A Divide-And-Conquer Algorithm for Quantum State Preparation
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Simulating Quantum Field Theory with a Quantum Computer
Simulating quantum field theory with a quantum computer John Preskill Lattice 2018 28 July 2018 This talk has two parts (1) Near-term prospects for quantum computing. (2) Opportunities in quantum simulation of quantum field theory. Exascale digital computers will advance our knowledge of QCD, but some challenges will remain, especially concerning real-time evolution and properties of nuclear matter and quark-gluon plasma at nonzero temperature and chemical potential. Digital computers may never be able to address these (and other) problems; quantum computers will solve them eventually, though I’m not sure when. The physics payoff may still be far away, but today’s research can hasten the arrival of a new era in which quantum simulation fuels progress in fundamental physics. 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 particle collision molecular chemistry entangled electrons A quantum computer can simulate efficiently any physical process that occurs in Nature. (Maybe. We don’t actually know for sure.) superconductor black hole early universe 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 We know examples of problems that can be solved efficiently by a quantum computer, where we believe the problems are hard for classical computers. -
Arxiv:1803.04114V2 [Quant-Ph] 16 Nov 2018
Learning the quantum algorithm for state overlap Lukasz Cincio,1 Yiğit Subaşı,1 Andrew T. Sornborger,2 and Patrick J. Coles1 1Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA. 2Information Sciences, Los Alamos National Laboratory, Los Alamos, NM 87545, USA. Short-depth algorithms are crucial for reducing computational error on near-term quantum com- puters, for which decoherence and gate infidelity remain important issues. Here we present a machine-learning approach for discovering such algorithms. We apply our method to a ubiqui- tous primitive: computing the overlap Tr(ρσ) between two quantum states ρ and σ. The standard algorithm for this task, known as the Swap Test, is used in many applications such as quantum support vector machines, and, when specialized to ρ = σ, quantifies the Renyi entanglement. Here, we find algorithms that have shorter depths than the Swap Test, including one that has a constant depth (independent of problem size). Furthermore, we apply our approach to the hardware-specific connectivity and gate sets used by Rigetti’s and IBM’s quantum computers and demonstrate that the shorter algorithms that we derive significantly reduce the error - compared to the Swap Test - on these computers. I. INTRODUCTION hyperparameters, we optimize the algorithm in a task- oriented manner, i.e., by minimizing a cost function that quantifies the discrepancy between the algorithm’s out- Quantum supremacy [1] may be coming soon [2]. put and the desired output. The task is defined by a While it is an exciting time for quantum computing, de- training data set that exemplifies the desired computa- coherence and gate fidelity continue to be important is- tion. -
Quantum Machine Learning: Benefits and Practical Examples
Quantum Machine Learning: Benefits and Practical Examples Frank Phillipson1[0000-0003-4580-7521] 1 TNO, Anna van Buerenplein 1, 2595 DA Den Haag, The Netherlands [email protected] Abstract. A quantum computer that is useful in practice, is expected to be devel- oped in the next few years. An important application is expected to be machine learning, where benefits are expected on run time, capacity and learning effi- ciency. In this paper, these benefits are presented and for each benefit an example application is presented. A quantum hybrid Helmholtz machine use quantum sampling to improve run time, a quantum Hopfield neural network shows an im- proved capacity and a variational quantum circuit based neural network is ex- pected to deliver a higher learning efficiency. Keywords: Quantum Machine Learning, Quantum Computing, Near Future Quantum Applications. 1 Introduction Quantum computers make use of quantum-mechanical phenomena, such as superposi- tion and entanglement, to perform operations on data [1]. Where classical computers require the data to be encoded into binary digits (bits), each of which is always in one of two definite states (0 or 1), quantum computation uses quantum bits, which can be in superpositions of states. These computers would theoretically be able to solve certain problems much more quickly than any classical computer that use even the best cur- rently known algorithms. Examples are integer factorization using Shor's algorithm or the simulation of quantum many-body systems. This benefit is also called ‘quantum supremacy’ [2], which only recently has been claimed for the first time [3]. There are two different quantum computing paradigms. -
