Hyperfine Interactions and Quantum Information Processing in Quantum
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What Is Quantum Information?
What Is Quantum Information? Robert B. Griffiths Carnegie-Mellon University Pittsburgh, Pennsylvania Research supported by the National Science Foundation References (work by R. B. Griffiths) • \Nature and location of quantum information." Ph◦ys. Rev. A 66 (2002) 012311; quant-ph/0203058 \Channel kets, entangled states, and the location of quan◦ tum information," Phys. Rev. A 71 (2005) 042337; quant-ph/0409106 Consistent Quantum Theory (Cambridge 2002) http://quan◦ tum.phys.cmu.edu/ What Is Quantum Information? 01. 100.01.tex Introduction What is quantum information? Precede by: • What is information? ◦ What is classical information theory? ◦ What is information? Example, newspaper • Symbolic representation of some situation ◦ Symbols in newspaper correlated with situation ◦ Information is about that situation ◦ What Is Quantum Information? 04. 100.04.tex Classical Information Theory Shannon: • \Mathematical Theory of Communication" (1948) ◦ One of major scientific developments of 20th century ◦ Proposed quantitative measure of information ◦ Information entropy • H(X) = p log p − X i i i Logarithmic measure of missing information ◦ Probabilistic model: pi are probabilities ◦ Applies to classical (macroscopic)f g signals ◦ Coding theorem: Bound on rate of transmission of information• through noisy channel What Is Quantum Information? 05. 100.05.tex Quantum Information Theory (QIT) Goal of QIT: \Quantize Shannon" • Extend Shannon's ideas to domain where quantum effects◦ are important Find quantum counterpart of H(X) ◦ We live in a quantum world, so • QIT should be the fundamental info theory ◦ Classical theory should emerge from QIT ◦ Analogy: relativity theory Newton for v c ◦ ! What Is Quantum Information? 06. 100.06.tex QIT: Current Status Enormous number of published papers • Does activity = understanding? ◦ Some topics of current interest: • Entanglement ◦ Quantum channels ◦ Error correction ◦ Quantum computation ◦ Decoherence ◦ Unifying principles have yet to emerge • At least, they are not yet widely recognized ◦ What Is Quantum Information? 07. -
Key Concepts for Future QIS Learners Workshop Output Published Online May 13, 2020
Key Concepts for Future QIS Learners Workshop output published online May 13, 2020 Background and Overview On behalf of the Interagency Working Group on Workforce, Industry and Infrastructure, under the NSTC Subcommittee on Quantum Information Science (QIS), the National Science Foundation invited 25 researchers and educators to come together to deliberate on defining a core set of key concepts for future QIS learners that could provide a starting point for further curricular and educator development activities. The deliberative group included university and industry researchers, secondary school and college educators, and representatives from educational and professional organizations. The workshop participants focused on identifying concepts that could, with additional supporting resources, help prepare secondary school students to engage with QIS and provide possible pathways for broader public engagement. This workshop report identifies a set of nine Key Concepts. Each Concept is introduced with a concise overall statement, followed by a few important fundamentals. Connections to current and future technologies are included, providing relevance and context. The first Key Concept defines the field as a whole. Concepts 2-6 introduce ideas that are necessary for building an understanding of quantum information science and its applications. Concepts 7-9 provide short explanations of critical areas of study within QIS: quantum computing, quantum communication and quantum sensing. The Key Concepts are not intended to be an introductory guide to quantum information science, but rather provide a framework for future expansion and adaptation for students at different levels in computer science, mathematics, physics, and chemistry courses. As such, it is expected that educators and other community stakeholders may not yet have a working knowledge of content covered in the Key Concepts. -
