DOCSLIB.ORG

Quantum Computing in the UK Today Dr Rupesh Srivastava, User Engagement May 2021

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Quantum Computing in the UK Today Dr Rupesh Srivastava, User Engagement May 2021 Quantum Computing in the UK today Dr Rupesh Srivastava, User Engagement May 2021 For BCS Berkshire For BCS Berkshire Members What we’ll cover 1. What is Quantum Computing and why the excitement? 2. The status and outlook for Quantum Computing & Simulation 3. The UK QT Programme 4. How to engage with Quantum Computing Question: When will Quantum Computing make an impact? For BCS Berkshire Members “Quantum information is a radical departure in information technology, more fundamentally different from current technology than the digital computer is from the abacus.” W. D. Phillips Nobel Laureate 1997 Saunpan Abacus Modern Laptop Computer A recent history of science and computation For BCS Berkshire Members 19th 20th 21st Quantum 2.0 ENIAC Babbage Difference Engine Colossus at Bletchley Park Summit Supercomputer QCS Hub Research For BCS Berkshire Members Classical Physics influences the design of the latest chips Some components may use quantum principles in their operation – but the chip does not use quantum for computation 32-core AMD Epyc (2017) 19,200,000,000 transistors (14 nm) BREAKING NEWS 2021 For BCS Berkshire Members Why build a quantum computer? The first question is, What kind of computer are we going to use to simulate physics? But the physical world is quantum mechanical, and therefore the proper problem is the simulation of quantum physics. Can you do it with a new kind of computer, a Richard Feynman quantum computer? Nobel laureate … It’s not a Turing machine, but a machine of a different kind. For BCS Berkshire Members Why build a quantum computer? Opportunity New era of discoveries Motivation Moore’s Law can’t continue forever Timing Because now we can!* * 40 years later For BCS Berkshire Members Timing – is key Theory Experiment You need a happy confluence of theory, experiment and engineering Engineering For BCS Berkshire Members Timing – what about now? Theory Experiment It’s just possible to engineer a quantum computer Engineering For BCS Berkshire Members Quantum Computing and Qubits Use and manipulate phenomena of quantum physics • Superposition: • Qubits being in multiple states at the same time, e.g. ‘0’ and ‘1’ • Entanglement: • Grouped behaviour of multiple ‘qubits’ • Interference • Utilising wave properties to amplify the “right” answers and (Source: Blackett Review, 2017) cancel out the “wrong” ones For BCS Berkshire Members Quantum Computing and Qubits In order to simulate N qubits requires 2N classical bits N 2N Comment 3 8 easy! 6 20 ~1x10 laptop 15 50 ~1x10 supercomputer 90 (Source: Blackett Review, 2017) 300 ~2x10 > atoms in known universe For BCS Berkshire Members Illustrating superposition with light A ‘photon’ is a particle of light 1 0 Which path? Quantum physics says that even a single photon can pass through both slits A single photon encodes a “qubit” – a superposition of “0” + “1” For BCS Berkshire Members Why the excitement? • A Quantum Computer’s power doubles with every qubit added • Speedups beyond the capability of future digital computing • Able to solve ‘hard problems’ • Able to mimic real world quantum systems • Expected high impact on most industry sectors, national economies, national security and research and discovery • Estimated impact, $450-800bn operating income/yr* *(Source: Where will Quantum Computer Create Value – And When?, BCG, 2019) Source: The Business Potential of Quantum Computing, BCG @ Q2B, Dec 2019 For BCS Berkshire Members A variety of application areas… starting with M • Medicine • Machine Learning • Materials • Mobility • Molecules • Manufacturing • Modelling & Simulation • Mass Communication • Money Markets • Mysteries of the universe For BCS Berkshire Members Application areas (cont’) (Source: The Business Potential of Quantum Computing, BCG, 2019) For BCS Berkshire Members A variety of ways to build quantum computers Superconducting Solid Cold Nano Ion-traps Photonics circuits state atoms wires Oxford Quantum Oxford Ionics Duality Photonics Quantum Motions Cold Quanta Microsoft Circuits Universal Quantum ORCA Computing Intel Atom Computing IBM IonQ PsiQuantum Quantum Brilliance Pasqal Google Atos Xanadu Rigetti Honeywell QuiX Intel Alibaba MATERIALS IN SUPERCONDUCTING QUANTUM BITS box (a charge qubit) by Nakamura and co-workers 8 9 MATERIALS IN SUPERCONDUCTINGin 1999. In QUANTUM 2002, Vion BITS et al. developed the Trapped-ion qubitsTrapped for -quantumion qubits for computing quantum computingquantronium qubit (a modifi ed charge qubit) with a T2 coherence time of hundreds of nanoseconds David Lucas, NQIT OxfordFor BCS Berkshire Members David Lucas, NQIT Oxford based on the concept of design and operation Quantum computing: some qubit technologies at fi rst-order noise-insensitive bias points. Example ion traps: box (a charge qubit)Burkard by Nakamura et al. and 1 0 co-workerselucidated the importance Example ion traps: 1mm in 1999. 