TOPOLOGY, DR. BLOCK, SPRING 2016, NOTES, PART 6
... loop with base point z is the function c : I → X defined by c(t) = z for each t ∈ I. 611. Lemma. Let p be a path in X with initial point y and terminal point z, and let c be the constant loop with base point z. Then the paths p and p ∗ c are path homotopic. 612. Lemma. Let p be a path in X with init ...
... loop with base point z is the function c : I → X defined by c(t) = z for each t ∈ I. 611. Lemma. Let p be a path in X with initial point y and terminal point z, and let c be the constant loop with base point z. Then the paths p and p ∗ c are path homotopic. 612. Lemma. Let p be a path in X with init ...
Experimental one-way quantum computing
... Standard quantum computation is based on sequences of unitary quantum logic gates that process qubits. The one-way quantum computer proposed by Raussendorf and Briegel is entirely different. It has changed our understanding of the requirements for quantum computation and more generally how we think ...
... Standard quantum computation is based on sequences of unitary quantum logic gates that process qubits. The one-way quantum computer proposed by Raussendorf and Briegel is entirely different. It has changed our understanding of the requirements for quantum computation and more generally how we think ...
Matrix Product States for Lattice Gauge Theories
... particles are made. For example, by measuring the spin of the electron it becomes either up or down. Furthermore, then also the spin of the positron is immediately determined. It must be either down or up respectively. No matter how far electron and positron are apart, the measurement on one particl ...
... particles are made. For example, by measuring the spin of the electron it becomes either up or down. Furthermore, then also the spin of the positron is immediately determined. It must be either down or up respectively. No matter how far electron and positron are apart, the measurement on one particl ...
Quantum Structures
... theory. Is it an epistemic state (representing knowledge, information, or belief) or an ontic state (a direct reflection of reality)? In the ontological models framework, quantum states correspond to probability measures over more fundamental states of reality. The quantum state is then ontic if eve ...
... theory. Is it an epistemic state (representing knowledge, information, or belief) or an ontic state (a direct reflection of reality)? In the ontological models framework, quantum states correspond to probability measures over more fundamental states of reality. The quantum state is then ontic if eve ...
Quantum Mechanics
... Now allow ψ to evolve in time according to the Schrödinger equation (9). We define, ρ(x, t) = |ψ(x, t)|2 Thus, from eqn (13), ρ(x, 0) is a correctly normalized probability density. We will now show that this remains true at all subsequent times, provided |ψ(x, t)| → 0 sufficiently fast as ...
... Now allow ψ to evolve in time according to the Schrödinger equation (9). We define, ρ(x, t) = |ψ(x, t)|2 Thus, from eqn (13), ρ(x, 0) is a correctly normalized probability density. We will now show that this remains true at all subsequent times, provided |ψ(x, t)| → 0 sufficiently fast as ...
Chapter 4 MANY PARTICLE SYSTEMS
... as to the kind of systems to which they are intended to apply. Thus, although we have considered numerous examples drawn from the quantum mechanics of a single particle, the postulates themselves are intended to apply to all quantum systems, including those containing more than one and possibly very ...
... as to the kind of systems to which they are intended to apply. Thus, although we have considered numerous examples drawn from the quantum mechanics of a single particle, the postulates themselves are intended to apply to all quantum systems, including those containing more than one and possibly very ...
Creating arbitrary quantum vibrational states in a carbon nanotube
... The peculiar feature of quantum states is that they can be in a superposition of their basis states. Preparation, manipulation, and measurement of Fock states, which are quantum states with fixed numbers of quanta, and their superpositions are especially important for quantum computation with trappe ...
... The peculiar feature of quantum states is that they can be in a superposition of their basis states. Preparation, manipulation, and measurement of Fock states, which are quantum states with fixed numbers of quanta, and their superpositions are especially important for quantum computation with trappe ...
EXPONENTIAL SEPARATION OF QUANTUM AND CLASSICAL
... than the randomized one remained open. We resolve this in the affirmative, by exhibiting a problem for which the quantum complexity is exponentially smaller than the randomized one. 1.1. Related work. The area of quantum communication complexity was introduced by Yao [25]. Since then, a series of pa ...
... than the randomized one remained open. We resolve this in the affirmative, by exhibiting a problem for which the quantum complexity is exponentially smaller than the randomized one. 1.1. Related work. The area of quantum communication complexity was introduced by Yao [25]. Since then, a series of pa ...
Pure Wave Mechanics and the Very Idea of Empirical Adequacy
... in a deterministic linear way: ψ(t1 )S = Û (t0 , t1 )ψ(t0 )S . b. Nonlinear collapse dynamics: If a measurement is made, the system S randomly, instantaneously, and nonlinearly jumps to an eigenstate of the observable being measured: the probability of jumping to φS when O is measured is |ψφ|2 . Th ...
... in a deterministic linear way: ψ(t1 )S = Û (t0 , t1 )ψ(t0 )S . b. Nonlinear collapse dynamics: If a measurement is made, the system S randomly, instantaneously, and nonlinearly jumps to an eigenstate of the observable being measured: the probability of jumping to φS when O is measured is |ψφ|2 . Th ...
A Manifestation toward the Nambu-Goldstone Geometry
... An interesting and important tool to characterize a compact Riemannian manifold is provided by a Laplacian 4. We introduce the following known theorem: Let (M, g) be a C ∞ -class compact Riemannian manifold, and let Dp (M ) be a space of p-forms defined over the manifold. Then the eigenvalues of 4 a ...
... An interesting and important tool to characterize a compact Riemannian manifold is provided by a Laplacian 4. We introduce the following known theorem: Let (M, g) be a C ∞ -class compact Riemannian manifold, and let Dp (M ) be a space of p-forms defined over the manifold. Then the eigenvalues of 4 a ...
EM genius and mystery
... of a single particle the sort that Dirac was looking for initially. The combination of relativity and quantum mechanics inevitably leads to theories with unlimited numbers of particles. In such theories, the ‘true dynamical variables’ on which the wave function depends are not the position of one pa ...
... of a single particle the sort that Dirac was looking for initially. The combination of relativity and quantum mechanics inevitably leads to theories with unlimited numbers of particles. In such theories, the ‘true dynamical variables’ on which the wave function depends are not the position of one pa ...
Quantum Energy Teleportation - UWSpace
... The relation between energy and information has intrigued physicists for quite some time now. Usually, we speak of such a relation in the context of thermodynamics or black hole physics. Recently, quite a bit of work has been interested in the thermodynamics of spacetime itself[37, 14], and on emerg ...
... The relation between energy and information has intrigued physicists for quite some time now. Usually, we speak of such a relation in the context of thermodynamics or black hole physics. Recently, quite a bit of work has been interested in the thermodynamics of spacetime itself[37, 14], and on emerg ...
What is the Entropy in Entropic Gravity?
... The existence of a profound relationship between gravity and entropy has been recognized since the formulation of the laws of black hole mechanics [1] and the derivation of the BekensteinHawking entropy [2, 3]. More recently, ideas such as the holographic principle [4, 5], black hole complementarity ...
... The existence of a profound relationship between gravity and entropy has been recognized since the formulation of the laws of black hole mechanics [1] and the derivation of the BekensteinHawking entropy [2, 3]. More recently, ideas such as the holographic principle [4, 5], black hole complementarity ...