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]. -
Quantum Information Science, NIST, and Future Technological Implications National Institute of Standards & Technology Http
Quantum Information Science, NIST, and Future Technological Implications Carl J. Williams, Chief Atomic Physics Division National Institute of Standards & Technology http://qubit.nist.gov NIST – Atomic Physics Division Carl J. Williams, Chief What is Quantum Information? “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, 1997 Nobel Prize Winner in Physics A convergence of two of the 20th Century’s great revolutions A new science! Quantum Mechanics Information Science (i.e. computer science, (i.e. atoms, photons, JJ’s, communications, physics of computation) cryptology) The second quantum revolution NIST – Atomic Physics Division Carl J. Williams, Chief Second Quantum Revolution We are witnessing the second quantum revolution • First quantum revolution (1920’s - 1980’s) – Described how nature works at the quantum level – Weirdness of QM discovered and debated – Wave-particle duality -> Wavefunctions – Spooky action at a distance -> Entanglement – Technology uses semiclassical properties – quantization & wave properties • Second quantum revolution (starts ~1980’s - ) – Exploits how nature works at the quantum level – Interactions are how Nature computes! – Weirdness of QM exploited – Information storage capacity of superposed wavefunctions – Information transmittal accomplished by entanglement, teleportation – Information exchange accomplished by interactions – Technology uses the weird properties of quantum mechanics NIST – Atomic Physics Division Carl J. Williams, Chief Classical Bits vs. Quantum Bits • Classical Bits: two-state systems Classical bits: 0 (off) or 1 (on) (switch) • Quantum Bits are also two-level(state) systems ⎜↑〉 ⎜1〉 Atom ⎜0〉 ⎜↓〉 Internal State Motional State Ö But: Quantum Superpositions are possible Ψ= α|↓〉 + β|↑〉 = α|0〉 + β|1〉 NIST – Atomic Physics Division Carl J. -
Quantum Computation and Complexity Theory
Quantum computation and complexity theory Course given at the Institut fÈurInformationssysteme, Abteilung fÈurDatenbanken und Expertensysteme, University of Technology Vienna, Wintersemester 1994/95 K. Svozil Institut fÈur Theoretische Physik University of Technology Vienna Wiedner Hauptstraûe 8-10/136 A-1040 Vienna, Austria e-mail: [email protected] December 5, 1994 qct.tex Abstract The Hilbert space formalism of quantum mechanics is reviewed with emphasis on applicationsto quantum computing. Standardinterferomeric techniques are used to construct a physical device capable of universal quantum computation. Some consequences for recursion theory and complexity theory are discussed. hep-th/9412047 06 Dec 94 1 Contents 1 The Quantum of action 3 2 Quantum mechanics for the computer scientist 7 2.1 Hilbert space quantum mechanics ..................... 7 2.2 From single to multiple quanta Ð ªsecondº ®eld quantization ...... 15 2.3 Quantum interference ............................ 17 2.4 Hilbert lattices and quantum logic ..................... 22 2.5 Partial algebras ............................... 24 3 Quantum information theory 25 3.1 Information is physical ........................... 25 3.2 Copying and cloning of qbits ........................ 25 3.3 Context dependence of qbits ........................ 26 3.4 Classical versus quantum tautologies .................... 27 4 Elements of quantum computatability and complexity theory 28 4.1 Universal quantum computers ....................... 30 4.2 Universal quantum networks ........................ 31 4.3 Quantum recursion theory ......................... 35 4.4 Factoring .................................. 36 4.5 Travelling salesman ............................. 36 4.6 Will the strong Church-Turing thesis survive? ............... 37 Appendix 39 A Hilbert space 39 B Fundamental constants of physics and their relations 42 B.1 Fundamental constants of physics ..................... 42 B.2 Conversion tables .............................. 43 B.3 Electromagnetic radiation and other wave phenomena ......... -