8 In 2002,of Vion symmetry et al. 9 indeveloped qubit designs, the which in con- Superconducting Superconducting1mmIons circuits Diamond quantronium qubit (ajunction modifi ed with charge Bertet qubit) et al. with brought persistent- current fl ux qubit coherence times into the a T2 coherence time of hundreds of nanoseconds 1 1 IBM based on the conceptfew ofmicroseconds design and operation range. In 2005–2006, 12 13 at fi rst-order noise-insensitiveIthier et al. and bias Yoshihara points. et al. extensively measured the noise properties of quantro- Burkard et al. 1 0 elucidated the importance 5mm Microfabricated surface traps with nium and fl ux qubits, respectively, to better integrated microwaveof circuitry symmetry in qubit designs, which in con- Superconducting circuitsMacroscopicMacroscopic ion trap understand the sources of decoherence. The Oxford junction with Bertet et al. brought persistent- 5mm “blade”Microfabricated trap surface traps with ~1 cm“transmon” qubit developed by Schoelkopf integrated microwave circuitry current fl ux qubitand coherence co-workers times signifi into cantlythe reduced the IBM Macroscopic ion trap Key features: few microseconds range. 1 1 In 2005–2006, • Electric circuits made from charge sensitivity+ of the Cooper pair box • room temperature operations Ithier et al. 12 and Yoshiharasingle Ca etion al. 13 extensively superconducting materials• high -vacuum 9-qubit “memory register” by adding a shunt interdigitated capacitor, • 10μm – 100μm feature sizes measured the noisewhich properties would later of quantro-bring microsecond times • Fabricated using semiconductor Key features: • optical (laser) and electronic control nium and fl ux qubits,to the respectively, cavity-QED (quantumto better electrodynamic) industry cleanroom techniques + • room temperature operations understandsingle the Ca sourcesionarchitecture. of decoherence. 14 , 15 An MIT/NEC The group increased Oxford • high-vacuum 9-qubit “memory register” “transmon” qubit Tdeveloped above 20 µby s withSchoelkopf a persistent-current fl ux • Operated at very low Microfabricatedtemperature 9 qubit 2 • 10μm – 100μm feature sizes and co-workers qubitsignifi incantly a 2D reduced geometry the using dynamical to make them quantum “chip” trap “memory register” • Electric circuits made• optical from (laser) and electronic control charge sensitivitydecoupling of the Cooper sequences, pair 1 6box and the 3D-cavity superconducting •materialsControlled using microwaves by adding a shuntapproach interdigitated developed capacitor, at Yale 1 7 and now used Oliver & Welander ~ 2 nm Figure 1. Superconducting qubits and their coherence. (a) The three fundamentalwhich would laterby bring several microsecond groups has timesfurther increased this • Fabricated using •semiconductorIn ~20 years of development, MRS Bulletin 2013 coherencesuperconducting has improved qubit modalities: >1000x charge, f ux, and phase. Each includes oneto theor more cavity-QED time (quantum to around electrodynamic) 100 µ s. 1 8 More recently, improve- industry cleanroom techniquesJosephson junctions (shown in red). Illustration by Corey Reed, adapted from Reference 3. architecture. 14 , 15 Anments MIT/NEC in substrate group increasedpreparation and materials (b) The Josephson junction acts as both an inductor, L J , and capacitor, CJ . External inductors Superconducting Circuits for Quantum Computing — Peter Leek choices, addressing issues elucidated by the 3D • Operated at very low temperatureand capacitors, Lext and Cext , can be added to modify the qubit’s potentialT 2energy above 20 µ s with a persistent-current fl ux to make them quantumlandscape and reduce sensitivity to noise. (c) Because the Josephson junctionqubit inductance in a 2D geometrygeometries, using have dynamicalled to improved coherence is nonlinear, the qubit potential is anharmonic. The qubit comprises the two-lowest states 1 9 , 2 0 of 2D 1 6 geometries. T h i s fi ve-orders-of- and is addressed at a unique frequency, f01 . (d) 15 years of progress in qubit coherdecouplingence times, sequences, and the 3D-cavity • Controlled using microwavesreminiscent of Moore’s Law for semiconductor electronics. On average, the doublingapproach rate for developed magnitude at Yale improvement 1 7 and now used in the primary single- coherence times in superconducting qubitsOliver is about & Welanderonce per year. Improvements have been qubit metric can be justly termed a “Moore’s • In ~20 Figure years 1. Superconducting of development,driven qubits by both and new their device coherence. designs (a)and The materials three fundamentaladvances. Qubit modalitiesby represented several groups has further increased this MRS
