DOCSLIB.ORG

Measuring and Simulating T1 and T2 for Qubits

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Measuring and Simulating T1 and T2 for Qubits Measuring and Simulating T1 and T2 for Qubits Rahaf Youssef and Supervisor: Adam Lyon Saint Olaf College, MN 50557 and Fermi National Accelerator Laboratory, Batavia, IL 60510 (Dated: August 7, 2020) Quantum computers are computational devices that employ quantum-mechanical phenomena in solving problems that are classically intractable. Future applications of quantum computers include prime factorization of large numbers, implementing more efficient search algorithms, among various applications. Most quantum algorithms utilize superposition of states in solving a given problem. Therefore, the decay of the superposition of states is a limitation to performing complex quantum algorithms. Quantum decoherence is usually characterized by measuring two constants: T1 (thermal relaxation time) and T2 (dephasing time). Here we present an overview of measuring and simulating T1 and T2 for qubits and qudits using QuTip and Qiskit. I. INTRODUCTION this report, we provide an approach as to how T1 and T2 values are calculated and simulated for quantum systems. Quantum computers perform computations exploiting In addition, we compare simulated values of T1 and T2 quantum mechanics to a possible advantage, allowing us with those of a real quantum computer’s measurements. to prepare and manipulate states that do not have a clas- IBMQ Experience is used to prepare, run and measure sical equivalent. In particular, phenomena like superpo- quantum states, while QuTip is used for simulation. sition and entanglement may enable quantum computers to outperform their classical counterparts in certain ap- plications. In fact, it has been shown that the number of II. BACKGROUND steps required to find the prime factors of an integer in- creases exponentially as the integer increases [1]. Shor’s The basic unit of information for quantum computers factoring algorithm, however, can factor prime numbers is a qubit. In classical computers, bits are manifested in polynomial time. In fact, there has been promising re- by transistors that are turned on or off through applying sults from the D-Wave 2000Q computer as it was able to electrical pulses. The value of bit is deterministic and is factor the number 376289 using 94 logical qubit gates [2]. measured to be either 0 or 1. For quantum computers, It is thus essential to develop new encryption protocols qubits are implemented as a two-state device exhibiting since the security of online transactions assumes the im- desired quantum-mechanical phenomena such as super- possibility of factoring large numbers in a reasonable time position or entanglement. using classical algorithms. Furthermore, quantum com- Theoretically, qubits are represented as vectors in puters hold promise of efficiently simulating large atomic Hilbert space, a complex vector space with an inner prod- systems in order to understand their properties. The uct. Qubits can exist in the state j0i or j1i or a su- calculation time scales exponentially using classical com- perposition of both states such that j i= αj0i + βj1i, puters as the number of atoms grows, while it grows poly- where α and β are probability amplitudes, implying that nomially on quantum computers [3]. α2 + β2 = 1. Quantum gates are defined as opera- Implementing these useful quantum algorithms is con- tions on quantum states represented by unitary matrices, tingent upon building accurate quantum hardware that is U yU=UU y=I, making quantum computations reversible. not affected by noise. Environmental noise decreases co- Gates may be visualized as rotations around the Bloch herence time of qubits, meaning that qubits do not stay sphere in Figure 1. The Bloch sphere has basis states in a desired state long enough to carry out a complex given by the x, y, and z axes. The direction of the state computation. Right now, the coherence time of qubits is , the red vector on the sphere, determines the state of on the order of 10’s of microseconds, which is not long the qubit. For example, if is pointing in the positive z- enough to solve interesting problems. Therefore, mitigat- direction, the qubit is in the j0i state and if it is pointing ing noise and designing noise-tolerant quantum comput- in the negative z-direction, the qubit is in the j1i state. ers is a necessity. To that end, harnessing the full power If is pointing anywhere between j0i or j1i, the qubit is of quantum computers necessitate characterization and in a superposition of both states. It is also worth noting understanding of noise sources and how they impact a that the Bloch Sphere is a viable representation of a sin- given quantum system. gle qubit only, as states of higher dimensions cannot be Often times, T1 and T2 are used to quantify noise. In visualized. 