Classical Variational Simulation of the Quantum Approximate Optimization Algorithm ✉ Matija Medvidović 1,2 and Giuseppe Carleo3
Total Page:16
File Type:pdf, Size:1020Kb
Load more
Recommended publications
-
BCG) Is a Global Management Consulting Firm and the World’S Leading Advisor on Business Strategy
The Next Decade in Quantum Computing— and How to Play Boston Consulting Group (BCG) is a global management consulting firm and the world’s leading advisor on business strategy. We partner with clients from the private, public, and not-for-profit sectors in all regions to identify their highest-value opportunities, address their most critical challenges, and transform their enterprises. Our customized approach combines deep insight into the dynamics of companies and markets with close collaboration at all levels of the client organization. This ensures that our clients achieve sustainable competitive advantage, build more capable organizations, and secure lasting results. Founded in 1963, BCG is a private company with offices in more than 90 cities in 50 countries. For more information, please visit bcg.com. THE NEXT DECADE IN QUANTUM COMPUTING— AND HOW TO PLAY PHILIPP GERBERT FRANK RUESS November 2018 | Boston Consulting Group CONTENTS 3 INTRODUCTION 4 HOW QUANTUM COMPUTERS ARE DIFFERENT, AND WHY IT MATTERS 6 THE EMERGING QUANTUM COMPUTING ECOSYSTEM Tech Companies Applications and Users 10 INVESTMENTS, PUBLICATIONS, AND INTELLECTUAL PROPERTY 13 A BRIEF TOUR OF QUANTUM COMPUTING TECHNOLOGIES Criteria for Assessment Current Technologies Other Promising Technologies Odd Man Out 18 SIMPLIFYING THE QUANTUM ALGORITHM ZOO 21 HOW TO PLAY THE NEXT FIVE YEARS AND BEYOND Determining Timing and Engagement The Current State of Play 24 A POTENTIAL QUANTUM WINTER, AND THE OPPORTUNITY THEREIN 25 FOR FURTHER READING 26 NOTE TO THE READER 2 | The Next Decade in Quantum Computing—and How to Play INTRODUCTION he experts are convinced that in time they can build a Thigh-performance quantum computer. -
Quantum Computing in the NISQ Era and Beyond
Quantum Computing in the NISQ era and beyond John Preskill Institute for Quantum Information and Matter and Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena CA 91125, USA 30 July 2018 Noisy Intermediate-Scale Quantum (NISQ) technology will be available in the near future. Quantum computers with 50-100 qubits may be able to perform tasks which surpass the capabilities of today’s classical digital computers, but noise in quantum gates will limit the size of quantum circuits that can be executed reliably. NISQ devices will be useful tools for exploring many-body quantum physics, and may have other useful applications, but the 100-qubit quantum computer will not change the world right away — we should regard it as a significant step toward the more powerful quantum technologies of the future. Quantum technologists should continue to strive for more accurate quantum gates and, eventually, fully fault-tolerant quantum computing. 1 Introduction Now is an opportune time for a fruitful discussion among researchers, entrepreneurs, man- agers, and investors who share an interest in quantum computing. There has been a recent surge of investment by both large public companies and startup companies, a trend that has surprised many quantumists working in academia. While we have long recognized the commercial potential of quantum technology, this ramping up of industrial activity has happened sooner and more suddenly than most of us expected. In this article I assess the current status and future potential of quantum computing. Because quantum computing technology is so different from the information technology we use now, we have only a very limited ability to glimpse its future applications, or to project when these applications will come to fruition. -
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 -
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. -
Learning Nonlinear Input–Output Maps with Dissipative Quantum Systems