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. -
Quantum Inductive Learning and Quantum Logic Synthesis
Portland State University PDXScholar Dissertations and Theses Dissertations and Theses 2009 Quantum Inductive Learning and Quantum Logic Synthesis Martin Lukac Portland State University Follow this and additional works at: https://pdxscholar.library.pdx.edu/open_access_etds Part of the Electrical and Computer Engineering Commons Let us know how access to this document benefits ou.y Recommended Citation Lukac, Martin, "Quantum Inductive Learning and Quantum Logic Synthesis" (2009). Dissertations and Theses. Paper 2319. https://doi.org/10.15760/etd.2316 This Dissertation is brought to you for free and open access. It has been accepted for inclusion in Dissertations and Theses by an authorized administrator of PDXScholar. For more information, please contact [email protected]. QUANTUM INDUCTIVE LEARNING AND QUANTUM LOGIC SYNTHESIS by MARTIN LUKAC A dissertation submitted in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY in ELECTRICAL AND COMPUTER ENGINEERING. Portland State University 2009 DISSERTATION APPROVAL The abstract and dissertation of Martin Lukac for the Doctor of Philosophy in Electrical and Computer Engineering were presented January 9, 2009, and accepted by the dissertation committee and the doctoral program. COMMITTEE APPROVALS: Irek Perkowski, Chair GarrisoH-Xireenwood -George ^Lendaris 5artM ?teven Bleiler Representative of the Office of Graduate Studies DOCTORAL PROGRAM APPROVAL: Malgorza /ska-Jeske7~Director Electrical Computer Engineering Ph.D. Program ABSTRACT An abstract of the dissertation of Martin Lukac for the Doctor of Philosophy in Electrical and Computer Engineering presented January 9, 2009. Title: Quantum Inductive Learning and Quantum Logic Synhesis Since Quantum Computer is almost realizable on large scale and Quantum Technology is one of the main solutions to the Moore Limit, Quantum Logic Synthesis (QLS) has become a required theory and tool for designing Quantum Logic Circuits. -
Nearest Centroid Classification on a Trapped Ion Quantum Computer
www.nature.com/npjqi ARTICLE OPEN Nearest centroid classification on a trapped ion quantum computer ✉ Sonika Johri1 , Shantanu Debnath1, Avinash Mocherla2,3,4, Alexandros SINGK2,3,5, Anupam Prakash2,3, Jungsang Kim1 and Iordanis Kerenidis2,3,6 Quantum machine learning has seen considerable theoretical and practical developments in recent years and has become a promising area for finding real world applications of quantum computers. In pursuit of this goal, here we combine state-of-the-art algorithms and quantum hardware to provide an experimental demonstration of a quantum machine learning application with provable guarantees for its performance and efficiency. In particular, we design a quantum Nearest Centroid classifier, using techniques for efficiently loading classical data into quantum states and performing distance estimations, and experimentally demonstrate it on a 11-qubit trapped-ion quantum machine, matching the accuracy of classical nearest centroid classifiers for the MNIST handwritten digits dataset and achieving up to 100% accuracy for 8-dimensional synthetic data. npj Quantum Information (2021) 7:122 ; https://doi.org/10.1038/s41534-021-00456-5 INTRODUCTION Thus, one might hope that noisy quantum computers are 1234567890():,; Quantum technologies promise to revolutionize the future of inherently better suited for machine learning computations than information and communication, in the form of quantum for other types of problems that need precise computations like computing devices able to communicate and process massive factoring or search problems. amounts of data both efficiently and securely using quantum However, there are significant challenges to be overcome to resources. Tremendous progress is continuously being made both make QML practical. -
Signing Perfect Currency Bonds
Signing Perfect Currency Bonds Subhayan Roy Moulick∗ and Prasanta K. Panigrahiy Indian Institute of Science Education and Research Kolkata, Mohanpur 741246, West Bengal, India (Dated: May 23, 2019) We propose the idea of a Quantum Cheque Scheme, a cryptographic protocol in which any legiti- mate client of a trusted bank can issue a cheque, that cannot be counterfeited or altered in anyway, and can be verified by a bank or any of its branches. We formally define a Quantum Cheque and present the first Unconditionally Secure Quantum Cheque Scheme and show it to be secure against any no-signaling adversary. The proposed Quantum Cheque Scheme can been perceived as the quantum analog of Electronic Data Interchange, as an alternate for current e-Payment Gateways. PACS numbers: 03.67.Dd, 03.67.Hk, 03.67.Ac