Classical Optimizers for Noisy Intermediate-Scale Quantum Devices
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An Update on Google's Quantum Computing Initiative
An Update on Google’s Quantum Computing Initiative January 31, 2019 [email protected] Copyright 2018 Google LLC Our Brains are Wired for Newtonian Physics Brains that recognize and anticipate behaviors of Heat, Light, Momentum, Gravity, etc. have an Evolutionary Advantage. Quantum phenomena contradict our intuition. Quantum Phenomena Contradict Intuition Interference, “Erasure”, etc. 0 Quantum Theory Explains ( 1) Cleanly… ...but the Math looks Strange 1 1 1 1 i i How can a Particle be √2 √2 i 1 On Two Paths at the Same Time? 1 1 √2 i P u 1 1 i P ( r) √2 i 1 Copyright 2017-2019 Google LLC Superposed States, Superposed Information l0〉 2 ( |0〉+|1〉 ) |0〉 + |1〉 = |00〉+|01〉+|10〉+|11〉 l1〉 Copyright 2017-2019 Google LLC 01 Macroscopic QM Enables New Technology Control of single quantum systems, to quantum computers 1 nm 1 μm 1 mm H atom wavefunctions: Problem: Light is 1000x larger Large “atom” has room for complex control Copyright 2017-2019 Google LLC Xmon: Direct coupling + Tunable Transmons ● Direct qubit-qubit capacitive coupling ● Turn interaction on and off with frequency g control “OFF” “ON” f10 f 21 Δ Frequency η Frequency Coupling g Qubit Qubit SQUID 2 2 Coupling rate Ωzz ≈ 4ηg / Δ Qubit A Qubit B Copyright 2017-2019 Google LLC Logic Built from Universal Gates Classical circuit: Quantum circuit: 1 bit NOT 1 qubit rotation 2 bit AND 1 Input Gates 2 qubit CNOT Wiring fan-out No copy 2 Input Gates (space+time ) time Copyright 2017-2019 Google LLC Execution of a Quantum Simulation arXiv:1512.06860 Copyright 2017-2019 Google LLC Quantum -
Advances in Interior Point Methods and Column Generation
Advances in Interior Point Methods and Column Generation Pablo Gonz´alezBrevis Doctor of Philosophy University of Edinburgh 2013 Declaration I declare that this thesis was composed by myself and that the work contained therein is my own, except where explicitly stated otherwise in the text. (Pablo Gonz´alezBrevis) ii To my endless inspiration and angels on earth: Paulina, Crist´obal and Esteban iii Abstract In this thesis we study how to efficiently combine the column generation technique (CG) and interior point methods (IPMs) for solving the relaxation of a selection of integer programming problems. In order to obtain an efficient method a change in the column generation technique and a new reoptimization strategy for a primal-dual interior point method are proposed. It is well-known that the standard column generation technique suffers from un- stable behaviour due to the use of optimal dual solutions that are extreme points of the restricted master problem (RMP). This unstable behaviour slows down column generation so variations of the standard technique which rely on interior points of the dual feasible set of the RMP have been proposed in the literature. Among these tech- niques, there is the primal-dual column generation method (PDCGM) which relies on sub-optimal and well-centred dual solutions. This technique dynamically adjusts the column generation tolerance as the method approaches optimality. Also, it relies on the notion of the symmetric neighbourhood of the central path so sub-optimal and well-centred solutions are obtained. We provide a thorough theoretical analysis that guarantees the convergence of the primal-dual approach even though sub-optimal solu- tions are used in the course of the algorithm. -
A Tutorial Introduction to Quantum Circuit Programming in Dependently Typed Proto-Quipper
A tutorial introduction to quantum circuit programming in dependently typed Proto-Quipper Peng Fu1, Kohei Kishida2, Neil J. Ross1, and Peter Selinger1 1 Dalhousie University, Halifax, NS, Canada ffrank-fu,neil.jr.ross,[email protected] 2 University of Illinois, Urbana-Champaign, IL, U.S.A. [email protected] Abstract. We introduce dependently typed Proto-Quipper, or Proto- Quipper-D for short, an experimental quantum circuit programming lan- guage with linear dependent types. We give several examples to illustrate how linear dependent types can help in the construction of correct quan- tum circuits. Specifically, we show how dependent types enable program- ming families of circuits, and how dependent types solve the problem of type-safe uncomputation of garbage qubits. We also discuss other lan- guage features along the way. Keywords: Quantum programming languages · Linear dependent types · Proto-Quipper-D 1 Introduction Quantum computers can in principle outperform conventional computers at cer- tain crucial tasks that underlie modern computing infrastructures. Experimental quantum computing is in its early stages and existing devices are not yet suitable for practical computing. However, several groups of researchers, in both academia and industry, are now building quantum computers (see, e.g., [2,11,16]). Quan- tum computing also raises many challenging questions for the programming lan- guage community [17]: How should we design programming languages for quan- tum computation? How should we compile and optimize quantum programs? How should we test and verify quantum programs? How should we understand the semantics of quantum programming languages? In this paper, we focus on quantum circuit programming using the linear dependently typed functional language Proto-Quipper-D. -
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. -