Quantum Information Processing (2019) 18:198 https://doi.org/10.1007/s11128-019-2311-9 Learning nonlinear input–output maps with dissipative quantum systems Jiayin Chen1 · Hendra I. Nurdin1 Received: 17 October 2018 / Accepted: 3 May 2019 / Published online: 15 May 2019 © Springer Science+Business Media, LLC, part of Springer Nature 2019 Abstract In this paper, we develop a theory of learning nonlinear input–output maps with fading memory by dissipative quantum systems, as a quantum counterpart of the theory of approximating such maps using classical dynamical systems. The theory identifies the properties required for a class of dissipative quantum systems to be universal, in that any input–output map with fading memory can be approximated arbitrarily closely by an element of this class. We then introduce an example class of dissipative quantum systems that is provably universal. Numerical experiments illustrate that with a small number of qubits, this class can achieve comparable performance to classical learning schemes with a large number of tunable parameters. Further numerical analysis sug- gests that the exponentially increasing Hilbert space presents a potential resource for dissipative quantum systems to surpass classical learning schemes for input–output maps. Keywords Machine learning with quantum systems · Dissipative quantum systems · Universality property · Reservoir computing · Nonlinear input–output maps · Fading memory maps · Nonlinear time series · Stone–Weierstrass theorem 1 Introduction We are in the midst of the noisy intermediate-scale quantum (NISQ) technology era [1], marked by noisy quantum computers consisting of roughly tens to hundreds of qubits. Currently, there is a substantial interest in early applications of these machines that can accelerate the development of practical quantum computers, akin to how the humble hearing aid stimulated the development of integrated circuit (IC) technology [2]. -
Tackling the Qubit Mapping Problem for NISQ-Era Quantum Devices
Tackling the Qubit Mapping Problem for NISQ-Era Quantum Devices Gushu Li Yufei Ding Yuan Xie University of California University of California University of California Santa Barbara, CA Santa Barbara, CA Santa Barbara, CA [email protected] [email protected] [email protected] Abstract 1 Introduction Due to little consideration in the hardware constraints, e.g., Quantum Computing (QC) has been rapidly growing in the limited connections between physical qubits to enable two- last few decades because of its potential in various important qubit gates, most quantum algorithms cannot be directly applications, including integer factorization [47], database executed on the Noisy Intermediate-Scale Quantum (NISQ) search [15], quantum simulation [36], etc. Recently, IBM, devices. Dynamically remapping logical qubits to physical Intel, and Google released their QC devices with 50, 49, and qubits in the compiler is needed to enable the two-qubit 72 qubits respectively [22, 23, 56]. IBM and Rigetti also pro- gates in the algorithm, which introduces additional oper- vide cloud QC services [18, 40], allowing more people to ations and inevitably reduces the fidelity of the algorithm. study real quantum hardware. We are expected to enter the Previous solutions in finding such remapping suffer from Noisy Intermediate-Scale Quantum (NISQ) era in the next high complexity, poor initial mapping quality, and limited few years [39], when QC devices with dozens to hundreds of flexibility and controllability. qubits will be available. Though the number of qubits is insuf- To address these drawbacks mentioned above, this paper ficient for Quantum Error Correction (QEC), .it is expected proposes a SWAP-based BidiREctional heuristic search al- that these devices will be used to solve real-world problems gorithm (SABRE), which is applicable to NISQ devices with beyond the capability of available classical computers [5, 38]. -
Dance with Noise in NISQ Era — a NASA Perspective on Quantum Computing
Dance with Noise in NISQ Era — A NASA Perspective on Quantum Computing Zhihui Wang1,2 Eleanor Rieffel1 [email protected] [email protected] 1. NASA Quantum Artificial Intelligence Lab (QuAIL) 2. Universities Space Research Association ICCAD 2019, West Minster, CO Quantum Computing: Explore “bizarre” features of quantum mechanics Superposition Entanglement Quantum Tunneling Article developed fast, high-fidelity gates that can be executed simultaneously a across a two-dimensional qubit array. We calibrated and benchmarked the processor at both the component and system level using a powerful new tool: cross-entropy benchmarking11. Finally, we used component- level fidelities to accurately predict the performance of the whole sys- tem, further showing that quantum information behaves as expected when scaling to large systems. A suitable computational task To demonstrate quantum supremacy, we compare our quantum proces- sor against state-of-the-art classical computers in the task of sampling the output of a pseudo-random quantum circuit11,13,14. Random circuits are a suitable choice for benchmarking because they do not possess The Noisy Intermediate-Scale Quantum (NISQ) Era structure and therefore allow for limited guarantees of computational hardness10–12. We design the circuits to entangle a set of quantum bits (qubits) by repeated application of single-qubit and two-qubit logi- cal operations. Sampling the quantum circuit’s output produces a set Qubit Adjustable coupler of bitstrings, for example {0000101, 1011100, …}. Owing to quantum interference, the probability distribution of the bitstrings resembles b a speckled intensity pattern produced by light interference in laser Google scatter, such that some bitstrings are much more likely to occur than others. -
