In IBM Qiskit and Quantum Experience, the custom U3 gate is defined as $$ U(\theta, \phi, \lambda) = \begin{pmatrix} \cos\left(\frac{\theta}{2}\right) & -e^{i\lambda} \sin\left(\frac{\theta}{2}\right) \\ e^{i\phi} \sin\left(\frac{\theta}{2}\right) & e^{i(\lambda + \phi)} \cos\left(\frac{\thet...

Can someone help me derive from the original nonlinear Hamiltonian to the effective Kerr-type Hamiltonian?

In quantum mechanics, we generally deal with unitary matrices. In the IBM cloud computers and Qiskit, the general $2\times 2$ unitary is defined as $$U(\theta, \phi, \lambda) = \begin{pmatrix} \cos\left(\frac{\theta}{2}\right) & -e^{i\lambda} \sin\left(\frac{\theta}{2}\right) \\ e^{i\phi} \si...

The Grover algorithm allows you to search for multiple elements. Assuming my search space contains four elements, if I only search for one element, I get the one I'm looking for Element with a probability of 100%. So far so good. Assuming I search for two elements within the four elements, then ...

Found the closest thing to what I'm trying to achieve here which is based on a closed qunatum system Then tried to create a GRAPE implementation for open quantum system # File to emulate maker # import jate.py from qutip.operators import sigmax, sigmay, sigmaz, identity, qeye ...

Assume we are given an $n$-qubit system and complex numbers $a_0, \ldots, a_{m-1}$ with $m = 2^n$. Assume further we start with the initial state $|0 \ldots 0\rangle$ and want to make the transformation $$|0 \ldots 0\rangle \rightarrow \sum_{i=0}^{m-1} a_i |i\rangle.$$ My question is now: What is...