2 putational basis i.e. the j+i,|−i basis or the j0i,j1i basis. Measuring the state of the system causes the wave func- tion to collapse into one state, destroying the quantum state. However, creative techniques, such as quantum non-demolishing measurement(QND), have been devel- oped to observe the state of the system without causing its state decay. That way, it is possible to continuously monitor the state of the qubit for some time before it eventually decays due to energy dissipation. III. METHODS In order to simulate quantum systems, the following Figure 1: The Bloch Sphere tools were used Experimentally, there are numerous techniques to • Qiskit: IBMQ Experience is an online platform fabricate qubits. Generally, in order for a qubit to per- that enables the general public to run quantum form well, it must satisfy some requirements such as be- algorithms on real quantum computers. Qiskit, ing loosely coupled to their environment and strongly an open-source software development kit, provides coupled to a classical control system. It is also imper- users with pulse-level control. The used model ative for the qubit to be an anharmonic oscillator. A of computation is quantum circuits, where quan- harmonic oscillator would not work because all levels are tum algorithms consist of consecutive gates. IBM’s uniformly spaced, so a pulse that excites the first tran- quantum computers consist of superconducting sition would also excite the second (and third and any transmon qubits that are based in their research others)[4]. Hence, the goal is to design an anharmonic centers [7]. oscillator where the two lowest energy levels are used • QuTip: an open-source software for simulating the as qubit.For the purpose of this report, only the real- dynamics of quantum systems. It contains built- ization of transmission line shunted plasma oscillation in functions that represent different noise models, qubits (transmon qubits) will be discussed. The trans- offering an easy-to-use simulation of open quantum mon circuit, as shown in Figure 2, consists of a Josephson systems. Finally, QuTip is Python-based and can Junction shunted by a relatively large capacitor so that be run on Jupyter notebooks [8]. noise charge is reduced [5]. The Josephson Junction is responsible for anharmonicity, which allows for selective Measuring T1: thermal relaxation time is defined as qubit control. The circuit then could be conceived as an the time needed for a qubit to move from the excited artificial atom. This design minimizes energy dissipation, state j1i to the ground state j0i. The process could be resulting in longer coherence time ≈100µs and allowing formulated by the density matrix ρ = αj ih j + βjgihgj for longer computations to take place [6]. where α2 is the probability that the qubit is in state j i whereas β2 is the probability that a qubit is in the ground state jgi. As time goes by, the value of β2 approaches 1. Experimentally, T1 is the time by which the population of excited state decays to 1/e of its initial value, Pe(t) = −t=T1 Pe(0)e [5]. Figure 2: Transmon Qubit:the transmon qubit circuit con- tains a Josephson Junction shunted by a relatively large ca- pacitor so that EJ EC , where Ec is the charging energy (kinetic energy in capacitor) and EJ is the potential energy stored in the Josephson Junction Measurement After applying gates to qubits, a mea- surement should be done in order to identify the state of the system. Measurement is performed in a given com- 3 Experimentally, the value of T1 is measured through the following sequence of operations [5]: 1. Prepare the qubit in the excited state by sending a π-pulse to the qubit. 2. Wait some time t. 3. Measure the state of the qubit. Measuring T2: dephasing time is defined as the elapsed time before a qubit’s resonance frequency be- comes unidentified. T2 could be thought of as the loss Figure 3: A measurement of T1 for a qubit in µs. of quantum coherence over time. The measurement of T2 is achieved through the following sequence of opera- tions [5]: 1. Prepare the qubit in superposition state p1 (jgi + 2 π ijei) by applying a 2 -pulse to the qubit. 2. Wait some time t. π 3. Apply another 2 -pulse to bring back the qubit to ground state. 4. measure the state of the qubit. Figure 4: A measurement of T2 for a qubit in µs. IV. RESULTS Using Qiskit: for the experiments presented in Fig- ures 1 and 2, the ibmqx2 device was used. Ibmqx2 is a five-qubit computer that is based in Yorktown, New York. Both experiments, measuring T1 and T2, were pre- pared, run and measured on the first qubit (qubit 0) with 1024 shots (number of times the system was prepared, run, and measured). According to IBM’s specifications of the device, on average, the qubit’s T1 ≈ 52 µs, while the value of T2 ≈ 77 µs. Though our experiments did not yield these exact numbers, it still provided insights Figure 5: Simulation of T of the first excited state for into the order of magnitude for both values, which is µs.
