The two ways of defining spin networks are equivalent because they use the same Lie group (G = SU(2)) and the same representations for the edges (elements of G^L). In the first way, the nodes are colored with elements of G^N, while in the second way the nodes are colored with intertwiners...
This article discusses the development of a new device that can measure the movement of particles at the nanoscale. This device, known as an ion trap, uses electric fields to trap and measure the motion of ions (charged atoms). The article explains how this approach could be used to accurately...
The value of Planck's constant, h, will be determined experimentally. The values of the other fundamental constants, c, me, α, and Rc, will be calculated from the exact value of h, c, and the measured values of me, α, and Rc.
The exact requirements for intensity, duration, and repetition frequency for EIT realized with pulsed laser will depend on the specific application and the characteristics of the system you are using. Generally, the intensity should be high enough to ensure that the stimulated transition is...
Your attempt looks correct so far. The next step would be to substitute in the definition of ##\psi## and evaluate the integral. This should give you a result in momentum space.
The idea here is that when the momentum operator p is applied to an eigenstate, it will produce a state with the same energy (eigenvalue) as before. However, when the momentum operator squared, p^2, is applied to this same eigenstate, the result will be a state with a different energy. This is...
Yes, you are correct. The convention that is usually used is that the wave function should have a positive energy, and so the time derivative of the wave function should be positive. Therefore, the coefficient of the cosine term must be +i in order for the wave function to satisfy this requirement.
I've also written a blog post about the development of the simulator.https://medium.com/@BobWalance/building-a-quantum-computer-simulator-with-python-on-a-raspberry-pi-86c5e9f2513b
Yes, there is a subset of the Y impacts on the left screen so that the yi would mimic the case where one of the right slit is not open. This can be achieved by choosing the Y impacts such that the interference pattern on the right screen is minimized. To do this, the Y impacts should be chosen...
Concurrence is a measure of entanglement between two qubits, or two spin-1/2 particles. It measures the degree of correlation between the two particles and is defined using the density matrix of the two-qubit system. When two qubits are in a maximally entangled state, the concurrence is 1, and...
ityThe explanation for why the dissociation rate is proportional to current^(N) is that the more electrons that are involved in the process, the faster the reaction will occur. This is because the electrons must all be in the same place at the same time to initiate the reaction. When there are...
Yes, the controlled unitary used in the Hamiltonian simulation part of Quantum Phase Estimation depends on the Hermitian matrix coefficients. Specifically, the controlled unitary is constructed from the matrix coefficients of the Hermitian matrix that describes the system’s Hamiltonian. The...
The K-L condition is a mathematical theorem that states that a given error correction code must have certain properties in order for it to be valid and correct errors in quantum systems. To satisfy this condition, projection operators onto the codespace must be found. These projection operators...
Here is a QUBO expression that will find the two ways of summing the 5 numbers {1, 2, 3, 4, 5) to 8 by selecting 3 of the numbers: QUBO: minimize (x1 + 2x2 + 3x3 + 4x4 + 5x5 - 8)^2 + (x1 + x2 + x3 - 3)^2 + (x1x2 + x2x3 + x1x3)where x1, x2, x3, x4, x5 are binary variables (0 or 1). The first two...