I. INTRODUCTION in addition to security against counterfeiters, owing its origin to the pioneering works of Mosca and Stebila [11]. Replication of classical information is a significant nui- They proposed a scheme based on blind quantum com- sance in copy-protection. Any physical entity created putation that required a verifier to do an obfuscated ver- classically can be, in principle, copied. Currency bonds, ification with the bank and learn only the validity of the printed on textile and paper, are no exception, and any quantum coin. This however is a private key protocol adversary, given sufficient time and resources, can be and requires communication with the bank. able to counterfeit currency bonds. However, the quan- In this paper we propose the idea of Quantum Cheques tum regime can circumvent this problem, exploiting the and present a construction of an Quantum Cheque `No Cloning Theorem' [1], and pave way for unforgeable Scheme with Perfect Security against any No-Signaling Quantum Currency that are impossible to counterfeit adversary. -
Quantum Information & Quantum Computation
CS290A, Spring 2005: Quantum Information & Quantum Computation Wim van Dam Engineering 1, Room 5109 vandam@cs http://www.cs.ucsb.edu/~vandam/teaching/CS290/ Administrative • The Final Examination will be: Monday June 6, 12:00–15:00, PHELPS 1401 • New Exercises are posted Try to answer Question 2 before Thursday. Last Week / This Week • Last week we looked at quantum money and quantum cryptography, which uses the qubit states 0,1,+,–. • This week we will extend this idea to describe “quantum fingerprinting”. • Also this week: superdense quantum coding and quantum teleportation of quantum states. Fingerprinting Assume two parties A and B that each have data in the form of a (long) string x and y ∈{0,1} N. A and B want to check if they have the same data, without revealing a priori to the other their strings. They do this by sending (publicly) information about their strings (x and y) to a trusted third party C, who decides. Sending the whole strings is not allowed because the strings are too long / risk of eavesdropping. A and B want to have a way of fingerprinting their strings. Quantum Fingerprinting “Quantum Fingerprinting” refers to a way of mapping the ∈ N strings x,y {0,1} to quantum states | φx〉 and | φy〉, that live in a ‘much smaller than 2 N’-dimensional Hilbert space, such that from ψ and φ we can tell decide whether x=y. ∈ N The set { |φx〉 : x {0,1} } cannot be mutually orthogonal. Instead we will have to work with near orthogonal states. ∈ N Central Idea: Encode x {0,1} into m qubit state |φx〉 (with m much smaller than N). -
Modeling Observers As Physical Systems Representing the World from Within: Quantum Theory As a Physical and Self-Referential Theory of Inference
Modeling observers as physical systems representing the world from within: Quantum theory as a physical and self-referential theory of inference John Realpe-G´omez1∗ Theoretical Physics Group, School of Physics and Astronomy, The University of Manchestery, Manchester M13 9PL, United Kingdom and Instituto de Matem´aticas Aplicadas, Universidad de Cartagena, Bol´ıvar130001, Colombia (Dated: June 13, 2019) In 1929 Szilard pointed out that the physics of the observer may play a role in the analysis of experiments. The same year, Bohr pointed out that complementarity appears to arise naturally in psychology where both the objects of perception and the perceiving subject belong to `our mental content'. Here we argue that the formalism of quantum theory can be derived from two related intu- itive principles: (i) inference is a classical physical process performed by classical physical systems, observers, which are part of the experimental setup|this implies non-commutativity and imaginary- time quantum mechanics; (ii) experiments must be described from a first-person perspective|this leads to self-reference, complementarity, and a quantum dynamics that is the iterative construction of the observer's subjective state. This approach suggests a natural explanation for the origin of Planck's constant as due to the physical interactions supporting the observer's information process- ing, and sheds new light on some conceptual issues associated to the foundations of quantum theory. It also suggests that fundamental equations in physics are typically -
Quantum Computing Methods for Supervised Learning Arxiv