A New Trust Region Method with Simple Model for Large-Scale Optimization ∗
A New Trust Region Method with Simple Model for Large-Scale Optimization ∗ Qunyan Zhou,y Wenyu Sunz and Hongchao Zhangx Abstract In this paper a new trust region method with simple model for solv- ing large-scale unconstrained nonlinear optimization is proposed. By employing generalized weak quasi-Newton equations, we derive several schemes to construct variants of scalar matrices as the Hessian approx- imation used in the trust region subproblem. Under some reasonable conditions, global convergence of the proposed algorithm is established in the trust region framework. The numerical experiments on solving the test problems with dimensions from 50 to 20000 in the CUTEr li- brary are reported to show efficiency of the algorithm. Key words. unconstrained optimization, Barzilai-Borwein method, weak quasi-Newton equation, trust region method, global convergence AMS(2010) 65K05, 90C30 1. Introduction In this paper, we consider the unconstrained optimization problem min f(x); (1.1) x2Rn where f : Rn ! R is continuously differentiable with dimension n relatively large. Trust region methods are a class of powerful and robust globalization ∗This work was supported by National Natural Science Foundation of China (11171159, 11401308), the Natural Science Fund for Universities of Jiangsu Province (13KJB110007), the Fund of Jiangsu University of Technology (KYY13012). ySchool of Mathematics and Physics, Jiangsu University of Technology, Changzhou 213001, Jiangsu, China. Email: [email protected] zCorresponding author. School of Mathematical Sciences, Jiangsu Key Laboratory for NSLSCS, Nanjing Normal University, Nanjing 210023, China. Email: [email protected] xDepartment of Mathematics, Louisiana State University, USA. Email: [email protected] 1 methods for solving (1.1). -
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. -
Constrained Multifidelity Optimization Using Model Calibration
Struct Multidisc Optim (2012) 46:93–109 DOI 10.1007/s00158-011-0749-1 RESEARCH PAPER Constrained multifidelity optimization using model calibration Andrew March · Karen Willcox Received: 4 April 2011 / Revised: 22 November 2011 / Accepted: 28 November 2011 / Published online: 8 January 2012 c Springer-Verlag 2012 Abstract Multifidelity optimization approaches seek to derivative-free and sequential quadratic programming meth- bring higher-fidelity analyses earlier into the design process ods. The method uses approximately the same number of by using performance estimates from lower-fidelity models high-fidelity analyses as a multifidelity trust-region algo- to accelerate convergence towards the optimum of a high- rithm that estimates the high-fidelity gradient using finite fidelity design problem. Current multifidelity optimization differences. methods generally fall into two broad categories: provably convergent methods that use either the high-fidelity gradient Keywords Multifidelity · Derivative-free · Optimization · or a high-fidelity pattern-search, and heuristic model cali- Multidisciplinary · Aerodynamic design bration approaches, such as interpolating high-fidelity data or adding a Kriging error model to a lower-fidelity function. This paper presents a multifidelity optimization method that bridges these two ideas; our method iteratively calibrates Nomenclature lower-fidelity information to the high-fidelity function in order to find an optimum of the high-fidelity design prob- A Active and violated constraint Jacobian lem. The -
Quantum Approximation for Wireless Scheduling
applied sciences Article Quantum Approximation for Wireless Scheduling Jaeho Choi 1 , Seunghyeok Oh 2 and Joongheon Kim 2,* 1 School of Computer Science and Engineering, Chung-Ang University, Seoul 06974, Korea; [email protected] 2 School of Electrical Engineering, Korea University, Seoul 02841, Korea; [email protected] * Correspondence: [email protected]; Tel.: +82-2-3290-3223 Received: 2 September 2020; Accepted: 6 October 2020; Published: 13 October 2020 Abstract: This paper proposes an application algorithm based on a quantum approximate optimization algorithm (QAOA) for wireless scheduling problems. QAOA is one of the promising hybrid quantum-classical algorithms to solve combinatorial optimization problems and it provides great approximate solutions to non-deterministic polynomial-time (NP) hard problems. QAOA maps the given problem into Hilbert space, and then it generates the Hamiltonian for the given objective and constraint. Then, QAOA finds proper parameters from the classical optimization loop in order to optimize the expectation value of the generated Hamiltonian. Based on the parameters, the optimal solution to the given problem can be obtained from the optimum of the expectation value of the Hamiltonian. Inspired by QAOA, a quantum approximate optimization for scheduling (QAOS) algorithm is proposed. The proposed QAOS designs the Hamiltonian of the wireless scheduling problem which is formulated by the maximum weight independent set (MWIS). The designed Hamiltonian is converted into a unitary operator and implemented as a quantum gate operation. After that, the iterative QAOS sequence solves the wireless scheduling problem. The novelty of QAOS is verified with simulation results implemented via Cirq and TensorFlow-Quantum. -
Heuristics for Quantum Compiling with a Continuous Gate Set Marc Grau Davis, Ethan Smith, Ana Tudor, Koushik Sen, Irfan Siddiqi, Costin Iancu