Load more

Recommended publications
  • Key Concepts for Future QIS Learners Workshop Output Published Online May 13, 2020
    Key Concepts for Future QIS Learners Workshop output published online May 13, 2020 Background and Overview On behalf of the Interagency Working Group on Workforce, Industry and Infrastructure, under the NSTC Subcommittee on Quantum Information Science (QIS), the National Science Foundation invited 25 researchers and educators to come together to deliberate on defining a core set of key concepts for future QIS learners that could provide a starting point for further curricular and educator development activities. The deliberative group included university and industry researchers, secondary school and college educators, and representatives from educational and professional organizations. The workshop participants focused on identifying concepts that could, with additional supporting resources, help prepare secondary school students to engage with QIS and provide possible pathways for broader public engagement. This workshop report identifies a set of nine Key Concepts. Each Concept is introduced with a concise overall statement, followed by a few important fundamentals. Connections to current and future technologies are included, providing relevance and context. The first Key Concept defines the field as a whole. Concepts 2-6 introduce ideas that are necessary for building an understanding of quantum information science and its applications. Concepts 7-9 provide short explanations of critical areas of study within QIS: quantum computing, quantum communication and quantum sensing. The Key Concepts are not intended to be an introductory guide to quantum information science, but rather provide a framework for future expansion and adaptation for students at different levels in computer science, mathematics, physics, and chemistry courses. As such, it is expected that educators and other community stakeholders may not yet have a working knowledge of content covered in the Key Concepts.
    [Show full text]
  • Quantum Computing: Principles and Applications
    Journal of International Technology and Information Management Volume 29 Issue 2 Article 3 2020 Quantum Computing: Principles and Applications Yoshito Kanamori University of Alaska Anchorage, [email protected] Seong-Moo Yoo University of Alabama in Huntsville, [email protected] Follow this and additional works at: https://scholarworks.lib.csusb.edu/jitim Part of the Communication Technology and New Media Commons, Computer and Systems Architecture Commons, Information Security Commons, Management Information Systems Commons, Science and Technology Studies Commons, Technology and Innovation Commons, and the Theory and Algorithms Commons Recommended Citation Kanamori, Yoshito and Yoo, Seong-Moo (2020) "Quantum Computing: Principles and Applications," Journal of International Technology and Information Management: Vol. 29 : Iss. 2 , Article 3. Available at: https://scholarworks.lib.csusb.edu/jitim/vol29/iss2/3 This Article is brought to you for free and open access by CSUSB ScholarWorks. It has been accepted for inclusion in Journal of International Technology and Information Management by an authorized editor of CSUSB ScholarWorks. For more information, please contact [email protected]. Journal of International Technology and Information Management Volume 29, Number 2 2020 Quantum Computing: Principles and Applications Yoshito Kanamori (University of Alaska Anchorage) Seong-Moo Yoo (University of Alabama in Huntsville) ABSTRACT The development of quantum computers over the past few years is one of the most significant advancements in the history of quantum computing. D-Wave quantum computer has been available for more than eight years. IBM has made its quantum computer accessible via its cloud service. Also, Microsoft, Google, Intel, and NASA have been heavily investing in the development of quantum computers and their applications.