Load more

Recommended publications
  • Yes, More Decoherence: a Reply to Critics
    Yes, More Decoherence: A Reply to Critics Elise M. Crull∗ Submitted 11 July 2017; revised 24 August 2017 1 Introduction A few years ago I published an article in this journal titled \Less interpretation and more decoherence in quantum gravity and inflationary cosmology" (Crull, 2015) that generated replies from three pairs of authors: Vassallo and Esfeld (2015), Okon and Sudarsky (2016) and Fortin and Lombardi (2017). As a philosopher of physics it is my chief aim to engage physicists and philosophers alike in deeper conversation regarding scientific theories and their implications. In as much as my earlier paper provoked a suite of responses and thereby brought into sharper relief numerous misconceptions regarding decoherence, I welcome the occasion provided by the editors of this journal to continue the discussion. In what follows, I respond to my critics in some detail (wherein the devil is often found). I must be clear at the outset, however, that due to the nature of these criticisms, much of what I say below can be categorized as one or both of the following: (a) a repetition of points made in the original paper, and (b) a reiteration of formal and dynamical aspects of quantum decoherence considered uncontroversial by experts working on theoretical and experimental applications of this process.1 I begin with a few paragraphs describing what my 2015 paper both was, and was not, about. I then briefly address Vassallo's and Esfeld's (hereafter VE) relatively short response to me, dedicating the bulk of my reply to the lengthy critique of Okon and Sudarsky (hereafter OS).
    [Show full text]
  • Qiskit Backend Specifications for Openqasm and Openpulse
    Qiskit Backend Specifications for OpenQASM and OpenPulse Experiments David C. McKay1,∗ Thomas Alexander1, Luciano Bello1, Michael J. Biercuk2, Lev Bishop1, Jiayin Chen2, Jerry M. Chow1, Antonio D. C´orcoles1, Daniel Egger1, Stefan Filipp1, Juan Gomez1, Michael Hush2, Ali Javadi-Abhari1, Diego Moreda1, Paul Nation1, Brent Paulovicks1, Erick Winston1, Christopher J. Wood1, James Wootton1 and Jay M. Gambetta1 1IBM Research 2Q-CTRL Pty Ltd, Sydney NSW Australia September 11, 2018 Abstract As interest in quantum computing grows, there is a pressing need for standardized API's so that algorithm designers, circuit designers, and physicists can be provided a common reference frame for designing, executing, and optimizing experiments. There is also a need for a language specification that goes beyond gates and allows users to specify the time dynamics of a quantum experiment and recover the time dynamics of the output. In this document we provide a specification for a common interface to backends (simulators and experiments) and a standarized data structure (Qobj | quantum object) for sending experiments to those backends via Qiskit. We also introduce OpenPulse, a language for specifying pulse level control (i.e. control of the continuous time dynamics) of a general quantum device independent of the specific arXiv:1809.03452v1 [quant-ph] 10 Sep 2018 hardware implementation. ∗[email protected] 1 Contents 1 Introduction3 1.1 Intended Audience . .4 1.2 Outline of Document . .4 1.3 Outside of the Scope . .5 1.4 Interface Language and Schemas . .5 2 Qiskit API5 2.1 General Overview of a Qiskit Experiment . .7 2.2 Provider . .8 2.3 Backend .