T|Ket〉: a Retargetable Compiler for NISQ Devices
View metadata, citation and similar papers at core.ac.uk brought to you by CORE Page 1 of 43 AUTHOR SUBMITTED MANUSCRIPT - QST-100727.R1 provided by University of Strathclyde Institutional Repository 1 2 3 4 5 6 7 8 9 10 t|keti: A Retargetable Compiler for NISQ Devices 11 12 Seyon Sivarajah1∗†, Silas Dilkes1∗, Alexander Cowtan1∗, 13 1∗ 1 1,2 14 Will Simmons , Alec Edgington , and Ross Duncan 15 1 Cambridge Quantum Computing Ltd, 9a Bridge Street, Cambridge, United Kingdom 16 2 Department of Computer and Information Sciences, University of Strathclyde, 17 26 Richmond Street, Glasgow, United Kingdom 18 19 ∗ These authors contributed equally to this work. 20 21 Abstract. We present t|keti, a quantum software development platform produced 22 by Cambridge Quantum Computing Ltd. The heart of t|keti is a language-agnostic 23 optimising compiler designed to generate code for a variety of NISQ devices, which has 24 25 several features designed to minimise the influence of device error. The compiler has 26 been extensively benchmarked and outperforms most competitors in terms of circuit 27 optimisation and qubit routing. 28 29 30 31 1. Introduction 32 33 Quantum computing devices promise significant advantages for a wide variety of 34 35 information processing tasks [1, 2, 3]. For some tasks, notably the simulation of condensed- 36 matter physics, the abstract structure of the problem may be sufficiently similar to 37 the physical structure of the device that translation from one to the other is natural 38 39 and (relatively) straightforward [4]. However, for most problems, and most quantum 40 computers, this is not the case. -
What's Next After Quantum Supremacy?
What’s Next After Quantum Supremacy? Credit: Erik Lucero/Google John Preskill Q2B 2019 11 December 2019 Quantum 2, 79 (2018), arXiv:1801.00862 Based on a Keynote Address delivered at Quantum Computing for Business, 5 December 2017 Nature 574, pages 505–510 (2019), 23 October 2019 The promise of quantum computers is that certain computational tasks might be executed exponentially faster on a quantum processor than on a classical processor. A fundamental challenge is to build a high-fidelity processor capable of running quantum algorithms in an exponentially large computational space. Here we report the use of a processor with programmable superconducting qubits to create quantum states on 53 qubits, corresponding to a computational state-space of dimension 253 (about 1016). Measurements from repeated experiments sample the resulting probability distribution, which we verify using classical simulations. Our Sycamore processor takes about 200 seconds to sample one instance of a quantum circuit a million times—our benchmarks currently indicate that the equivalent task for a state-of-the-art classical supercomputer would take approximately 10,000 years. This dramatic increase in speed compared to all known classical algorithms is an experimental realization of quantum supremacy for this specific computational task, heralding a much anticipated computing paradigm. Classical systems cannot simulate quantum systems efficiently (a widely believed but unproven conjecture). Arguably the most interesting thing we know about the difference between quantum and classical. Each qubit is also connected to its neighboring qubits using a new adjustable coupler [31, 32]. Our coupler design allows us to quickly tune the qubit-qubit coupling from completely off to 40 MHz. -
Arxiv:1910.11333V2 [Quant-Ph] 28 Dec 2019 D
