A quantum computer that is useful in practice, is expected to be devel- oped in the next few years. An important application is expected to be machine learning, where benefits are expected on run time, capacity and learning effi- ciency. In this paper, these benefits are presented and for each benefit an example application is presented. A quantum hybrid Helmholtz machine use quantum sampling to improve run time, a quantum Hopfield neural network shows an im- proved capacity and a variational quantum circuit based neural network is ex- pected to deliver a higher learning efficiency. Keywords: Quantum Machine Learning, Quantum Computing, Near Future Quantum Applications. 1 Introduction Quantum computers make use of quantum-mechanical phenomena, such as superposi- tion and entanglement, to perform operations on data [1]. Where classical computers require the data to be encoded into binary digits (bits), each of which is always in one of two definite states (0 or 1), quantum computation uses quantum bits, which can be in superpositions of states. These computers would theoretically be able to solve certain problems much more quickly than any classical computer that use even the best cur- rently known algorithms. Examples are integer factorization using Shor's algorithm or the simulation of quantum many-body systems. This benefit is also called ‘quantum supremacy’ [2], which only recently has been claimed for the first time [3]. There are two different quantum computing paradigms.
    [Show full text]
  • COVID-19 Detection on IBM Quantum Computer with Classical-Quantum Transfer Learning
    medRxiv preprint doi: https://doi.org/10.1101/2020.11.07.20227306; this version posted November 10, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY-NC-ND 4.0 International license . Turk J Elec Eng & Comp Sci () : { © TUB¨ ITAK_ doi:10.3906/elk- COVID-19 detection on IBM quantum computer with classical-quantum transfer learning Erdi ACAR1*, Ihsan_ YILMAZ2 1Department of Computer Engineering, Institute of Science, C¸anakkale Onsekiz Mart University, C¸anakkale, Turkey 2Department of Computer Engineering, Faculty of Engineering, C¸anakkale Onsekiz Mart University, C¸anakkale, Turkey Received: .201 Accepted/Published Online: .201 Final Version: ..201 Abstract: Diagnose the infected patient as soon as possible in the coronavirus 2019 (COVID-19) outbreak which is declared as a pandemic by the world health organization (WHO) is extremely important. Experts recommend CT imaging as a diagnostic tool because of the weak points of the nucleic acid amplification test (NAAT). In this study, the detection of COVID-19 from CT images, which give the most accurate response in a short time, was investigated in the classical computer and firstly in quantum computers. Using the quantum transfer learning method, we experimentally perform COVID-19 detection in different quantum real processors (IBMQx2, IBMQ-London and IBMQ-Rome) of IBM, as well as in different simulators (Pennylane, Qiskit-Aer and Cirq). By using a small number of data sets such as 126 COVID-19 and 100 Normal CT images, we obtained a positive or negative classification of COVID-19 with 90% success in classical computers, while we achieved a high success rate of 94-100% in quantum computers.
    [Show full text]
  • Arxiv:Quant-Ph/0002039V2 1 Aug 2000
    Methodology for quantum logic gate construction 1,2 3,2 2 Xinlan Zhou ∗, Debbie W. Leung †, and Isaac L. Chuang ‡ 1 Department of Applied Physics, Stanford University, Stanford, California 94305-4090 2 IBM Almaden Research Center, 650 Harry Road, San Jose, California 95120 3 Quantum Entanglement Project, ICORP, JST Edward Ginzton Laboratory, Stanford University, Stanford, California 94305-4085 (October 29, 2018) We present a general method to construct fault-tolerant quantum logic gates with a simple primitive, which is an analog of quantum teleportation. The technique extends previous results based on traditional quantum teleportation (Gottesman and Chuang, Nature 402, 390, 1999) and leads to straightforward and systematic construction of many fault-tolerant encoded operations, including the π/8 and Toffoli gates. The technique can also be applied to the construction of remote quantum operations that cannot be directly performed. I. INTRODUCTION Practical realization of quantum information processing requires specific types of quantum operations that may be difficult to construct. In particular, to perform quantum computation robustly in the presence of noise, one needs fault-tolerant implementation of quantum gates acting on states that are block-encoded using quantum error correcting codes [1–4]. Fault-tolerant quantum gates must prevent propagation of single qubit errors to multiple qubits within any code block so that small correctable errors will not grow to exceed the correction capability of the code. This requirement greatly restricts the types of unitary operations that can be performed on the encoded qubits. Certain fault-tolerant operations can be implemented easily by performing direct transversal operations on the encoded qubits, in which each qubit in a block interacts only with one corresponding qubit, either in another block or in a specialized ancilla.
