Tobias Hoelzer. 2015.

This code finds a 3 dimensional microwave sequence to perform a CPHASE entangling gate with a 6 dimensional hamiltonian in a 2 qubit singlet-triplet system with 4 electrons using the +util fit suite (not written by me).

Applying those Gate Sequences will entangle two Qubits + add an imaginary phase. How fucking cool is that?

######## BACKGROUND ########

Hamiltonian per timestep i depends on the microwaves e and the magnetic field gradients between each quantum dot. -> H_i([e_12_i,e_23_i,e_34_i],[b_12,b_23,b_34]) I assume b's to be constant during the experiment -> H{i,b_12,b_23,b34}([e_12_i,e_23_i,e_34_i]) I allow different amount of timesteps T. for the experiment The Unitary Operator can be estimated by assuming a timewise constant Hamiltonian. So U becomes the Product of all timewise constant Hamiltonians -> U = PRODUCT_{i=1 to T} [exp(-2ipiH_i)] I am looking for an Unitary Operator that acts as an Entangler, such as CPHASE -> CPHASE = sqrt(2)/2 [1+1i 0 0 0; 0 1+1i 0 0 ; 0 0 1+1i 0 ; 0 0 0 -1-1i];

tldr; For a given amount of timesteps T and a given Magnetic Field [b_12,_b23_b34], I am looking for a Tx3 dimensional vector of [e_12, e_23, e_34] that solves:

U = PRODUCT_{i=1 to T} [exp(-2ipiH_{i,[b_12,_b23_b34]}(e_12_i,e_23_i,e_34_i))] = CPHASE = sqrt(2)/2 [1+1i 0 0 0; 0 1+1i 0 0 ; 0 0 1+1i 0 ; 0 0 0 -1-1i];

######## QUICKSTART GUIDE ########

1. Run ./Optimization/s_MAIN_RUN_OPTIMIZATION.m [set magnetic field and allow different amount of timesteps]

2. Load the Solution from ./Results

3. Analyze the Data with ./Analysis/ShowRun.m

4. See the Real and Imaginary part of the CPHASE Matrix in ./Plots