    [Show full text]
  • Optimization of Transmon Design for Longer Coherence Time
    Optimization of transmon design for longer coherence time Simon Burkhard Semester thesis Spring semester 2012 Supervisor: Dr. Arkady Fedorov ETH Zurich Quantum Device Lab Prof. Dr. A. Wallraff Abstract Using electrostatic simulations, a transmon qubit with new shape and a large geometrical size was designed. The coherence time of the qubits was increased by a factor of 3-4 to about 4 µs. Additionally, a new formula for calculating the coupling strength of the qubit to a transmission line resonator was obtained, allowing reasonably accurate tuning of qubit parameters prior to production using electrostatic simulations. 2 Contents 1 Introduction 4 2 Theory 5 2.1 Coplanar waveguide resonator . 5 2.1.1 Quantum mechanical treatment . 5 2.2 Superconducting qubits . 5 2.2.1 Cooper pair box . 6 2.2.2 Transmon . 7 2.3 Resonator-qubit coupling (Jaynes-Cummings model) . 9 2.4 Effective transmon network . 9 2.4.1 Calculation of CΣ ............................... 10 2.4.2 Calculation of β ............................... 10 2.4.3 Qubits coupled to 2 resonators . 11 2.4.4 Charge line and flux line couplings . 11 2.5 Transmon relaxation time (T1) ........................... 11 3 Transmon simulation 12 3.1 Ansoft Maxwell . 12 3.1.1 Convergence of simulations . 13 3.1.2 Field integral . 13 3.2 Optimization of transmon parameters . 14 3.3 Intermediate transmon design . 15 3.4 Final transmon design . 15 3.5 Comparison of the surface electric field . 17 3.6 Simple estimate of T1 due to coupling to the charge line . 17 3.7 Simulation of the magnetic flux through the split junction .
    [Show full text]
  • It Is a Great Pleasure to Write This Letter on Behalf of Dr. Maria
    Rigorous Quantum-Classical Path Integral Formulation of Real-Time Dynamics Nancy Makri Departments of Chemistry and Physics University of Illinois The path integral formulation of time-dependent quantum mechanics provides the ideal framework for rigorous quantum-classical or quantum-semiclassical treatments, as the spatially localized, trajectory-like nature of the quantum paths circumvents the need for mean-field-type assumptions. However, the number of system paths grows exponentially with the number of propagation steps. In addition, each path of the quantum system generally gives rise to a distinct classical solvent trajectory. This exponential proliferation of trajectories with propagation time is the quantum-classical manifestation of nonlocality. A rigorous real-time quantum-classical path integral (QCPI) methodology has been developed, which converges to the stationary phase limit of the full path integral with respect to the degrees of freedom comprising the system’s environment. The starting point is the identification of two components in the effects induced on a quantum system by a polyatomic environment. The first, “classical decoherence mechanism” is associated with phonon absorption and induced emission and is dominant at high temperature. Within the QCPI framework, the memory associated with classical decoherence is removable. A second, nonlocal in time, “quantum decoherence process”, which is associated with spontaneous phonon emission, becomes important at low temperatures and is responsible for detailed balance. The QCPI methodology takes advantage of the memory-free nature of system-independent solvent trajectories to account for all classical decoherence effects on the dynamics of the quantum system in an inexpensive fashion. Inclusion of the residual quantum decoherence is accomplished via phase factors in the path integral expression, which is amenable to large time steps and iterative decompositions.
