Quantum Information and Computation Chapter 5
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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. -
Free-Electron Qubits
Free-Electron Qubits Ori Reinhardt†, Chen Mechel†, Morgan Lynch, and Ido Kaminer Department of Electrical Engineering and Solid State Institute, Technion - Israel Institute of Technology, 32000 Haifa, Israel † equal contributors Free-electron interactions with laser-driven nanophotonic nearfields can quantize the electrons’ energy spectrum and provide control over this quantized degree of freedom. We propose to use such interactions to promote free electrons as carriers of quantum information and find how to create a qubit on a free electron. We find how to implement the qubit’s non-commutative spin-algebra, then control and measure the qubit state with a universal set of 1-qubit gates. These gates are within the current capabilities of femtosecond-pulsed laser-driven transmission electron microscopy. Pulsed laser driving promise configurability by the laser intensity, polarizability, pulse duration, and arrival times. Most platforms for quantum computation today rely on light-matter interactions of bound electrons such as in ion traps [1], superconducting circuits [2], and electron spin systems [3,4]. These form a natural choice for implementing 2-level systems with spin algebra. Instead of using bound electrons for quantum information processing, in this letter we propose using free electrons and manipulating them with femtosecond laser pulses in optical frequencies. Compared to bound electrons, free electron systems enable accessing high energy scales and short time scales. Moreover, they possess quantized degrees of freedom that can take unbounded values, such as orbital angular momentum (OAM), which has also been proposed for information encoding [5-10]. Analogously, photons also have the capability to encode information in their OAM [11,12]. -
Design of a Qubit and a Decoder in Quantum Computing Based on a Spin Field Effect
Design of a Qubit and a Decoder in Quantum Computing Based on a Spin Field Effect A. A. Suratgar1, S. Rafiei*2, A. A. Taherpour3, A. Babaei4 1 Assistant Professor, Electrical Engineering Department, Faculty of Engineering, Arak University, Arak, Iran. 1 Assistant Professor, Electrical Engineering Department, Amirkabir University of Technology, Tehran, Iran. 2 Young Researchers Club, Aligudarz Branch, Islamic Azad University, Aligudarz, Iran. *[email protected] 3 Professor, Chemistry Department, Faculty of Science, Islamic Azad University, Arak Branch, Arak, Iran. 4 faculty member of Islamic Azad University, Khomein Branch, Khomein, ABSTRACT In this paper we present a new method for designing a qubit and decoder in quantum computing based on the field effect in nuclear spin. In this method, the position of hydrogen has been studied in different external fields. The more we have different external field effects and electromagnetic radiation, the more we have different distribution ratios. Consequently, the quality of different distribution ratios has been applied to the suggested qubit and decoder model. We use the nuclear property of hydrogen in order to find a logical truth value. Computational results demonstrate the accuracy and efficiency that can be obtained with the use of these models. Keywords: quantum computing, qubit, decoder, gyromagnetic ratio, spin. 1. Introduction different hydrogen atoms in compound applied for the qubit and decoder designing. Up to now many papers deal with the possibility to realize a reversible computer based on the laws of 2. An overview on quantum concepts quantum mechanics [1]. In this chapter a short introduction is presented Modern quantum chemical methods provide into the interesting field of quantum in physics, powerful tools for theoretical modeling and Moore´s law and a summary of the quantum analysis of molecular electronic structures. -
A Theoretical Study of Quantum Memories in Ensemble-Based Media