Heuristics for Quantum Compiling with a Continuous Gate Set Marc Grau Davis, Ethan Smith, Ana Tudor, Koushik Sen, Irfan Siddiqi, Costin Iancu Abstract factor in the near future of NISQ devices, this metric has been We present an algorithm for compiling arbitrary unitaries targeted by others [25, 28, 50, 56]. into a sequence of gates native to a quantum processor. As The algorithm is inspired by the A* [22] search strategy accurate CNOT gates are hard for the foreseeable Noisy- and works as follows. Given the unitary associated with a Intermediate-Scale Quantum devices era, our A* inspired quantum transformation, we attempt to alternate layers of algorithm attempts to minimize their count, while accounting single qubit gates and CNOT gates. For each layer of single for connectivity. We discuss the search strategy together with qubit gates we assign the parameterized single qubit unitary to “metrics” to expand the solution frontier. For a workload of all the qubits. We then try to place a CNOT gate wherever the circuits with complexity appropriate for the NISQ era, we pro- chip connectivity allows, and add another layer of single qubit duce solutions well within the best upper bounds published in gates. We pass the parameterized circuit into an optimizer [44], literature and match or exceed hand tuned implementations, which instantiates the parameters for the partial solution such as well as other existing synthesis alternatives. In particular, that it minimizes a distance function. At each step of the when comparing against state-of-the-art available synthesis search, the solution with the shortest “heuristic” distance from packages we show 2:4× average (up to 5:3×) reduction in the original unitary is expanded. -
Computing a Trust Region Step
Distribution Category: Mathematics and Computers ANL--81-83 (UC-32) DE82 005656 ANIr81483 ARGONNE NATIONAL LABORATORY 9700 South Cass Avenue Argonne, Illinois 60439 COMPUTING A TRUST REGION STEP Jorge J. Mord and D. C. Sorensen Applied Mathematics Division DISCLAIMER - -. ".,.,... December 1981 Computing a Trust Region Step Jorge J. Mord and D. C. Sorensen Applied Mathematics Division Argonne National Laboratory Argonne Illinois 60439 1. Introduction. In an important class of minimization algorithms called "trust region methods" (see, for example, Sorensen [1981]), the calculation of the step between iterates requires the solution of a problem of the form (1.1) minij(w): 1|w |isAl where A is a positive parameter, I- II is the Euclidean norm in R", and (1.2) #(w) = g w + Mw7Bw, with g E R", and B E R a symmetric matrix. The quadratic function ' generally represents a local model to the objective function defined by interpolatory data at an iterate and thus it is important to be able to solve (1.1) for any symmetric matrix B; in particular, for a matrix B with negative eigenvalues. In trust region methods it is sometimes helpful to include a scaling matrix for the variables. In this case, problem (1.1) is replaced by (1.3) mint%(v):IIDu Is A where D E R""" is a nonsingular matrix. The change of variables Du = w shows that problem (1.3) is equivalent to (1.4) minif(w):1|w| Is Al where f(w) _%f(D-'w), and that the solutions of problems (1.3) and (1.4) are related by Dv = w. -
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. -
EU–US Collaboration on Quantum Technologies Emerging Opportunities for Research and Standards-Setting
Research EU–US collaboration Paper on quantum technologies International Security Programme Emerging opportunities for January 2021 research and standards-setting Martin Everett Chatham House, the Royal Institute of International Affairs, is a world-leading policy institute based in London. Our mission is to help governments and societies build a sustainably secure, prosperous and just world. EU–US collaboration on quantum technologies Emerging opportunities for research and standards-setting Summary — While claims of ‘quantum supremacy’ – where a quantum computer outperforms a classical computer by orders of magnitude – continue to be contested, the security implications of such an achievement have adversely impacted the potential for future partnerships in the field. — Quantum communications infrastructure continues to develop, though technological obstacles remain. The EU has linked development of quantum capacity and capability to its recovery following the COVID-19 pandemic and is expected to make rapid progress through its Quantum Communication Initiative. — Existing dialogue between the EU and US highlights opportunities for collaboration on quantum technologies in the areas of basic scientific research and on communications standards. While the EU Quantum Flagship has already had limited engagement with the US on quantum technology collaboration, greater direct cooperation between EUPOPUSA and the Flagship would improve the prospects of both parties in this field. — Additional support for EU-based researchers and start-ups should be provided where possible – for example, increasing funding for representatives from Europe to attend US-based conferences, while greater investment in EU-based quantum enterprises could mitigate potential ‘brain drain’. — Superconducting qubits remain the most likely basis for a quantum computer. Quantum computers composed of around 50 qubits, as well as a quantum cloud computing service using greater numbers of superconducting qubits, are anticipated to emerge in 2021.