    [Show full text]
  • Fault-Tolerant Interface Between Quantum Memories and Quantum Processors
    ARTICLE DOI: 10.1038/s41467-017-01418-2 OPEN Fault-tolerant interface between quantum memories and quantum processors Hendrik Poulsen Nautrup 1, Nicolai Friis 1,2 & Hans J. Briegel1 Topological error correction codes are promising candidates to protect quantum computa- tions from the deteriorating effects of noise. While some codes provide high noise thresholds suitable for robust quantum memories, others allow straightforward gate implementation 1234567890 needed for data processing. To exploit the particular advantages of different topological codes for fault-tolerant quantum computation, it is necessary to be able to switch between them. Here we propose a practical solution, subsystem lattice surgery, which requires only two-body nearest-neighbor interactions in a fixed layout in addition to the indispensable error correction. This method can be used for the fault-tolerant transfer of quantum information between arbitrary topological subsystem codes in two dimensions and beyond. In particular, it can be employed to create a simple interface, a quantum bus, between noise resilient surface code memories and flexible color code processors. 1 Institute for Theoretical Physics, University of Innsbruck, Technikerstr. 21a, 6020 Innsbruck, Austria. 2 Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria. Correspondence and requests for materials should be addressed to H.P.N. (email: [email protected]) NATURE COMMUNICATIONS | 8: 1321 | DOI: 10.1038/s41467-017-01418-2 | www.nature.com/naturecommunications 1 ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/s41467-017-01418-2 oise and decoherence can be considered as the major encoding k = n − s qubits. We denote the normalizer of S by Nobstacles for large-scale quantum information processing.
    [Show full text]
  • Realization of the Quantum Toffoli Gate
    Realization of the quantum Toffoli gate Realization of the quantum Toffoli gate Based on: Monz, T; Kim, K; Haensel, W; et al Realization of the quantum Toffoli gate with trapped ions Phys. Rev. Lett. 102, 040501 (2009) Lanyon, BP; Barbieri, M; Almeida, MP; et al. Simplifying quantum logic using higher dimensional Hilbert spaces Nat. Phys. 5, 134 (2009) Realization of the quantum Toffoli gate Outline 1. Motivation 2. Principles of the quantum Toffoli gate 3. Implementation with trapped ions 4. Implementation with photons 5. Comparison and conclusion 6. Summary 6. Dezember 2010 Jakob Buhmann Jeffrey Gehrig 1 Realization of the quantum Toffoli gate 1. Motivation • Universal quantum logic gate sets are needed to implement algorithms • Implementation of algorithms is difficult due to the finite fidelity and large amount of gates • Use of other degrees of freedom to store information • Reduction of complexity and runtime 6. Dezember 2010 Jakob Buhmann Jeffrey Gehrig 2 Realization of the quantum Toffoli gate 2. Principles of the Toffoli gate • Three-qubit gate (C1, C2, T) • Logic flip of T depending on (C1 AND C2) Truth table Matrix form Input Output C1 C2 T C1 C2 T 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 0 1 0 0 1 1 0 1 1 1 0 0 1 0 0 1 0 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 0 6. Dezember 2010 Jakob Buhmann Jeffrey Gehrig 3 Realization of the quantum Toffoli gate 2. Principles of the Toffoli gate • Qubit Implementation • Qutrit Implementation Qutrit states: and 6.
    [Show full text]
  • Nearest Centroid Classification on a Trapped Ion Quantum Computer
    www.nature.com/npjqi ARTICLE OPEN Nearest centroid classification on a trapped ion quantum computer ✉ Sonika Johri1 , Shantanu Debnath1, Avinash Mocherla2,3,4, Alexandros SINGK2,3,5, Anupam Prakash2,3, Jungsang Kim1 and Iordanis Kerenidis2,3,6 Quantum machine learning has seen considerable theoretical and practical developments in recent years and has become a promising area for finding real world applications of quantum computers. In pursuit of this goal, here we combine state-of-the-art algorithms and quantum hardware to provide an experimental demonstration of a quantum machine learning application with provable guarantees for its performance and efficiency. In particular, we design a quantum Nearest Centroid classifier, using techniques for efficiently loading classical data into quantum states and performing distance estimations, and experimentally demonstrate it on a 11-qubit trapped-ion quantum machine, matching the accuracy of classical nearest centroid classifiers for the MNIST handwritten digits dataset and achieving up to 100% accuracy for 8-dimensional synthetic data. npj Quantum Information (2021) 7:122 ; https://doi.org/10.1038/s41534-021-00456-5 INTRODUCTION Thus, one might hope that noisy quantum computers are 1234567890():,; Quantum technologies promise to revolutionize the future of inherently better suited for machine learning computations than information and communication, in the form of quantum for other types of problems that need precise computations like computing devices able to communicate and process massive factoring or search problems. amounts of data both efficiently and securely using quantum However, there are significant challenges to be overcome to resources. Tremendous progress is continuously being made both make QML practical.