    [Show full text]
  • Is Quantum Search Practical?
    Q UANTUM C OMPUTING IS QUANTUM SEARCH PRACTICAL? Gauging a quantum algorithm’s practical significance requires weighing it against the best conventional techniques applied to useful instances of the same problem. The authors show that several commonly suggested applications of Grover’s quantum search algorithm fail to offer computational improvements over the best conventional algorithms. ome researchers suggest achieving mas- polynomial-time algorithm for number factoring sive speedups in computing by exploiting is known, and the security of the RSA code used quantum-mechanical effects such as su- on the Internet relies on this problem’s difficulty. perposition (quantum parallelism) and If a large and error-tolerant quantum computer Sentanglement.1 A quantum algorithm typically were available today, running Shor’s algorithm on consists of applying quantum gates to quantum it could compromise e-commerce. states, but because the input to the algorithm Lov Grover’s quantum search algorithm is also might be normal classical bits (or nonquantum), widely studied. It must compete with advanced it only affects the selection of quantum gates. Af- classical search techniques in applications that use ter all the gates are applied, quantum measure- parallel processing3 or exploit problem structure, ment is performed, producing the algorithm’s often implicitly. Despite its promise, though, it is nonquantum output. Deutsch’s algorithm, for in- by no means clear whether, or how soon, quantum stance, solves a certain artificial problem in fewer computing methods will offer better performance steps than any classical (nonquantum) algorithm, in useful applications.4 Traditional complexity and its relative speedup grows with the problem analysis of Grover’s algorithm doesn’t consider the size.
    [Show full text]
  • Quantum Algorithms
    An Introduction to Quantum Algorithms Emma Strubell COS498 { Chawathe Spring 2011 An Introduction to Quantum Algorithms Contents Contents 1 What are quantum algorithms? 3 1.1 Background . .3 1.2 Caveats . .4 2 Mathematical representation 5 2.1 Fundamental differences . .5 2.2 Hilbert spaces and Dirac notation . .6 2.3 The qubit . .9 2.4 Quantum registers . 11 2.5 Quantum logic gates . 12 2.6 Computational complexity . 19 3 Grover's Algorithm 20 3.1 Quantum search . 20 3.2 Grover's algorithm: How it works . 22 3.3 Grover's algorithm: Worked example . 24 4 Simon's Algorithm 28 4.1 Black-box period finding . 28 4.2 Simon's algorithm: How it works . 29 4.3 Simon's Algorithm: Worked example . 32 5 Conclusion 33 References 34 Page 2 of 35 An Introduction to Quantum Algorithms 1. What are quantum algorithms? 1 What are quantum algorithms? 1.1 Background The idea of a quantum computer was first proposed in 1981 by Nobel laureate Richard Feynman, who pointed out that accurately and efficiently simulating quantum mechanical systems would be impossible on a classical computer, but that a new kind of machine, a computer itself \built of quantum mechanical elements which obey quantum mechanical laws" [1], might one day perform efficient simulations of quantum systems. Classical computers are inherently unable to simulate such a system using sub-exponential time and space complexity due to the exponential growth of the amount of data required to completely represent a quantum system. Quantum computers, on the other hand, exploit the unique, non-classical properties of the quantum systems from which they are built, allowing them to process exponentially large quantities of information in only polynomial time.