A theoretical study of quantum memories in ensemble-based media Karl Bruno Surmacz St. Hugh's College, Oxford A thesis submitted to the Mathematical and Physical Sciences Division for the degree of Doctor of Philosophy in the University of Oxford Michaelmas Term, 2007 Atomic and Laser Physics, University of Oxford i A theoretical study of quantum memories in ensemble-based media Karl Bruno Surmacz, St. Hugh's College, Oxford Michaelmas Term 2007 Abstract The transfer of information from flying qubits to stationary qubits is a fundamental component of many quantum information processing and quantum communication schemes. The use of photons, which provide a fast and robust platform for encoding qubits, in such schemes relies on a quantum memory in which to store the photons, and retrieve them on-demand. Such a memory can consist of either a single absorber, or an ensemble of absorbers, with a ¤-type level structure, as well as other control ¯elds that a®ect the transfer of the quantum signal ¯eld to a material storage state. Ensembles have the advantage that the coupling of the signal ¯eld to the medium scales with the square root of the number of absorbers. In this thesis we theoretically study the use of ensembles of absorbers for a quantum memory. We characterize a general quantum memory in terms of its interaction with the signal and control ¯elds, and propose a ¯gure of merit that measures how well such a memory preserves entanglement. We derive an analytical expression for the entanglement ¯delity in terms of fluctuations in the stochastic Hamiltonian parameters, and show how this ¯gure could be measured experimentally. -
CS286.2 Lectures 5-6: Introduction to Hamiltonian Complexity, QMA-Completeness of the Local Hamiltonian Problem
CS286.2 Lectures 5-6: Introduction to Hamiltonian Complexity, QMA-completeness of the Local Hamiltonian problem Scribe: Jenish C. Mehta The Complexity Class BQP The complexity class BQP is the quantum analog of the class BPP. It consists of all languages that can be decided in quantum polynomial time. More formally, Definition 1. A language L 2 BQP if there exists a classical polynomial time algorithm A that ∗ maps inputs x 2 f0, 1g to quantum circuits Cx on n = poly(jxj) qubits, where the circuit is considered a sequence of unitary operators each on 2 qubits, i.e Cx = UTUT−1...U1 where each 2 2 Ui 2 L C ⊗ C , such that: 2 i. Completeness: x 2 L ) Pr(Cx accepts j0ni) ≥ 3 1 ii. Soundness: x 62 L ) Pr(Cx accepts j0ni) ≤ 3 We say that the circuit “Cx accepts jyi” if the first output qubit measured in Cxjyi is 0. More j0i specifically, letting P1 = j0ih0j1 be the projection of the first qubit on state j0i, j0i 2 Pr(Cx accepts jyi) =k (P1 ⊗ In−1)Cxjyi k2 The Complexity Class QMA The complexity class QMA (or BQNP, as Kitaev originally named it) is the quantum analog of the class NP. More formally, Definition 2. A language L 2 QMA if there exists a classical polynomial time algorithm A that ∗ maps inputs x 2 f0, 1g to quantum circuits Cx on n + q = poly(jxj) qubits, such that: 2q i. Completeness: x 2 L ) 9jyi 2 C , kjyik2 = 1, such that Pr(Cx accepts j0ni ⊗ 2 jyi) ≥ 3 2q 1 ii. -
Taking the Quantum Leap with Machine Learning
Introduction Quantum Algorithms Current Research Conclusion Taking the Quantum Leap with Machine Learning Zack Barnes University of Washington Bellevue College Mathematics and Physics Colloquium Series [email protected] January 15, 2019 Zack Barnes University of Washington UW Quantum Machine Learning Introduction Quantum Algorithms Current Research Conclusion Overview 1 Introduction What is Quantum Computing? What is Machine Learning? Quantum Power in Theory 2 Quantum Algorithms HHL Quantum Recommendation 3 Current Research Quantum Supremacy(?) 4 Conclusion Zack Barnes University of Washington UW Quantum Machine Learning Introduction Quantum Algorithms Current Research Conclusion What is Quantum Computing? \Quantum computing focuses on studying the problem of storing, processing and transferring information encoded in quantum mechanical systems.\ [Ciliberto, Carlo et al., 2018] Unit of quantum information is the qubit, or quantum binary integer. Zack Barnes University of Washington UW Quantum Machine Learning Supervised Uses labeled examples to predict future events Unsupervised Not classified or labeled Introduction Quantum Algorithms Current Research Conclusion What is Machine Learning? \Machine learning is the scientific study of algorithms and statistical models that computer systems use to progressively improve their performance on a specific task.\ (Wikipedia) Zack Barnes University of Washington UW Quantum Machine Learning Uses labeled examples to predict future events Unsupervised Not classified or labeled Introduction Quantum -
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. -
Interactive Proofs for Quantum Computations