    [Show full text]
  • Qubit Coupled Cluster Singles and Doubles Variational Quantum Eigensolver Ansatz for Electronic Structure Calculations
    Quantum Science and Technology PAPER Qubit coupled cluster singles and doubles variational quantum eigensolver ansatz for electronic structure calculations To cite this article: Rongxin Xia and Sabre Kais 2020 Quantum Sci. Technol. 6 015001 View the article online for updates and enhancements. This content was downloaded from IP address 128.210.107.25 on 20/10/2020 at 12:02 Quantum Sci. Technol. 6 (2021) 015001 https://doi.org/10.1088/2058-9565/abbc74 PAPER Qubit coupled cluster singles and doubles variational quantum RECEIVED 27 July 2020 eigensolver ansatz for electronic structure calculations REVISED 14 September 2020 Rongxin Xia and Sabre Kais∗ ACCEPTED FOR PUBLICATION Department of Chemistry, Department of Physics and Astronomy, and Purdue Quantum Science and Engineering Institute, Purdue 29 September 2020 University, West Lafayette, United States of America ∗ PUBLISHED Author to whom any correspondence should be addressed. 20 October 2020 E-mail: [email protected] Keywords: variational quantum eigensolver, electronic structure calculations, unitary coupled cluster singles and doubles excitations Abstract Variational quantum eigensolver (VQE) for electronic structure calculations is believed to be one major potential application of near term quantum computing. Among all proposed VQE algorithms, the unitary coupled cluster singles and doubles excitations (UCCSD) VQE ansatz has achieved high accuracy and received a lot of research interest. However, the UCCSD VQE based on fermionic excitations needs extra terms for the parity when using Jordan–Wigner transformation. Here we introduce a new VQE ansatz based on the particle preserving exchange gate to achieve qubit excitations. The proposed VQE ansatz has gate complexity up-bounded to O(n4)for all-to-all connectivity where n is the number of qubits of the Hamiltonian.
    [Show full text]
  • Quantum Computers
    Quantum Computers ERIK LIND. PROFESSOR IN NANOELECTRONICS Erik Lind EIT, Lund University 1 Disclaimer Erik Lind EIT, Lund University 2 Quantum Computers Classical Digital Computers Why quantum computers? Basics of QM • Spin-Qubits • Optical qubits • Superconducting Qubits • Topological Qubits Erik Lind EIT, Lund University 3 Classical Computing • We build digital electronics using CMOS • Boolean Logic • Classical Bit – 0/1 (Defined as a voltage level 0/+Vdd) +vDD +vDD +vDD Inverter NAND Logic is built by connecting gates Erik Lind EIT, Lund University 4 Classical Computing • We build digital electronics using CMOS • Boolean Logic • Classical Bit – 0/1 • Very rubust! • Modern CPU – billions of transistors (logic and memory) • We can keep a logical state for years • We can easily copy a bit • Mainly through irreversible computing However – some problems are hard to solve on a classical computer Erik Lind EIT, Lund University 5 Computing Complexity Searching an unsorted list Factoring large numbers Grovers algo. – Shor’s Algorithm BQP • P – easy to solve and check on a 푛 classical computer ~O(N) • NP – easy to check – hard to solve on a classical computer ~O(2N) P P • BQP – easy to solve on a quantum computer. ~O(N) NP • BQP is larger then P • Some problems in P can be more efficiently solved by a quantum computer Simulating quantum systems Note – it is still not known if 푃 = 푁푃. It is very hard to build a quantum computer… Erik Lind EIT, Lund University 6 Basics of Quantum Mechanics A state is a vector (ray) in a complex Hilbert Space Dimension of space – possible eigenstates of the state For quantum computation – two dimensional Hilbert space ۧ↓ Example - Spin ½ particle - ȁ↑ۧ 표푟 Spin can either be ‘up’ or ‘down’ Erik Lind EIT, Lund University 7 Basics of Quantum Mechanics • A state of a system is a vector (ray) in a complex vector (Hilbert) Space.