Virtual Conference Contents
Virtual Conference Contents 등록 및 발표장 안내 03 2020 한국물리학회 가을 학술논문발표회 및 05 임시총회 전체일정표 구두발표논문 시간표 13 포스터발표논문 시간표 129 발표자 색인 189 이번 호의 표지는 김요셉 (공동 제1저자), Yong Siah Teo (공동 제1저자), 안대건, 임동길, 조영욱, 정현석, 김윤호 회원의 최근 논문 Universal Compressive Characterization of Quantum Dynamics, Phys. Rev. Lett. 124, 210401 (2020) 에서 모티 브를 채택했다. 이 논문에서는 효율적이고 신뢰할 수 있는 양자 채널 진단을 위한 적응형 압축센싱 방법을 제안하고 이를 실험 으로 시연하였다. 이번 가을학술논문발표회 B11-ap 세션에서 김요셉 회원이 관련 주제에 대해서 발표할 예정(B11.02)이다. 2 등록 및 발표장 안내 (Registration & Conference Room) 1. Epitome Any KPS members can download the pdf files on the KPS homepage. (http://www.kps.or.kr) 2. Membership & Registration Fee Category Fee (KRW) Category Fee (KRW) Fellow/Regular member 130,000 Subscription 1 journal 80,000 Student member 70,000 (Fellow/Regular 2 journals 120,000 Registration Nonmember (general) 300,000 member) Nonmember 150,000 1 journal 40,000 (invited speaker or student) Subscription Fellow 100,000 (Student member) 2 journals 60,000 Membership Regular member 50,000 Student member 20,000 Enrolling fee New member 10,000 3. Virtual Conference Rooms Oral sessions Special sessions Division Poster sessions (Zoom rooms) (Zoom rooms) Particle and Field Physics 01, 02 • General Assembly: 20 Nuclear Physics 03 • KPS Fellow Meeting: 20 Condensed Matter Physics 05, 06, 07, 08 • NPSM Senior Invited Lecture: 20 Applied Physics 09, 10, 11 Virtual Poster rooms • Heavy Ion Accelerator Statistical Physics 12 (Nov. 2~Nov. 6) Complex, RAON: 19 Physics Teaching 13 • Computational science: 20 On-line Plasma Physics 14 • New accelerator: 20 Discussion(mandatory): • KPS-KOFWST Young Optics and Quantum Electonics 15 Nov. -
Models of Quantum Complexity Growth
Models of quantum complexity growth Fernando G.S.L. Brand~ao,a;b;c;d Wissam Chemissany,b Nicholas Hunter-Jones,* e;b Richard Kueng,* b;c John Preskillb;c;d aAmazon Web Services, AWS Center for Quantum Computing, Pasadena, CA bInstitute for Quantum Information and Matter, California Institute of Technology, Pasadena, CA 91125 cDepartment of Computing and Mathematical Sciences, California Institute of Technology, Pasadena, CA 91125 dWalter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, CA 91125 ePerimeter Institute for Theoretical Physics, Waterloo, ON N2L 2Y5 *Corresponding authors: [email protected] and [email protected] Abstract: The concept of quantum complexity has far-reaching implications spanning theoretical computer science, quantum many-body physics, and high energy physics. The quantum complexity of a unitary transformation or quantum state is defined as the size of the shortest quantum computation that executes the unitary or prepares the state. It is reasonable to expect that the complexity of a quantum state governed by a chaotic many- body Hamiltonian grows linearly with time for a time that is exponential in the system size; however, because it is hard to rule out a short-cut that improves the efficiency of a computation, it is notoriously difficult to derive lower bounds on quantum complexity for particular unitaries or states without making additional assumptions. To go further, one may study more generic models of complexity growth. We provide a rigorous connection between complexity growth and unitary k-designs, ensembles which capture the randomness of the unitary group. This connection allows us to leverage existing results about design growth to draw conclusions about the growth of complexity. -
Lecture 6: Quantum Error Correction and Quantum Capacity
