Quantum Expanders: Motivation and Constructions
... The algebraic definition of expansion views a regular graph G = (V, E) as a linear operator on a Hilbert space V of dimension |V |. In this view an element v ∈ V is identified with a basis vector |vi ∈ V, and a distribution π on V corresponds to the vector |πi = ∑v∈V π(v) |vi. The action of G on V i ...
... The algebraic definition of expansion views a regular graph G = (V, E) as a linear operator on a Hilbert space V of dimension |V |. In this view an element v ∈ V is identified with a basis vector |vi ∈ V, and a distribution π on V corresponds to the vector |πi = ∑v∈V π(v) |vi. The action of G on V i ...
... In order to complete the simulation of random quantum computers by classical computers of an infinite number of bits, we need first to simulate the five requirements imposed by DiVincenzo (Nakahara, 2004) on operative quantum computers. These five requirements are the following: a) The quantum degre ...
algunos resultados asociados a problemas
... case must be considered. Namely, the case where the particle disappears upon reaching a wall and then appears at the other end must be considered. This type of movement (which is very unusual because the particle is not actually trapped between the two walls) corresponds to that of a quantum particl ...
... case must be considered. Namely, the case where the particle disappears upon reaching a wall and then appears at the other end must be considered. This type of movement (which is very unusual because the particle is not actually trapped between the two walls) corresponds to that of a quantum particl ...
An Introduction to Nonequilibrium Many
... spoils the expansion. Finally, even if the ground state is assumed to be nondegenerate, excited states |ni appearing in the nonequilibrium density matrix ρ can be degenerate so they can be mixed by a non-Abelian Berry phase under adiabatic evolution, which once again invalidates the conventional pro ...
... spoils the expansion. Finally, even if the ground state is assumed to be nondegenerate, excited states |ni appearing in the nonequilibrium density matrix ρ can be degenerate so they can be mixed by a non-Abelian Berry phase under adiabatic evolution, which once again invalidates the conventional pro ...
Quantum Factorization of 143 on a Dipolar
... Hp ¼ Hpi is a summation of all the bitwise Hamiltonians. In this way, the ground state of Hp encodes the two factors that satisfy all the bitwise equations and is the answer to our factoring problem. Thus the spectrum of Hp will not scale with N but log2 N. However, Schaller and Schützhold’s scheme ...
... Hp ¼ Hpi is a summation of all the bitwise Hamiltonians. In this way, the ground state of Hp encodes the two factors that satisfy all the bitwise equations and is the answer to our factoring problem. Thus the spectrum of Hp will not scale with N but log2 N. However, Schaller and Schützhold’s scheme ...
White Paper
... dimensional thin layer grows at first, and then, dislocation free high density three dimensional islands of InAs are self-assembled in order to release the strain energy. This is analogical to our daily experience that we see water droplets on the waxed body of a car. InAs islands on the GaAs substr ...
... dimensional thin layer grows at first, and then, dislocation free high density three dimensional islands of InAs are self-assembled in order to release the strain energy. This is analogical to our daily experience that we see water droplets on the waxed body of a car. InAs islands on the GaAs substr ...
25 – 27 MAY 2016, ATHENS, GREECE
... 3+1D. The model generalises the 3+1D Kitaev quantum double replacing the finite group with a finite 2-group. Such a model describes a lattice realisation of BF-CG theory which is proposed to describe topological gauge theories which are both partially Higgsed and partially confined. Furthermore we p ...
... 3+1D. The model generalises the 3+1D Kitaev quantum double replacing the finite group with a finite 2-group. Such a model describes a lattice realisation of BF-CG theory which is proposed to describe topological gauge theories which are both partially Higgsed and partially confined. Furthermore we p ...
The Schrödinger equation Combining the classical Hamilton
... The function ψ(r , t) is called ‘state function’, or ‘wave function’. As in classical mechanics, where the Hamilton function includes kinetic and potential energies, H = T + V , the Hamilton operator is extended c = Tb + Vb . to include parts for both kinetic and potential energy, H For application ...
... The function ψ(r , t) is called ‘state function’, or ‘wave function’. As in classical mechanics, where the Hamilton function includes kinetic and potential energies, H = T + V , the Hamilton operator is extended c = Tb + Vb . to include parts for both kinetic and potential energy, H For application ...
I. Wave Mechanics
... However, we have additional information. In the region x < 0, we have traveling harmonic waves, one incident from the left, the other reflected from the step and traveling toward the left. These cannot be normalized, so we’ll just set A = 1. On the other hand, in the region x > 0, the D = 0, because ...
... However, we have additional information. In the region x < 0, we have traveling harmonic waves, one incident from the left, the other reflected from the step and traveling toward the left. These cannot be normalized, so we’ll just set A = 1. On the other hand, in the region x > 0, the D = 0, because ...
QUANTUM PHENOMENA IN THE BIOLOGICAL
... given small element of volume of biological material when exposed to the rays is only affected by them when such a discrete act of absorption happens in the volume. The quantum of X-ray energy, when absorbed, is taken up by one atom of the absorbing substance and a high-speed photo-electron is liber ...
... given small element of volume of biological material when exposed to the rays is only affected by them when such a discrete act of absorption happens in the volume. The quantum of X-ray energy, when absorbed, is taken up by one atom of the absorbing substance and a high-speed photo-electron is liber ...
Arbitrarily Small Amount of Measurement Independence Is Sufficient
... introduced pinffiffiffi Table I can be violated for values larger than ð2 þ 2Þ=12. In fact, inequalities (6) and (7) can reveal quantum nonlocality for all h below the critical value of 13. This shows that the complete set presented here is better suited for the task of witnessing measurement dependent qu ...
... introduced pinffiffiffi Table I can be violated for values larger than ð2 þ 2Þ=12. In fact, inequalities (6) and (7) can reveal quantum nonlocality for all h below the critical value of 13. This shows that the complete set presented here is better suited for the task of witnessing measurement dependent qu ...
PowerPoint file of HBM_Intro _part I
... and fixed amount of progression steps When the Qpatch moves, then the pattern spreads out along the movement path When an event (creation, annihilation, sudden energy change) occurs, then the enumeration generation changes its mode ...
... and fixed amount of progression steps When the Qpatch moves, then the pattern spreads out along the movement path When an event (creation, annihilation, sudden energy change) occurs, then the enumeration generation changes its mode ...
Geometric Quantization - Texas Christian University
... Q : C ∞ (M ) → Op (H) mapping a classical observable (function on phase space (M, ω) ) to an operator on Hilbert space H. Following are the rules of canonical quantization. Q1: Q is R-linear. Q2: Q maps the constant function 1 to the identity 1 on H. Q3: Q (f )∗ = Q (f ) for all f ∈ C ∞ (M ). (ie re ...
... Q : C ∞ (M ) → Op (H) mapping a classical observable (function on phase space (M, ω) ) to an operator on Hilbert space H. Following are the rules of canonical quantization. Q1: Q is R-linear. Q2: Q maps the constant function 1 to the identity 1 on H. Q3: Q (f )∗ = Q (f ) for all f ∈ C ∞ (M ). (ie re ...