    [Show full text]
  • 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.
    [Show full text]
  • Machine Learning for Designing Fast Quantum Gates
    University of Calgary PRISM: University of Calgary's Digital Repository Graduate Studies The Vault: Electronic Theses and Dissertations 2016-01-26 Machine Learning for Designing Fast Quantum Gates Zahedinejad, Ehsan Zahedinejad, E. (2016). Machine Learning for Designing Fast Quantum Gates (Unpublished doctoral thesis). University of Calgary, Calgary, AB. doi:10.11575/PRISM/26805 http://hdl.handle.net/11023/2780 doctoral thesis University of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission. Downloaded from PRISM: https://prism.ucalgary.ca UNIVERSITY OF CALGARY Machine Learning for Designing Fast Quantum Gates by Ehsan Zahedinejad A THESIS SUBMITTED TO THE FACULTY OF GRADUATE STUDIES IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY GRADUATE PROGRAM IN PHYSICS AND ASTRONOMY CALGARY, ALBERTA January, 2016 c Ehsan Zahedinejad 2016 Abstract Fault-tolerant quantum computing requires encoding the quantum information into logical qubits and performing the quantum information processing in a code-space. Quantum error correction codes, then, can be employed to diagnose and remove the possible errors in the quantum information, thereby avoiding the loss of information. Although a series of single- and two-qubit gates can be employed to construct a quan- tum error correcting circuit, however this decomposition approach is not practically desirable because it leads to circuits with long operation times. An alternative ap- proach to designing a fast quantum circuit is to design quantum gates that act on a multi-qubit gate.
    [Show full text]
  • Modeling Observers As Physical Systems Representing the World from Within: Quantum Theory As a Physical and Self-Referential Theory of Inference
    Modeling observers as physical systems representing the world from within: Quantum theory as a physical and self-referential theory of inference John Realpe-G´omez1∗ Theoretical Physics Group, School of Physics and Astronomy, The University of Manchestery, Manchester M13 9PL, United Kingdom and Instituto de Matem´aticas Aplicadas, Universidad de Cartagena, Bol´ıvar130001, Colombia (Dated: June 13, 2019) In 1929 Szilard pointed out that the physics of the observer may play a role in the analysis of experiments. The same year, Bohr pointed out that complementarity appears to arise naturally in psychology where both the objects of perception and the perceiving subject belong to `our mental content'. Here we argue that the formalism of quantum theory can be derived from two related intu- itive principles: (i) inference is a classical physical process performed by classical physical systems, observers, which are part of the experimental setup|this implies non-commutativity and imaginary- time quantum mechanics; (ii) experiments must be described from a first-person perspective|this leads to self-reference, complementarity, and a quantum dynamics that is the iterative construction of the observer's subjective state. This approach suggests a natural explanation for the origin of Planck's constant as due to the physical interactions supporting the observer's information process- ing, and sheds new light on some conceptual issues associated to the foundations of quantum theory. It also suggests that fundamental equations in physics are typically
    [Show full text]
  • 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].
    [Show full text]
  • Arxiv:2010.00046V2 [Hep-Ph] 13 Oct 2020
    IPPP/20/41 Towards a Quantum Computing Algorithm for Helicity Amplitudes and Parton Showers Khadeejah Bepari,a Sarah Malik,b Michael Spannowskya and Simon Williamsb aInstitute for Particle Physics Phenomenology, Department of Physics, Durham University, Durham DH1 3LE, U.K. bHigh Energy Physics Group, Blackett Laboratory, Imperial College, Prince Consort Road, London, SW7 2AZ, United Kingdom E-mail: [email protected], [email protected], [email protected], [email protected] Abstract: The interpretation of measurements of high-energy particle collisions relies heavily on the performance of full event generators. By far the largest amount of time to predict the kinematics of multi-particle final states is dedicated to the calculation of the hard process and the subsequent parton shower step. With the continuous improvement of quantum devices, dedicated algorithms are needed to exploit the potential quantum computers can provide. We propose general and extendable algorithms for quantum gate computers to facilitate calculations of helicity amplitudes and the parton shower process. The helicity amplitude calculation exploits the equivalence between spinors and qubits and the unique features of a quantum computer to compute the helicities of each particle in- volved simultaneously, thus fully utilising the quantum nature of the computation. This advantage over classical computers is further exploited by the simultaneous computation of s and t-channel amplitudes for a 2 2 process. The parton shower algorithm simulates ! collinear emission for a two-step, discrete parton shower. In contrast to classical imple- mentations, the quantum algorithm constructs a wavefunction with a superposition of all shower histories for the whole parton shower process, thus removing the need to explicitly keep track of individual shower histories.
    [Show full text]