Minimization of Quantum Circuits Using Quantum Operator Forms
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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. -
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. -
IJSRP, Volume 2, Issue 7, July 2012 Edition
International Journal of Scientific and Research Publications, Volume 2, Issue 7, July 2012 1 ISSN 2250-3153 OF QUANTUM GATES AND COLLAPSING STATES- A DETERMINATE MODEL APRIORI AND DIFFERENTIAL MODEL APOSTEORI 1DR K N PRASANNA KUMAR, 2PROF B S KIRANAGI AND 3 PROF C S BAGEWADI ABSTRACT : We Investigate The Holistic Model With Following Composition : ( 1) Mpc (Measurement Based Quantum Computing)(2) Preparational Methodologies Of Resource States (Application Of Electric Field Magnetic Field Etc.)For Gate Teleportation(3) Quantum Logic Gates(4) Conditionalities Of Quantum Dynamics(5) Physical Realization Of Quantum Gates(6) Selective Driving Of Optical Resonances Of Two Subsystems Undergoing Dipole-Dipole Interaction By Means Of Say Ramsey Atomic Interferometry(7) New And Efficient Quantum Algorithms For Computation(8) Quantum Entanglements And No localities(9) Computation Of Minimum Energy Of A Given System Of Particles For Experimentation(10) Exponentially Increasing Number Of Steps For Such Quantum Computation(11) Action Of The Quantum Gates(12) Matrix Representation Of Quantum Gates And Vector Constitution Of Quantum States. Stability Conditions, Analysis, Solutional Behaviour Are Discussed In Detailed For The Consummate System. The System Of Quantum Gates And Collapsing States Show Contrast With The Documented Information Thereto. Paper may be extended to exponential time with exponentially increasing steps in the computation. INTRODUCTION: LITERATURE REVIEW: Double quantum dots: interdot interactions, co-tunneling, and Kondo resonances without spin (See for details Qing-feng Sun, Hong Guo ) Authors show that through an interdot off-site electron correlation in a double quantum-dot (DQD) device, Kondo resonances emerge in the local density of states without the electron spin-degree of freedom. -
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]. -
Optimization of Reversible Circuits Using Toffoli Decompositions with Negative Controls
S S symmetry Article Optimization of Reversible Circuits Using Toffoli Decompositions with Negative Controls Mariam Gado 1,2,* and Ahmed Younes 1,2,3 1 Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, Alexandria 21568, Egypt; [email protected] 2 Academy of Scientific Research and Technology(ASRT), Cairo 11516, Egypt 3 School of Computer Science, University of Birmingham, Birmingham B15 2TT, UK * Correspondence: [email protected]; Tel.: +203-39-21595; Fax: +203-39-11794 Abstract: The synthesis and optimization of quantum circuits are essential for the construction of quantum computers. This paper proposes two methods to reduce the quantum cost of 3-bit reversible circuits. The first method utilizes basic building blocks of gate pairs using different Toffoli decompositions. These gate pairs are used to reconstruct the quantum circuits where further optimization rules will be applied to synthesize the optimized circuit. The second method suggests using a new universal library, which provides better quantum cost when compared with previous work in both cost015 and cost115 metrics; this proposed new universal library “Negative NCT” uses gates that operate on the target qubit only when the control qubit’s state is zero. A combination of the proposed basic building blocks of pairs of gates and the proposed Negative NCT library is used in this work for synthesis and optimization, where the Negative NCT library showed better quantum cost after optimization compared with the NCT library despite having the same circuit size. The reversible circuits over three bits form a permutation group of size 40,320 (23!), which Citation: Gado, M.; Younes, A. -
Design of Regular Reversible Quantum Circuits
Portland State University PDXScholar Dissertations and Theses Dissertations and Theses 1-1-2010 Design of Regular Reversible Quantum Circuits Dipal Shah Portland State University Follow this and additional works at: https://pdxscholar.library.pdx.edu/open_access_etds Let us know how access to this document benefits ou.y Recommended Citation Shah, Dipal, "Design of Regular Reversible Quantum Circuits" (2010). Dissertations and Theses. Paper 129. https://doi.org/10.15760/etd.129 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. Please contact us if we can make this document more accessible: [email protected]. Design of Regular Reversible Quantum Circuits by Dipal Shah A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Electrical and Computer Engineering Dissertation Committee: Marek A. Perkowski, Chair Garrison Greenwood Xiaoyu Song Cynthia Brown Laszlo Csanky Portland State University © 2010 ABSTRACT The computing power in terms of speed and capacity of today's digital computers has improved tremendously in the last decade. This improvement came mainly due to a revolution in manufacturing technology by developing the ability to manufacture smaller devices and by integrating more devices on a single die. Further development of the current technology will be restricted by physical limits since it won't be possible to shrink devices beyond a certain size. Eventually, classical electrical circuits will encounter the barrier of quantum mechanics. The laws of quantum mechanics can be used for building computing systems that work on the principles of quantum mechanics. -
Reversible Circuit Compilation with Space Constraints Alex Parent, Martin Roetteler, and Krysta M