    [Show full text]
  • On Counterfactual Computation
    On Counterfactual Computation Paolo Zuliani Department of Computer Science Princeton University Princeton, NJ 08544, USA [email protected] Abstract In this paper we pursue two targets. First, showing that counterfactual computa- tion can be rigorously formalised as a quantum computation. Second, presenting a new counterfactual protocol which improve previous protocols. Counterfactual computation makes use of quantum mechanics' peculiarities to infer the outcome of a quantum com- putation without running that computation. In this paper, we first cast the definition of counterfactual protocol in the quantum programming language qGCL, thereby show- ing that counterfactual computation is an example of quantum computation. Next, we formalise in qGCL a probabilistic extension of counterfactual protocol for decision r problems (whose result is either 0 or 1). If pG denotes for protocol G the probability of obtaining result r \for free" (i.e. without running the quantum computer), then we 0 1 show that for any probabilistic protocol pG + pG ≤ 1 (as for non-probabilistic pro- 0 1 tocols). Finally, we present a probabilistic protocol K which satisfies pK + pK = 1, thus being optimal. Furthermore, the result is attained with a single insertion of the quantum computer, while it has been shown that a non-probabilistic protocol would obtain the result only in the limit (i.e. with an infinite number of insertions). 1 Introduction Counterfactuality is the fact that the sole possibility for an event to occur allows one to gain some information about that event, even though it did not actually occur. Counterfac- tual computation [4, 5] uses peculiar features of quantum mechanics to infer counterfactual statements about the result of a computation.
    [Show full text]
  • Superconducting Transmon Machines
    Quantum Computing Hardware Platforms: Superconducting Transmon Machines • CSC591/ECE592 – Quantum Computing • Fall 2020 • Professor Patrick Dreher • Research Professor, Department of Computer Science • Chief Scientist, NC State IBM Q Hub 3 November 2020 Superconducting Transmon Quantum Computers 1 5 November 2020 Patrick Dreher Outline • Introduction – Digital versus Quantum Computation • Conceptual design for superconducting transmon QC hardware platforms • Construction of qubits with electronic circuits • Superconductivity • Josephson junction and nonlinear LC circuits • Transmon design with example IBM chip layout • Working with a superconducting transmon hardware platform • Quantum Mechanics of Two State Systems - Rabi oscillations • Performance characteristics of superconducting transmon hardware • Construct the basic CNOT gate • Entangled transmons and controlled gates • Appendices • References • Quantum mechanical solution of the 2 level system 3 November 2020 Superconducting Transmon Quantum Computers 2 5 November 2020 Patrick Dreher Digital Computation Hardware Platforms Based on a Base2 Mathematics • Design principle for a digital computer is built on base2 mathematics • Identify voltage changes in electrical circuits that map base2 math into a “zero” or “one” corresponding to an on/off state • Build electrical circuits from simple on/off states that apply these basic rules to construct digital computers 3 November 2020 Superconducting Transmon Quantum Computers 3 5 November 2020 Patrick Dreher From Previous Lectures It was
    [Show full text]
  • Quantum Distributed Computing Applied to Grover's Search Algorithm
    Quantum Distributed Computing Applied to Grover’s Search Algorithm B Debabrata Goswami( ) Indian Institute of Technology Kanpur, Kanpur 208016, India [email protected] Abstract. Grover’s Algorithm√ finds a unique element in an unsorted stock of N-elements in N queries through quantum search. A single- query solution can also be designed, but with an overhead of N log2 N steps to prepare and post process the query, which is worse than the classical N/2 queries. We show here that by distributing the computing load on a set of quantum computers, we achieve better information the- oretic bounds and relaxed space scaling. Howsoever small one quantum computing node is, by virtue of networking and sharing of data, we can virtually work with a sufficiently large qubit space. Keywords: Distributed quantum computing · Grover’s quantum search · Optical networking 1 Introduction Today’s digital computer is the cumulation of technological advancements that began with the mechanical clockwork ideas of Charles Babbage in the nineteenth century. However, it is surprising that logically, the high speed modern day com- puter is not fundamentally different from its gigantic 30 ton ancestors, the first of which were built in 1941 by the German engineer Konrad Zuse. Although comput- ers nowadays have become more compact and considerably faster in their perfor- mance, their primary execution methodology has remained the same, which is to derive a computationally useful result via the manipulation and interpretation of encoded bits. The underlying mathematical principles are indistinguishable from those outlined in the visionary Church-Turing hypothesis, proposed in the year 1936, much ahead of the birth of the first computer.