    [Show full text]
  • Arxiv:1812.09167V1 [Quant-Ph] 21 Dec 2018 It with the Tex Typesetting System Being a Prime Example
    Open source software in quantum computing Mark Fingerhutha,1, 2 Tomáš Babej,1 and Peter Wittek3, 4, 5, 6 1ProteinQure Inc., Toronto, Canada 2University of KwaZulu-Natal, Durban, South Africa 3Rotman School of Management, University of Toronto, Toronto, Canada 4Creative Destruction Lab, Toronto, Canada 5Vector Institute for Artificial Intelligence, Toronto, Canada 6Perimeter Institute for Theoretical Physics, Waterloo, Canada Open source software is becoming crucial in the design and testing of quantum algorithms. Many of the tools are backed by major commercial vendors with the goal to make it easier to develop quantum software: this mirrors how well-funded open machine learning frameworks enabled the development of complex models and their execution on equally complex hardware. We review a wide range of open source software for quantum computing, covering all stages of the quantum toolchain from quantum hardware interfaces through quantum compilers to implementations of quantum algorithms, as well as all quantum computing paradigms, including quantum annealing, and discrete and continuous-variable gate-model quantum computing. The evaluation of each project covers characteristics such as documentation, licence, the choice of programming language, compliance with norms of software engineering, and the culture of the project. We find that while the diversity of projects is mesmerizing, only a few attract external developers and even many commercially backed frameworks have shortcomings in software engineering. Based on these observations, we highlight the best practices that could foster a more active community around quantum computing software that welcomes newcomers to the field, but also ensures high-quality, well-documented code. INTRODUCTION Source code has been developed and shared among enthusiasts since the early 1950s.
    [Show full text]
  • Building Your Quantum Capability
    Building your quantum capability The case for joining an “ecosystem” IBM Institute for Business Value 2 Building your quantum capability A quantum collaboration Quantum computing has the potential to solve difficult business problems that classical computers cannot. Within five years, analysts estimate that 20 percent of organizations will be budgeting for quantum computing projects and, within a decade, quantum computing may be a USD15 billion industry.1,2 To place your organization in the vanguard of change, you may need to consider joining a quantum computing ecosystem now. The reality is that quantum computing ecosystems are already taking shape, with members focused on how to solve targeted scientific and business problems. Joining the right quantum ecosystem today could give your organization a competitive advantage tomorrow. Building your quantum capability 3 The quantum landscape Quantum computing is gathering momentum. By joining a burgeoning quantum computing Today, major tech companies are backing ecosystem, your organization can get a head What is quantum computing? sizeable R&D programs, venture capital funding start today. Unlike “classical” computers, has grown to at least $300 million, dozens of quantum computers can represent a superposition of multiple states at startups have been founded, quantum A quantum ecosystem brings together business the same time. This characteristic is conferences and research papers are climbing, experts with specialists from industry, expected to provide more efficient research, academia, engineering, physics and students from 1,500 schools have used quantum solutions for certain complex business software development/coding across the computing online, and governments, including and scientific problems, such as drug China and the European Union, have announced quantum stack to develop quantum solutions and materials development, logistics billion-dollar investment programs.3,4,5 that solve business and science problems that and artificial intelligence.
    [Show full text]
  • Less Decoherence and More Coherence in Quantum Gravity, Inflationary Cosmology and Elsewhere
    Less Decoherence and More Coherence in Quantum Gravity, Inflationary Cosmology and Elsewhere Elias Okon1 and Daniel Sudarsky2 1Instituto de Investigaciones Filosóficas, Universidad Nacional Autónoma de México, Mexico City, Mexico. 2Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Mexico City, Mexico. Abstract: In [1] it is argued that, in order to confront outstanding problems in cosmol- ogy and quantum gravity, interpretational aspects of quantum theory can by bypassed because decoherence is able to resolve them. As a result, [1] concludes that our focus on conceptual and interpretational issues, while dealing with such matters in [2], is avoidable and even pernicious. Here we will defend our position by showing in detail why decoherence does not help in the resolution of foundational questions in quantum mechanics, such as the measurement problem or the emergence of classicality. 1 Introduction Since its inception, more than 90 years ago, quantum theory has been a source of heated debates in relation to interpretational and conceptual matters. The prominent exchanges between Einstein and Bohr are excellent examples in that regard. An avoid- ance of such issues is often justified by the enormous success the theory has enjoyed in applications, ranging from particle physics to condensed matter. However, as people like John S. Bell showed [3], such a pragmatic attitude is not always acceptable. In [2] we argue that the standard interpretation of quantum mechanics is inadequate in cosmological contexts because it crucially depends on the existence of observers external to the studied system (or on an artificial quantum/classical cut). We claim that if the system in question is the whole universe, such observers are nowhere to be found, so we conclude that, in order to legitimately apply quantum mechanics in such contexts, an observer independent interpretation of the theory is required.
