Quantum Expanders: Motivation and Constructions
... change the entropy of a state. An operator has small degree if it can never add much entropy to the state it acts upon. Specifically, a degree D operator can never add more than log(D) entropy. Such a view is almost explicit in the work of Capalbo et al. [9], where they view expanders as entropy con ...
... change the entropy of a state. An operator has small degree if it can never add much entropy to the state it acts upon. Specifically, a degree D operator can never add more than log(D) entropy. Such a view is almost explicit in the work of Capalbo et al. [9], where they view expanders as entropy con ...
Calculating Floquet states of large quantum systems: A
... the problem to the diagonalization of a time-independent superHamiltonian [8, 21]. This is a reliable method to obtain Floquet spectrum of a system of a size up to a hundred of states. For larger systems, this strategy leads to a computational problem: the size of the super-Hamiltonian scales as N × ...
... the problem to the diagonalization of a time-independent superHamiltonian [8, 21]. This is a reliable method to obtain Floquet spectrum of a system of a size up to a hundred of states. For larger systems, this strategy leads to a computational problem: the size of the super-Hamiltonian scales as N × ...
07_Entanglement_in_nuclear_quadrupole_resonance_
... rhombic pyramid. The four-coordinated copper ion site, EFG is highly asymmetric (η≥0.92) while the five-coordinated copper ion site, EFG is ...
... rhombic pyramid. The four-coordinated copper ion site, EFG is highly asymmetric (η≥0.92) while the five-coordinated copper ion site, EFG is ...
Isolation of the Conceptual Ingredients of Quantum Theory by Toy
... data to unprecedented and unrivalled numerical precision. Not all were as easily swept up into the ‘shut up and calculate’[2] camp by this sort of empirical success however, and some continued to ponder the problem of understanding the theory and reconciling it with other important theories in Physi ...
... data to unprecedented and unrivalled numerical precision. Not all were as easily swept up into the ‘shut up and calculate’[2] camp by this sort of empirical success however, and some continued to ponder the problem of understanding the theory and reconciling it with other important theories in Physi ...
Matter-Light Condensates Reach Thermal Equilibrium
... “textbook” theory of a Bose-Einstein condensate of noninteracting bosons. However, this is somewhat surprising, as polaritons do interact. Indeed, in the absence of interactions, particles cannot scatter, and so do not reach thermal equilibrium. Moreover, in a two-dimensional system, which is the ca ...
... “textbook” theory of a Bose-Einstein condensate of noninteracting bosons. However, this is somewhat surprising, as polaritons do interact. Indeed, in the absence of interactions, particles cannot scatter, and so do not reach thermal equilibrium. Moreover, in a two-dimensional system, which is the ca ...
Programming with Quantum Communication
... I n = λψ : 0, ..2n → C · ψ For a linear operation A, the adjoint of A, written A† , is the (unique) operation, such that for any two states ψ and φ, hψ|Aφi = hA† ψ|φi. The unitary transformations that describe the evolution of an n-qubit quantum system are operations U defined on the system, such th ...
... I n = λψ : 0, ..2n → C · ψ For a linear operation A, the adjoint of A, written A† , is the (unique) operation, such that for any two states ψ and φ, hψ|Aφi = hA† ψ|φi. The unitary transformations that describe the evolution of an n-qubit quantum system are operations U defined on the system, such th ...
Lecture Notes for Ph219/CS219: Quantum Information and Computation Chapter 2 John Preskill
... oddity is that the Schrödinger equation is linear, while we are accustomed to nonlinear dynamical equations in classical physics. This property seems to beg for an explanation. But far more curious is a mysterious dualism; there are two quite distinct ways for a quantum state to change. On the one ...
... oddity is that the Schrödinger equation is linear, while we are accustomed to nonlinear dynamical equations in classical physics. This property seems to beg for an explanation. But far more curious is a mysterious dualism; there are two quite distinct ways for a quantum state to change. On the one ...
Slides
... We trust quantum over classical coin tossing because one can never rule out an insider attack on classical coin tossing, whereas an insider attack on a quantum coin toss based on a pure state is inconsistent with the beliefs that led to the pure-state assignment. ...
... We trust quantum over classical coin tossing because one can never rule out an insider attack on classical coin tossing, whereas an insider attack on a quantum coin toss based on a pure state is inconsistent with the beliefs that led to the pure-state assignment. ...
The Physical Implementation of Quantum Computation David P. DiVincenzo
... physical implementation must turn towards these. At least this result says that the required decoherence rate does not become ever smaller as the size and duration of the quantum computation grows. So, once the desired threshold is attainable, decoherence will not be an obstacle to scalable quantum ...
... physical implementation must turn towards these. At least this result says that the required decoherence rate does not become ever smaller as the size and duration of the quantum computation grows. So, once the desired threshold is attainable, decoherence will not be an obstacle to scalable quantum ...
Max Born
Max Born (German: [bɔɐ̯n]; 11 December 1882 – 5 January 1970) was a German physicist and mathematician who was instrumental in the development of quantum mechanics. He also made contributions to solid-state physics and optics and supervised the work of a number of notable physicists in the 1920s and 30s. Born won the 1954 Nobel Prize in Physics for his ""fundamental research in Quantum Mechanics, especially in the statistical interpretation of the wave function"".Born was born in 1882 in Breslau, then in Germany, now in Poland and known as Wrocław. He entered the University of Göttingen in 1904, where he found the three renowned mathematicians, Felix Klein, David Hilbert and Hermann Minkowski. He wrote his Ph.D. thesis on the subject of ""Stability of Elastica in a Plane and Space"", winning the University's Philosophy Faculty Prize. In 1905, he began researching special relativity with Minkowski, and subsequently wrote his habilitation thesis on the Thomson model of the atom. A chance meeting with Fritz Haber in Berlin in 1918 led to discussion of the manner in which an ionic compound is formed when a metal reacts with a halogen, which is today known as the Born–Haber cycle.In the First World War after originally being placed as a radio operator, due to his specialist knowledge he was moved to research duties regarding sound ranging. In 1921, Born returned to Göttingen, arranging another chair for his long-time friend and colleague James Franck. Under Born, Göttingen became one of the world's foremost centres for physics. In 1925, Born and Werner Heisenberg formulated the matrix mechanics representation of quantum mechanics. The following year, he formulated the now-standard interpretation of the probability density function for ψ*ψ in the Schrödinger equation, for which he was awarded the Nobel Prize in 1954. His influence extended far beyond his own research. Max Delbrück, Siegfried Flügge, Friedrich Hund, Pascual Jordan, Maria Goeppert-Mayer, Lothar Wolfgang Nordheim, Robert Oppenheimer, and Victor Weisskopf all received their Ph.D. degrees under Born at Göttingen, and his assistants included Enrico Fermi, Werner Heisenberg, Gerhard Herzberg, Friedrich Hund, Pascual Jordan, Wolfgang Pauli, Léon Rosenfeld, Edward Teller, and Eugene Wigner.In January 1933, the Nazi Party came to power in Germany, and Born, who was Jewish, was suspended. He emigrated to Britain, where he took a job at St John's College, Cambridge, and wrote a popular science book, The Restless Universe, as well as Atomic Physics, which soon became a standard text book. In October 1936, he became the Tait Professor of Natural Philosophy at the University of Edinburgh, where, working with German-born assistants E. Walter Kellermann and Klaus Fuchs, he continued his research into physics. Max Born became a naturalised British subject on 31 August 1939, one day before World War II broke out in Europe. He remained at Edinburgh until 1952. He retired to Bad Pyrmont, in West Germany. He died in hospital in Göttingen on 5 January 1970.