    [Show full text]
  • Quantum Computing : a Gentle Introduction / Eleanor Rieffel and Wolfgang Polak
    QUANTUM COMPUTING A Gentle Introduction Eleanor Rieffel and Wolfgang Polak The MIT Press Cambridge, Massachusetts London, England ©2011 Massachusetts Institute of Technology All rights reserved. No part of this book may be reproduced in any form by any electronic or mechanical means (including photocopying, recording, or information storage and retrieval) without permission in writing from the publisher. For information about special quantity discounts, please email [email protected] This book was set in Syntax and Times Roman by Westchester Book Group. Printed and bound in the United States of America. Library of Congress Cataloging-in-Publication Data Rieffel, Eleanor, 1965– Quantum computing : a gentle introduction / Eleanor Rieffel and Wolfgang Polak. p. cm.—(Scientific and engineering computation) Includes bibliographical references and index. ISBN 978-0-262-01506-6 (hardcover : alk. paper) 1. Quantum computers. 2. Quantum theory. I. Polak, Wolfgang, 1950– II. Title. QA76.889.R54 2011 004.1—dc22 2010022682 10987654321 Contents Preface xi 1 Introduction 1 I QUANTUM BUILDING BLOCKS 7 2 Single-Qubit Quantum Systems 9 2.1 The Quantum Mechanics of Photon Polarization 9 2.1.1 A Simple Experiment 10 2.1.2 A Quantum Explanation 11 2.2 Single Quantum Bits 13 2.3 Single-Qubit Measurement 16 2.4 A Quantum Key Distribution Protocol 18 2.5 The State Space of a Single-Qubit System 21 2.5.1 Relative Phases versus Global Phases 21 2.5.2 Geometric Views of the State Space of a Single Qubit 23 2.5.3 Comments on General Quantum State Spaces
    [Show full text]
  • Conceptual Framework for Quantum Affective Computing and Its Use in Fusion of Multi-Robot Emotions
    electronics Article Conceptual Framework for Quantum Affective Computing and Its Use in Fusion of Multi-Robot Emotions Fei Yan 1 , Abdullah M. Iliyasu 2,3,∗ and Kaoru Hirota 3,4 1 School of Computer Science and Technology, Changchun University of Science and Technology, Changchun 130022, China; [email protected] 2 College of Engineering, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia 3 School of Computing, Tokyo Institute of Technology, Yokohama 226-8502, Japan; [email protected] 4 School of Automation, Beijing Institute of Technology, Beijing 100081, China * Correspondence: [email protected] Abstract: This study presents a modest attempt to interpret, formulate, and manipulate the emotion of robots within the precepts of quantum mechanics. Our proposed framework encodes emotion information as a superposition state, whilst unitary operators are used to manipulate the transition of emotion states which are subsequently recovered via appropriate quantum measurement operations. The framework described provides essential steps towards exploiting the potency of quantum mechanics in a quantum affective computing paradigm. Further, the emotions of multi-robots in a specified communication scenario are fused using quantum entanglement, thereby reducing the number of qubits required to capture the emotion states of all the robots in the environment, and therefore fewer quantum gates are needed to transform the emotion of all or part of the robots from one state to another. In addition to the mathematical rigours expected of the proposed framework, we present a few simulation-based demonstrations to illustrate its feasibility and effectiveness. This exposition is an important step in the transition of formulations of emotional intelligence to the quantum era.
    [Show full text]
  • A Game Plan for Quantum Computing
    February 2020 A game plan for quantum computing Thanks to technology advances, some companies may reap real gains from quantum computing within five years. What should you do to prepare for this next big wave in computers? by Alexandre Ménard, Ivan Ostojic, Mark Patel, and Daniel Volz Pharmaceutical companies have an abiding interest in enzymes. These proteins catalyze all kinds of biochemical interactions, often by targeting a single type of molecule with great precision. Harnessing the power of enzymes may help alleviate the major diseases of our time. Unfortunately, we don’t know the exact molecular structure of most enzymes. In principle, chemists could use computers to model these molecules in order to identify how the molecules work, but enzymes are such complex structures that most are impossible for classical computers to model. A sufficiently powerful quantum computer, however, could accurately predict in a matter of hours the properties, structure, and reactivity of such substances—an advance that could revolutionize drug development and usher in a new era in healthcare. Quantum computers have the potential to resolve problems of this complexity and magnitude across many different industries and applications, including finance, transportation, chemicals, and cybersecurity. Solving the impossible in a few hours of computing time, finding answers to problems that have bedeviled science and society for years, unlocking unprecedented capabilities for businesses of all kinds—those are the promises of quantum computing, a fundamentally different approach to computation. None of this will happen overnight. In fact, many companies and businesses won’t be able to reap significant value from quantum computing for a decade or more, although a few will see gains in the next five years.