    [Show full text]
  • Student User Experience with the IBM Qiskit Quantum Computing Interface
    Proceedings of Student-Faculty Research Day, CSIS, Pace University, May 4th, 2018 Student User Experience with the IBM QISKit Quantum Computing Interface Stephan Barabasi, James Barrera, Prashant Bhalani, Preeti Dalvi, Ryan Kimiecik, Avery Leider, John Mondrosch, Karl Peterson, Nimish Sawant, and Charles C. Tappert Seidenberg School of CSIS, Pace University, Pleasantville, New York Abstract - The field of quantum computing is rapidly Schrödinger [11]. Quantum mechanics states that the position expanding. As manufacturers and researchers grapple with the of a particle cannot be predicted with precision as it can be in limitations of classical silicon central processing units (CPUs), Newtonian mechanics. The only thing an observer could quantum computing sheds these limitations and promises a know about the position of a particle is the probability that it boom in computational power and efficiency. The quantum age will be at a certain position at a given time [11]. By the 1980’s will require many skilled engineers, mathematicians, physicists, developers, and technicians with an understanding of quantum several researchers including Feynman, Yuri Manin, and Paul principles and theory. There is currently a shortage of Benioff had begun researching computers that operate using professionals with a deep knowledge of computing and physics this concept. able to meet the demands of companies developing and The quantum bit or qubit is the basic unit of quantum researching quantum technology. This study provides a brief information. Classical computers operate on bits using history of quantum computing, an in-depth review of recent complex configurations of simple logic gates. A bit of literature and technologies, an overview of IBM’s QISKit for information has two states, on or off, and is represented with implementing quantum computing programs, and two a 0 or a 1.
    [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]
  • Resource-Efficient Quantum Computing By
    Resource-Efficient Quantum Computing by Breaking Abstractions Fred Chong Seymour Goodman Professor Department of Computer Science University of Chicago Lead PI, the EPiQC Project, an NSF Expedition in Computing NSF 1730449/1730082/1729369/1832377/1730088 NSF Phy-1818914/OMA-2016136 DOE DE-SC0020289/0020331/QNEXT With Ken Brown, Ike Chuang, Diana Franklin, Danielle Harlow, Aram Harrow, Andrew Houck, John Reppy, David Schuster, Peter Shor Why Quantum Computing? n Fundamentally change what is computable q The only means to potentially scale computation exponentially with the number of devices n Solve currently intractable problems in chemistry, simulation, and optimization q Could lead to new nanoscale materials, better photovoltaics, better nitrogen fixation, and more n A new industry and scaling curve to accelerate key applications q Not a full replacement for Moore’s Law, but perhaps helps in key domains n Lead to more insights in classical computing q Previous insights in chemistry, physics and cryptography q Challenge classical algorithms to compete w/ quantum algorithms 2 NISQ Now is a privileged time in the history of science and technology, as we are witnessing the opening of the NISQ era (where NISQ = noisy intermediate-scale quantum). – John Preskill, Caltech IBM IonQ Google 53 superconductor qubits 79 atomic ion qubits 53 supercond qubits (11 controllable) Quantum computing is at the cusp of a revolution Every qubit doubles computational power Exponential growth in qubits … led to quantum supremacy with 53 qubits vs. Seconds Days Double exponential growth! 4 The Gap between Algorithms and Hardware The Gap between Algorithms and Hardware The Gap between Algorithms and Hardware The EPiQC Goal Develop algorithms, software, and hardware in concert to close the gap between algorithms and devices by 100-1000X, accelerating QC by 10-20 years.
    [Show full text]