Innovations in Computer Science 2010 Interactive Proofs For Quantum Computations Dorit Aharonov Michael Ben-Or Elad Eban School of Computer Science, The Hebrew University of Jerusalem, Israel [email protected] [email protected] [email protected] Abstract: The widely held belief that BQP strictly contains BPP raises fundamental questions: Upcoming generations of quantum computers might already be too large to be simulated classically. Is it possible to experimentally test that these systems perform as they should, if we cannot efficiently compute predictions for their behavior? Vazirani has asked [21]: If computing predictions for Quantum Mechanics requires exponential resources, is Quantum Mechanics a falsifiable theory? In cryptographic settings, an untrusted future company wants to sell a quantum computer or perform a delegated quantum computation. Can the customer be convinced of correctness without the ability to compare results to predictions? To provide answers to these questions, we define Quantum Prover Interactive Proofs (QPIP). Whereas in standard Interactive Proofs [13] the prover is computationally unbounded, here our prover is in BQP, representing a quantum computer. The verifier models our current computational capabilities: it is a BPP machine, with access to few qubits. Our main theorem can be roughly stated as: ”Any language in BQP has a QPIP, and moreover, a fault tolerant one” (providing a partial answer to a challenge posted in [1]). We provide two proofs. The simpler one uses a new (possibly of independent interest) quantum authentication scheme (QAS) based on random Clifford elements. This QPIP however, is not fault tolerant. Our second protocol uses polynomial codes QAS due to Ben-Or, Cr´epeau, Gottesman, Hassidim, and Smith [8], combined with quantum fault tolerance and secure multiparty quantum computation techniques. -
Quantum Supremacy
Quantum Supremacy Practical QS: perform some computational task on a well-controlled quantum device, which cannot be simulated in a reasonable time by the best-known classical algorithms and hardware. Theoretical QS: perform a computational task efficiently on a quantum device, and prove that task cannot be efficiently classically simulated. Since proving seems to be beyond the capabilities of our current civilization, we lower the standards for theoretical QS. One seeks to provide formal evidence that classical simulation is unlikely. For example: 3-SAT is NP-complete, so it cannot be efficiently classical solved unless P = NP. Theoretical QS: perform a computational task efficiently on a quantum device, and prove that task cannot be efficiently classically simulated unless “the polynomial Heierarchy collapses to the 3nd level.” Quantum Supremacy A common feature of QS arguments is that they consider sampling problems, rather than decision problems. They allow us to characterize the complexity of sampling measurements of quantum states. Which is more difficult: Task A: deciding if a circuit outputs 1 with probability at least 2/3s, or at most 1/3s Task B: sampling from the output of an n-qubit circuit in the computational basis Sampling from distributions is generically more difficult than approximating observables, since we can use samples to estimate observables, but not the other way around. One can imagine quantum systems whose local observables are easy to classically compute, but for which sampling the full state is computationally complex. By moving from decision problems to sampling problems, we make the task of classical simulation much more difficult. -
Physical Implementations of Quantum Computing
Physical implementations of quantum computing Andrew Daley Department of Physics and Astronomy University of Pittsburgh Overview (Review) Introduction • DiVincenzo Criteria • Characterising coherence times Survey of possible qubits and implementations • Neutral atoms • Trapped ions • Colour centres (e.g., NV-centers in diamond) • Electron spins (e.g,. quantum dots) • Superconducting qubits (charge, phase, flux) • NMR • Optical qubits • Topological qubits Back to the DiVincenzo Criteria: Requirements for the implementation of quantum computation 1. A scalable physical system with well characterized qubits 1 | i 0 | i 2. The ability to initialize the state of the qubits to a simple fiducial state, such as |000...