    [Show full text]
  • Quantum Computational Complexity Theory Is to Un- Derstand the Implications of Quantum Physics to Computational Complexity Theory
    Quantum Computational Complexity John Watrous Institute for Quantum Computing and School of Computer Science University of Waterloo, Waterloo, Ontario, Canada. Article outline I. Definition of the subject and its importance II. Introduction III. The quantum circuit model IV. Polynomial-time quantum computations V. Quantum proofs VI. Quantum interactive proof systems VII. Other selected notions in quantum complexity VIII. Future directions IX. References Glossary Quantum circuit. A quantum circuit is an acyclic network of quantum gates connected by wires: the gates represent quantum operations and the wires represent the qubits on which these operations are performed. The quantum circuit model is the most commonly studied model of quantum computation. Quantum complexity class. A quantum complexity class is a collection of computational problems that are solvable by a cho- sen quantum computational model that obeys certain resource constraints. For example, BQP is the quantum complexity class of all decision problems that can be solved in polynomial time by a arXiv:0804.3401v1 [quant-ph] 21 Apr 2008 quantum computer. Quantum proof. A quantum proof is a quantum state that plays the role of a witness or certificate to a quan- tum computer that runs a verification procedure. The quantum complexity class QMA is defined by this notion: it includes all decision problems whose yes-instances are efficiently verifiable by means of quantum proofs. Quantum interactive proof system. A quantum interactive proof system is an interaction between a verifier and one or more provers, involving the processing and exchange of quantum information, whereby the provers attempt to convince the verifier of the answer to some computational problem.
    [Show full text]
  • Pub50250.Pdf
    ARTICLE https://doi.org/10.1038/s41467-021-21982-y OPEN Removing leakage-induced correlated errors in superconducting quantum error correction M. McEwen 1,2, D. Kafri3, Z. Chen2, J. Atalaya3, K. J. Satzinger 2, C. Quintana2, P. V. Klimov2, D. Sank2, C. Gidney2, A. G. Fowler2, F. Arute2, K. Arya2, B. Buckley2, B. Burkett 2, N. Bushnell2, B. Chiaro2, R. Collins2, S. Demura 2, A. Dunsworth2, C. Erickson2, B. Foxen2, M. Giustina2, T. Huang2, S. Hong2, E. Jeffrey2, S. Kim2, K. Kechedzhi3, F. Kostritsa2, P. Laptev2, A. Megrant2,X.Mi2, J. Mutus2, O. Naaman 2, M. Neeley 2, C. Neill2, M. Niu3, A. Paler4,5, N. Redd 2, P. Roushan2, T. C. White2, J. Yao2, P. Yeh 2, A. Zalcman 2, Yu Chen2, ✉ V. N. Smelyanskiy3, John M. Martinis1, H. Neven2, J. Kelly2, A. N. Korotkov2,6, A. G. Petukhov2 & R. Barends2 1234567890():,; Quantum computing can become scalable through error correction, but logical error rates only decrease with system size when physical errors are sufficiently uncorrelated. During computation, unused high energy levels of the qubits can become excited, creating leakage states that are long-lived and mobile. Particularly for superconducting transmon qubits, this leakage opens a path to errors that are correlated in space and time. Here, we report a reset protocol that returns a qubit to the ground state from all relevant higher level states. We test its performance with the bit-flip stabilizer code, a simplified version of the surface code for quantum error correction. We investigate the accumulation and dynamics of leakage during error correction. Using this protocol, we find lower rates of logical errors and an improved scaling and stability of error suppression with increasing qubit number.
    [Show full text]