1 Reversible circuit compilation with space constraints Alex Parent, Martin Roetteler, and Krysta M. Svore Abstract We develop a framework for resource efficient compilation of higher-level programs into lower-level reversible circuits. Our main focus is on optimizing the memory footprint of the resulting reversible networks. This is motivated by the limited availability of qubits for the foreseeable future. We apply three main techniques to keep the number of required qubits small when computing classical, irreversible computations by means of reversible networks: first, wherever possible we allow the compiler to make use of in-place functions to modify some of the variables. Second, an intermediate representation is introduced that allows to trace data dependencies within the program, allowing to clean up qubits early. This realizes an analog to “garbage collection” for reversible circuits. Third, we use the concept of so-called pebble games to transform irreversible programs into reversible programs under space constraints, allowing for data to be erased and recomputed if needed. We introduce REVS, a compiler for reversible circuits that can translate a subset of the functional programming language F# into Toffoli networks which can then be further interpreted for instance in LIQuiji, a domain-specific language for quantum computing and which is also embedded into F#. We discuss a number of test cases that illustrate the advantages of our approach including reversible implementations of SHA-2 and other cryptographic hash-functions, reversible integer arithmetic, as well as a test-bench of combinational circuits used in classical circuit synthesis. Compared to Bennett’s method, REVS can reduce space complexity by a factor of 4 or more, while having an only moderate increase in circuit size as well as in the time it takes to compile the reversible networks. -
Toffoli Gates) – This Is Done by Physicists and Material Science People, – Requires Deep Understanding of Quantum Mechanics, – Big Costs, Expensive Labs
ReversibleReversible ComputingComputing forfor BeginnersBeginners Lecture 3. Marek Perkowski Some slides from Hugo De Garis, De Vos, Margolus, Toffoli, Vivek Shende & Aditya Prasad Reversible Computing • In the 60s and beyond, CS-physicists considered the ultimate limits of computing, e.g. • What is the maximum bit processing rate of a cubic centimeter of material? • What is the minimum amount of heat generated per bit processed? etc. • This led to the fundamental developments in computing - reversible logic. TheThe MostMost ImportantImportant aspectaspect ofof researchresearch isis MotivationMotivation Why I have motivation to work on Reversible Logic? ReasonsReasons toto workwork onon ReversibleReversible LogicLogic •Build Intelligent Robots •Save Power •Save our Civilization •and supremacy of advanced nations? HowHow toto buildbuild extremelyextremely largelarge finitefinite statestate machinesmachines withwith smallsmall powerpower consumption??consumption?? …and…and thisthis leadsleads usus toto thethe secondsecond reason…..reason….. SaveSave ourour CivilizationCivilization QuantumQuantum ComputersComputers willwill bebe reversiblereversible QuantumQuantum ComputersComputers willwill solvesolve NP-NP- hardhard problemsproblems inin polynomialpolynomial timetime IfIf QuantumQuantum ComputersComputers willwill bebe notnot build,build, USAUSA andand thethe worldworld willwill bebe inin troubletrouble Motivation for this work: Quantum Logic touches the future of our civilization • We live in a very exciting time. • US economy grows, despite crisis • World economy grows • Thanks to advances in information-processing technology. • Usefulness of computers has been enabled primarily by semiconductor-based electronic transistors. Moore’s Law • In 1965, Gordon Moore observed a trend of increasing performance in the first few generations of integrated-circuit technology. • He predicted that in fact it would continue to improve at an exponential rate - with the performance per unit cost increasing by a factor of 2 every 18 months or so - for at least the next 10 years. -
Decomposition of Reversible Logic Function Based on Cube-Reordering
Portland State University PDXScholar Electrical and Computer Engineering Faculty Publications and Presentations Electrical and Computer Engineering 12-2011 Decomposition of Reversible Logic Function Based on Cube-Reordering Martin Lukac Tohoku University Michitaka Kameyama Tohoku University Marek Perkowski Portland State University Pawel Kerntopf Warsaw University of Technology Follow this and additional works at: https://pdxscholar.library.pdx.edu/ece_fac Part of the Electrical and Computer Engineering Commons Let us know how access to this document benefits ou.y Citation Details Lukac, Martin, Michitaka Kameyama, Marek Perkowski, and Pawel Kerntopf. "Decomposition of reversible logic function based on cube-reordering." Facta universitatis-series: Electronics and Energetics 24, no. 3 (2011): 403-422. This Article is brought to you for free and open access. It has been accepted for inclusion in Electrical and Computer Engineering Faculty Publications and Presentations by an authorized administrator of PDXScholar. Please contact us if we can make this document more accessible: [email protected]. FACTA UNIVERSITATIS (NIS)ˇ SER.: ELEC. ENERG. vol. 24, no. 3, December 2011, 403-422 Decomposition of Reversible Logic Function Based on Cube-Reordering Martin Lukac, Michitaka Kameyama, Marek Perkowski, and Pawel Kerntopf Abstract: We present a novel approach to the synthesis of incompletely specified reversible logic functions. The method is based on cube grouping; the first step of the synthesis method analyzes the logic function and generates groupings of same cubes in such a manner that multiple sub-functions are realized by a single Toffoli gate. This process also reorders the function in such a manner that not only groups of similarly defined cubes are joined together but also don’t care cubes. -