Supplementary information for \Quantum supremacy using a programmable superconducting processor" [1] Google AI Quantum and collaboratorsy (Dated: January 1, 2020) CONTENTS 2. Universality for SU(2) 30 G. Circuit variants 30 I. Device design and architecture2 1. Gate elision 31 2. Wedge formation 31 II. Fabrication and layout2 VIII. Large scale XEB results 31 III. Qubit control and readout3 A. Limitations of full circuits 32 A. Control3 B. Patch circuits: a quick performance B. Readout3 indicator for large systems 33 C. Elided circuits: a more rigorous IV. XEB theory5 performance estimator for large systems 33 A. XEB of a small number of qubits5 D. Choice of unitary model for two-qubit B. XEB of a large number of qubits7 entangling gates 34 C. Two limiting cases8 E. Understanding system performance: error D. Measurement errors9 model prediction 35 F. Distribution of bitstring probabilities 36 V. Quantifying errors9 G. Statistical uncertainties of XEB measurements 39 VI. Metrology and calibration 11 H. System stability and systematic A. Calibration overview 11 uncertainties 40 1. Device registry 11 I. The fidelity result and the null hypothesis 2. Scheduling calibrations: \Optimus" 12 on quantum supremacy 41 B. Calibration procedure 12 1. Device configuration 12 IX. Sensitivity of XEB to errors 42 2. Root config: procedure 13 3. Single-qubit config: procedure 13 X. Classical simulations 44 4. Optimizing qubit operating frequencies 13 A. Local Schr¨odingerand 5. Grid config: procedure 14 Schr¨odinger-Feynman simulators 44 C. Two-qubit gate metrology 15 B. Feynman simulator 45 1. The natural two-qubit gate for transmon C. Supercomputer Schr¨odingersimulator 49 qubits 15 D. -
Superconducting Quantum Computing: a Review
SCIENCE CHINA Information Sciences August 2020, Vol. 63 180501:1–180501:32 . REVIEW . https://doi.org/10.1007/s11432-020-2881-9 Special Focus on Quantum Information Superconducting quantum computing: a review He-Liang HUANG1,2*, Dachao WU1,2, Daojin FAN1,2 & Xiaobo ZHU1,2* 1Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China; 2Shanghai Branch, CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China Received 25 February 2020/Accepted 16 April 2020/Published online 15 July 2020 Abstract Over the last two decades, tremendous advances have been made for constructing large-scale quantum computers. In particular, quantum computing platforms based on superconducting qubits have become the leading candidate for scalable quantum processor architecture, and the milestone of demonstrating quantum supremacy has been first achieved using 53 superconducting qubits in 2019. In this study, we provide a brief review on the experimental efforts towards the large-scale superconducting quantum computer, including qubit design, quantum control, readout techniques, and the implementations of error correction and quantum algorithms. Besides the state of the art, we finally discuss future perspectives, and which we hope will motivate further research. Keywords quantum computing, superconducting quantum computing, quantum bit, quantum algorithm, qubit design, qubit control, qubit readout Citation Huang H-L, Wu D C, Fan D J, et al. Superconducting quantum computing: a review. Sci China Inf Sci, 2020, 63(8): 180501, https://doi.org/10.1007/s11432-020-2881-9 1 Introduction Quantum computers harness the intrinsic properties of quantum mechanical, which offers the promise of efficiently solving certain problems that are intractable for classical computers [1,2]. -
Challenges at the Entanglement Frontier
Challenges at the entanglement frontier John Preskill DOE Kickoff 31 January 2019 Quantum Information Science Quantum sensing Improving sensitivity and spatial resolution. Quantum cryptography Privacy founded on fundamental laws of quantum physics. Quantum networking Distributing quantumness around the world. Quantum simulation Probes of exotic quantum many-body phenomena. Quantum computing Speeding up solutions to hard problems. Hardware challenges cut across all these application areas. Frontiers of Physics short distance long distance complexity Higgs boson Large scale structure “More is different” Neutrino masses Cosmic microwave Many-body entanglement background Supersymmetry Phases of quantum Dark matter matter Quantum gravity Dark energy Quantum computing String theory Gravitational waves Quantum spacetime Two fundamental ideas (1) Quantum complexity Why we think quantum computing is powerful. (2) Quantum error correction Why we think quantum computing is scalable. A complete description of a typical quantum state of just 300 qubits requires more bits than the number of atoms in the visible universe. Why we think quantum computing is powerful (1) Problems believed to be hard classically, which are easy for quantum computers. Factoring is the best known example. (2) Complexity theory arguments indicating that quantum computers are hard to simulate classically. (3) We don’t know how to simulate a quantum computer efficiently using a digital (“classical”) computer. The cost of the best known simulation algorithm rises exponentially with the number of qubits. But … the power of quantum computing is limited . For example, we don’t believe that quantum computers can efficiently solve worst-case instances of NP-hard optimization problems (e.g., the traveling salesman problem).