⟩ 1 | i 0 | i 3. Long relevant decoherence times, much longer than the gate operation time 4. A “universal” set of quantum gates control target (single qubit rotations + C-Not / C-Phase / .... ) U U 5. A qubit-specific measurement capability D. P. DiVincenzo “The Physical Implementation of Quantum Computation”, Fortschritte der Physik 48, p. 771 (2000) arXiv:quant-ph/0002077 Neutral atoms Advantages: • Production of large quantum registers • Massive parallelism in gate operations • Long coherence times (>20s) Difficulties: • Gates typically slower than other implementations (~ms for collisional gates) (Rydberg gates can be somewhat faster) • Individual addressing (but recently achieved) Quantum Register with neutral atoms in an optical lattice 0 1 | | Requirements: • Long lived storage of qubits • Addressing of individual qubits • Single and two-qubit gate operations • Array of singly occupied sites • Qubits encoded in long-lived internal states (alkali atoms - electronic states, e.g., hyperfine) • Single-qubit via laser/RF field coupling • Entanglement via Rydberg gates or via controlled collisions in a spin-dependent lattice Rb: Group II Atoms 87Sr (I=9/2): Extensively developed, 1 • P1 e.g., optical clocks 3 • Degenerate gases of Yb, Ca,.. -
IJSRP, Volume 2, Issue 7, July 2012 Edition
International Journal of Scientific and Research Publications, Volume 2, Issue 7, July 2012 1 ISSN 2250-3153 OF QUANTUM GATES AND COLLAPSING STATES- A DETERMINATE MODEL APRIORI AND DIFFERENTIAL MODEL APOSTEORI 1DR K N PRASANNA KUMAR, 2PROF B S KIRANAGI AND 3 PROF C S BAGEWADI ABSTRACT : We Investigate The Holistic Model With Following Composition : ( 1) Mpc (Measurement Based Quantum Computing)(2) Preparational Methodologies Of Resource States (Application Of Electric Field Magnetic Field Etc.)For Gate Teleportation(3) Quantum Logic Gates(4) Conditionalities Of Quantum Dynamics(5) Physical Realization Of Quantum Gates(6) Selective Driving Of Optical Resonances Of Two Subsystems Undergoing Dipole-Dipole Interaction By Means Of Say Ramsey Atomic Interferometry(7) New And Efficient Quantum Algorithms For Computation(8) Quantum Entanglements And No localities(9) Computation Of Minimum Energy Of A Given System Of Particles For Experimentation(10) Exponentially Increasing Number Of Steps For Such Quantum Computation(11) Action Of The Quantum Gates(12) Matrix Representation Of Quantum Gates And Vector Constitution Of Quantum States. Stability Conditions, Analysis, Solutional Behaviour Are Discussed In Detailed For The Consummate System. The System Of Quantum Gates And Collapsing States Show Contrast With The Documented Information Thereto. Paper may be extended to exponential time with exponentially increasing steps in the computation. INTRODUCTION: LITERATURE REVIEW: Double quantum dots: interdot interactions, co-tunneling, and Kondo resonances without spin (See for details Qing-feng Sun, Hong Guo ) Authors show that through an interdot off-site electron correlation in a double quantum-dot (DQD) device, Kondo resonances emerge in the local density of states without the electron spin-degree of freedom. -
Chapter 3 Quantum Circuit Model of Computation
Chapter 3 Quantum Circuit Model of Computation 3.1 Introduction In the previous chapter we saw that any Boolean function can be computed from a reversible circuit. In particular, in principle at least, this can be done from a small set of universal logical gates which do not dissipate heat dissi- pation (so we have logical reversibility as well as physical reversibility. We also saw that quantum evolution of the states of a system (e.g. a collection of quantum bits) is unitary (ignoring the reading or measurement process of the bits). A unitary matrix is of course invertible, but also conserves entropy (at the present level you can think of this as a conservation of scalar prod- uct which implies conservation of probabilities and entropies). So quantum evolution is also both \logically" and physically reversible. The next natural question is then to ask if we can use quantum operations to perform computational tasks, such as computing a Boolean function? Do the principles of quantum mechanics bring in new limitations with respect to classical computations? Or do they on the contrary bring in new ressources and advantages? These issues were raised and discussed by Feynman, Benioff and Manin in the early 1980's. In principle QM does not bring any new limitations, but on the contrary the superposition principle applied to many particle systems (many qubits) enables us to perform parallel computations, thereby speed- ing up classical computations. This was recognized very early by Feynman who argued that classical computers cannot simulate efficiently quantum me- chanical processes. The basic reason is that general quantum states involve 1 2 CHAPTER 3.