Lecture 6: Quantum error correction and quantum capacity Mark M. Wilde∗ The quantum capacity theorem is one of the most important theorems in quantum Shannon theory. It is a fundamentally \quantum" theorem in that it demonstrates that a fundamentally quantum information quantity, the coherent information, is an achievable rate for quantum com- munication over a quantum channel. The fact that the coherent information does not have a strong analog in classical Shannon theory truly separates the quantum and classical theories of information. The no-cloning theorem provides the intuition behind quantum error correction. The goal of any quantum communication protocol is for Alice to establish quantum correlations with the receiver Bob. We know well now that every quantum channel has an isometric extension, so that we can think of another receiver, the environment Eve, who is at a second output port of a larger unitary evolution. Were Eve able to learn anything about the quantum information that Alice is attempting to transmit to Bob, then Bob could not be retrieving this information|otherwise, they would violate the no-cloning theorem. Thus, Alice should figure out some subspace of the channel input where she can place her quantum information such that only Bob has access to it, while Eve does not. That the dimensionality of this subspace is exponential in the coherent information is perhaps then unsurprising in light of the above no-cloning reasoning. The coherent information is an entropy difference H(B) − H(E)|a measure of the amount of quantum correlations that Alice can establish with Bob less the amount that Eve can gain. -
Quantum Computational Complexity Theory Is to Un- Derstand the Implications of Quantum Physics to Computational Complexity Theory
Quantum Computational Complexity John Watrous Institute for Quantum Computing and School of Computer Science University of Waterloo, Waterloo, Ontario, Canada. Article outline I. Definition of the subject and its importance II. Introduction III. The quantum circuit model IV. Polynomial-time quantum computations V. Quantum proofs VI. Quantum interactive proof systems VII. Other selected notions in quantum complexity VIII. Future directions IX. References Glossary Quantum circuit. A quantum circuit is an acyclic network of quantum gates connected by wires: the gates represent quantum operations and the wires represent the qubits on which these operations are performed. The quantum circuit model is the most commonly studied model of quantum computation. Quantum complexity class. A quantum complexity class is a collection of computational problems that are solvable by a cho- sen quantum computational model that obeys certain resource constraints. For example, BQP is the quantum complexity class of all decision problems that can be solved in polynomial time by a arXiv:0804.3401v1 [quant-ph] 21 Apr 2008 quantum computer. Quantum proof. A quantum proof is a quantum state that plays the role of a witness or certificate to a quan- tum computer that runs a verification procedure. The quantum complexity class QMA is defined by this notion: it includes all decision problems whose yes-instances are efficiently verifiable by means of quantum proofs. Quantum interactive proof system. A quantum interactive proof system is an interaction between a verifier and one or more provers, involving the processing and exchange of quantum information, whereby the provers attempt to convince the verifier of the answer to some computational problem. -
Topological Quantum Computation Zhenghan Wang
Topological Quantum Computation Zhenghan Wang Microsoft Research Station Q, CNSI Bldg Rm 2237, University of California, Santa Barbara, CA 93106-6105, U.S.A. E-mail address: [email protected] 2010 Mathematics Subject Classification. Primary 57-02, 18-02; Secondary 68-02, 81-02 Key words and phrases. Temperley-Lieb category, Jones polynomial, quantum circuit model, modular tensor category, topological quantum field theory, fractional quantum Hall effect, anyonic system, topological phases of matter To my parents, who gave me life. To my teachers, who changed my life. To my family and Station Q, where I belong. Contents Preface xi Acknowledgments xv Chapter 1. Temperley-Lieb-Jones Theories 1 1.1. Generic Temperley-Lieb-Jones algebroids 1 1.2. Jones algebroids 13 1.3. Yang-Lee theory 16 1.4. Unitarity 17 1.5. Ising and Fibonacci theory 19 1.6. Yamada and chromatic polynomials 22 1.7. Yang-Baxter equation 22 Chapter 2. Quantum Circuit Model 25 2.1. Quantum framework 26 2.2. Qubits 27 2.3. n-qubits and computing problems 29 2.4. Universal gate set 29 2.5. Quantum circuit model 31 2.6. Simulating quantum physics 32 Chapter 3. Approximation of the Jones Polynomial 35 3.1. Jones evaluation as a computing problem 35 3.2. FP#P-completeness of Jones evaluation 36 3.3. Quantum approximation 37 3.4. Distribution of Jones evaluations 39 Chapter 4. Ribbon Fusion Categories 41 4.1. Fusion rules and fusion categories 41 4.2. Graphical calculus of RFCs 44 4.3. Unitary fusion categories 48 4.4. Link and 3-manifold invariants 49 4.5. -