Chapter 2 Quantum Gates
Chapter 2 Quantum Gates “When we get to the very, very small world—say circuits of seven atoms—we have a lot of new things that would happen that represent completely new opportunities for design. Atoms on a small scale behave like nothing on a large scale, for they satisfy the laws of quantum mechanics. So, as we go down and fiddle around with the atoms down there, we are working with different laws, and we can expect to do different things. We can manufacture in different ways. We can use, not just circuits, but some system involving the quantized energy levels, or the interactions of quantized spins.” – Richard P. Feynman1 Currently, the circuit model of a computer is the most useful abstraction of the computing process and is widely used in the computer industry in the design and construction of practical computing hardware. In the circuit model, computer scien- tists regard any computation as being equivalent to the action of a circuit built out of a handful of different types of Boolean logic gates acting on some binary (i.e., bit string) input. Each logic gate transforms its input bits into one or more output bits in some deterministic fashion according to the definition of the gate. By compos- ing the gates in a graph such that the outputs from earlier gates feed into the inputs of later gates, computer scientists can prove that any feasible computation can be performed. In this chapter we will look at the types of logic gates used within circuits and how the notions of logic gates need to be modified in the quantum context. -
Superconducting Qubits: Dephasing and Quantum Chemistry
UNIVERSITY of CALIFORNIA Santa Barbara Superconducting Qubits: Dephasing and Quantum Chemistry A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Physics by Peter James Joyce O'Malley Committee in charge: Professor John Martinis, Chair Professor David Weld Professor Chetan Nayak June 2016 The dissertation of Peter James Joyce O'Malley is approved: Professor David Weld Professor Chetan Nayak Professor John Martinis, Chair June 2016 Copyright c 2016 by Peter James Joyce O'Malley v vi Any work that aims to further human knowledge is inherently dedicated to future generations. There is one particular member of the next generation to which I dedicate this particular work. vii viii Acknowledgements It is a truth universally acknowledged that a dissertation is not the work of a single person. Without John Martinis, of course, this work would not exist in any form. I will be eter- nally indebted to him for ideas, guidance, resources, and|perhaps most importantly| assembling a truly great group of people to surround myself with. To these people I must extend my gratitude, insufficient though it may be; thank you for helping me as I ventured away from superconducting qubits and welcoming me back as I returned. While the nature of a university research group is to always be in flux, this group is lucky enough to have the possibility to continue to work together to build something great, and perhaps an order of magnitude luckier that we should wish to remain so. It has been an honor. Also indispensable on this journey have been all the members of the physics depart- ment who have provided the support I needed (and PCS, I apologize for repeatedly ending up, somehow, on your naughty list). -
Holistic Type Extension for Classical Logic Via Toffoli Quantum Gate
entropy Article Holistic Type Extension for Classical Logic via Toffoli Quantum Gate Hector Freytes 1, Roberto Giuntini 1,2,* and Giuseppe Sergioli 1 1 Dipartimento di Filosofia, University of Cagliari, Via Is Mirrionis 1, 09123 Cagliari, Italy 2 Centro Linceo Interdisciplinare “B. Segre”, 00165 Roma, Italy * Correspondence: [email protected] Received: 31 May 2019; Accepted: 25 June 2019; Published: 27 June 2019 Abstract: A holistic extension of classical propositional logic is introduced via Toffoli quantum gate. This extension is based on the framework of the so-called “quantum computation with mixed states”, where also irreversible transformations are taken into account. Formal aspects of this new logical system are detailed: in particular, the concepts of tautology and contradiction are investigated in this extension. These concepts turn out to receive substantial changes due to the non-separability of some quantum states; as an example, Werner states emerge as particular cases of “holistic” contradiction. Keywords: quantum computational logic; fuzzy logic; quantum Toffoli gate PACS: 02.10.Ab; 02.10.De 1. Introduction In recent years, an increasing interest in logical systems related to quantum mechanics has arisen. Most of these systems are not strictly related to the standard quantum logic, but they are motivated by concrete problems related to quantum information and quantum computation [1–7]. The notion of quantum computation first appeared in the 1980s by Richard Feynman. One of the central issues he posed was the difficulty to efficiently simulate the evolution of a quantum system on a classical computer. He pointed out the computational benefits that arise by employing quantum systems in place of classical ones.