Quantum Computing Methods for Supervised Learning Viraj Kulkarni1, Milind Kulkarni1, Aniruddha Pant2 1 Vishwakarma University 2 DeepTek Inc June 23, 2020 Abstract The last two decades have seen an explosive growth in the theory and practice of both quantum computing and machine learning. Modern machine learning systems process huge volumes of data and demand massive computational power. As silicon semiconductor miniaturization approaches its physics limits, quantum computing is increasingly being considered to cater to these computational needs in the future. Small-scale quantum computers and quantum annealers have been built and are already being sold commercially. Quantum computers can benefit machine learning research and application across all science and engineering domains. However, owing to its roots in quantum mechanics, research in this field has so far been confined within the purview of the physics community, and most work is not easily accessible to researchers from other disciplines. In this paper, we provide a background and summarize key results of quantum computing before exploring its application to supervised machine learning problems. By eschewing results from physics that have little bearing on quantum computation, we hope to make this introduction accessible to data scientists, machine learning practitioners, and researchers from across disciplines. 1 Introduction Supervised learning is the most commonly applied form of machine learning. It works in two arXiv:2006.12025v1 [quant-ph] 22 Jun 2020 stages. During the training stage, the algorithm extracts patterns from the training dataset that contains pairs of samples and labels and converts these patterns into a mathematical representation called a model. During the inference stage, this model is used to make predictions about unseen samples. -
Federated Quantum Machine Learning
entropy Article Federated Quantum Machine Learning Samuel Yen-Chi Chen * and Shinjae Yoo Computational Science Initiative, Brookhaven National Laboratory, Upton, NY 11973, USA; [email protected] * Correspondence: [email protected] Abstract: Distributed training across several quantum computers could significantly improve the training time and if we could share the learned model, not the data, it could potentially improve the data privacy as the training would happen where the data is located. One of the potential schemes to achieve this property is the federated learning (FL), which consists of several clients or local nodes learning on their own data and a central node to aggregate the models collected from those local nodes. However, to the best of our knowledge, no work has been done in quantum machine learning (QML) in federation setting yet. In this work, we present the federated training on hybrid quantum-classical machine learning models although our framework could be generalized to pure quantum machine learning model. Specifically, we consider the quantum neural network (QNN) coupled with classical pre-trained convolutional model. Our distributed federated learning scheme demonstrated almost the same level of trained model accuracies and yet significantly faster distributed training. It demonstrates a promising future research direction for scaling and privacy aspects. Keywords: quantum machine learning; federated learning; quantum neural networks; variational quantum circuits; privacy-preserving AI Citation: Chen, S.Y.-C.; Yoo, S. 1. Introduction Federated Quantum Machine Recently, advances in machine learning (ML), in particular deep learning (DL), have Learning. Entropy 2021, 23, 460. found significant success in a wide variety of challenging tasks such as computer vi- https://doi.org/10.3390/e23040460 sion [1–3], natural language processing [4], and even playing the game of Go with a superhuman performance [5]. -
Lecture 25: QMA(2) 1 Introduction 2 QMA(2): the 2-Prover
Quantum Computation (CMU 18-859BB, Fall 2015) Lecture 25: QMA(2) December 7, 2015 Lecturer: Ryan O'Donnell Scribe: Yongshan Ding 1 Introduction So far, we have seen two major quantum complexity classes, namely BQP and QMA. They are the quantum analogue of two famous classical complexity classes, P (or more precisely BPP) and NP, respectively. In today's lecture, we shall extend to a generalization of QMA that only arises in the Quantum setting. In particular, we denote QMA(k) for the case that quantum verifier uses k quantum certificates. Before we study the new complexity class, recall the following \swap test" circuit from homework 3: qudit SWAP qudit qubit j0i H • H Accept if j0i When we measure the last register, we \accept" if the outcome is j0i and \reject" if the outcome is j1i. We have shown that this is \similarity test". In particular we have the following: 1 1 2 1 2 • Pr[Accept j i ⊗ j'i] = 2 + 2 j h j'i j = 1 − 2 dtr(j i ; j'i) 1 1 Pd 2 • Pr[Accept ρ ⊗ ρ] = 2 + 2 i=1 pi , if ρ = fpi j iig. 2 QMA(2): The 2-Prover QMA Recall from last time, we introduced the QMA class where there is a prover who is trying to prove some instance x is in the language L, regardless of whether it is true or not. Figure. 1 is a simple picture that describes this. The complexity class we are going to look at today involves multiple provers. Kobayashi et al.