Quantum Information Science
Quantum Information Science Seth Lloyd Professor of Quantum-Mechanical Engineering Director, WM Keck Center for Extreme Quantum Information Theory (xQIT) Massachusetts Institute of Technology Article Outline: Glossary I. Definition of the Subject and Its Importance II. Introduction III. Quantum Mechanics IV. Quantum Computation V. Noise and Errors VI. Quantum Communication VII. Implications and Conclusions 1 Glossary Algorithm: A systematic procedure for solving a problem, frequently implemented as a computer program. Bit: The fundamental unit of information, representing the distinction between two possi- ble states, conventionally called 0 and 1. The word ‘bit’ is also used to refer to a physical system that registers a bit of information. Boolean Algebra: The mathematics of manipulating bits using simple operations such as AND, OR, NOT, and COPY. Communication Channel: A physical system that allows information to be transmitted from one place to another. Computer: A device for processing information. A digital computer uses Boolean algebra (q.v.) to processes information in the form of bits. Cryptography: The science and technique of encoding information in a secret form. The process of encoding is called encryption, and a system for encoding and decoding is called a cipher. A key is a piece of information used for encoding or decoding. Public-key cryptography operates using a public key by which information is encrypted, and a separate private key by which the encrypted message is decoded. Decoherence: A peculiarly quantum form of noise that has no classical analog. Decoherence destroys quantum superpositions and is the most important and ubiquitous form of noise in quantum computers and quantum communication channels. -
CLEO Conference
Executive Ballroom Executive Ballroom Executive Ballroom Executive Ballroom 210A 210B 210C 210D CLEO: QELS-Fundamental Science 08:00–10:00 08:00–10:00 08:00–10:00 08:00–10:00 FM1A • Quantum Engineering FM1B • Relativistic Laser-Plasma FM1C • Hyperbolic and Epsilon- FM1D • PT Symmetry and Presider: Nicholas Peters; Applied Interactions near-zero Materials Related Phenomena Communication Sciences, USA Presider: Sergei Tochitsky; Univ. Presider: Philippe Tassin; Presider: Matthias Heinrich, Univ. of California Los Angeles, USA Chalmers Univ., Sweden of Central Florida, USA FM1A.1 • 08:00 Tutorial FM1B.1 • 08:00 Invited FM1C.1 • 08:00 FM1D.1 • 08:00 Quantum Optomechanics, Markus Aspel- High energy ion acceleration and neutron Wave Propagation in Magnetized Epsilon- Beyond PT-symmetry: SUSY-mediated real meyer1; 1Universitat Wien, Austria. This production using relativistic transparency Near-Zero Metamaterials, Arthur Davoyan1, spectra in complex refractive index land- 1 1 1 tutorial provides an introduction to the cur- in solids, Markus Roth1, Daniel Jung2, Kat- Nader Engheta ; Univ. of Pennsylvania, USA. scapes, Mohammad-Ali Miri , Matthias Hein- 1 1 1 rent state-of-the-art, the challenges and the erina Falk2, Nevzat Guler2, Vincent Bagnoud3, In this work we theoretically study light propa- rich , Demetrios N. Christodoulides ; CREOL prospects of achieving quantum optical con- Stefan Bedacht1, Oliver Deppert1, Matthew gation in magnetized epsilon-near-zero (ENZ) The College of Optics and Photonics, Univ. of trol over nano-, micro- and macro-mechanical J. Devlin2, Andrea Favalli2, Juan Fernandez2, metamaterials. We reveal novel regimes of Central Florida, USA. In the presence of gain devices, i.e. quantum optomechanics.