Simulate the decoupled system and Wannerize the eigenstates voltages = {'left_1': -0.0036, 'left_2': -0.0086, 'right_1': -0.0086, 'right_2': -0.0036, 'top_1': -0.0037, 'top_2': -0.0037, 'global_accumul': -7e-05} summed_ham = sum(

Code sharing Read json files and plot them with open("simple_K_L_tuning.json", "r") as read_file: accuracy_time = json.load(read_file) acc = list(map(lambda x: np.mean(np.array(x)[:, 0]), accuracy_time.values())) T = list(map(lambda x: np.mean(np.array(x)[:, 1]), accuracy_time.values())) Accuracy, Time = {}, {} for i in range(1, 21):

Troubles faced in 2D dot array device The middle region is always at lower potential than the dot gate pads or dot gate fingers. Hence there is just a single potential well. Original space: Wannier function still produces independent basis vectors of the original space though that is not relevant for us. As the gate design is fixed and we can't do anything about that, possible scanarios that came to my mind are

Recap of the project about 2D quantum dot arrays Since January 2021, I have been discussing with Florian Unseld (Vandersypen lab) and Marcel Meyer (Veldhorst lab). We have been exchanging a lot of emails on several threads in the past one year. The project is a sub-project of the ~Spin_qubit_design and all the work is commited to the branch find-gate-structures in the same repository. branch - find-gate-structures As the name suggests, I was trying to find the gate patterns of the 2x2 arrays from the design file (.oas). Following is the side view of the heterostructure (also available on gitlab)

Andreev qubits - brainstorming People involved: Kostas, Sathish Basic idea Start with a simplest model and add electrostatics if necessary. What is the open question or bigger picture of the project ? Proof of concept for the experiments

Notes about two dimensional quantum dot arrays Date: 12.1.22 People involved: Sathish, Marcel, Florian and Sander Recap from last discussion: Last meeting was in July 2021. Discussed about incapability of my code to properly deposit the gates in overlapping fashion. Promised to fix it.

Exercise 1 The sum of two normally distributed random variables results in another normal disributed random variable with mean $\mu_1$ + $\mu_2$ and standard deviation $\sigma_1$ + $\sigma_2$. Exercise 2 Answer: y(106) = 12036 Approach Polynomial regression I did polynomial regression to find a polynomial that best fits the given data. Then use the polynomial to extrapolate the given data to find y(106).

Results on 29.10.2021 Changes: Set alpha = 1 in the second step of optimization. Differentiate the results based on the alpha = 1 and alpha < 1. Following that, plot the distribution of effective Hamiltonian and gate coupling strengths. Alpha For reference (same as the previous results)

Meeting on 28.10.2021 Results so far Distribution of alpha To avoid alpha converging outside the boundary (0, 1), I set bounds = (0, 1) in the least squares function. A significant improvement in alpha is established by removing the parameter ftol which was set to 1e^-2 before. ftol is the relative change in tolerance between the iterations. This resulted in higher alpha values but dots are positioned even beneath the plunger and barrier gates. Implemented soft-threshold function for the x and y positions of dots. This restricts dots to be only at legitimate positions as well.

Meeting notes: Results so far Ran 200 disordered samples which took less than an hour to finish with 50 cluster nodes. The speed seems very promising given the new approach to calculate the effective Hamiltonian and taking advantage of linearity of the Hamiltonian. Following is the distribution of alpha values: A fair amount of samples converged with alpha closer to 1. But many of them still didn't converge and few are even outside the range (0 - 1). Not to worry about the alpha values converged outside the range 0-1. Action point 1: Apply soft threshold (borrow from Hugo's project) for the dot positions. It allows bit more flexibility to the positions and allows alpha to converge.

Clean system (four dots) I got a problem in the optimization. Since we remove hoppings at the middle of a barrier gate and split the system into several halves (e.g., two halves for two quantum dots), optimizer considers the state at the edge of a region as a confined state. But it isn't. I tried having a range of chemical potential (0 - 5meV), tunnel couplings (0 - 50microeV) and dot positions. Disorder potential with the voltages same as the clean system (Untuned) Tuned system with disorder for index, x in enumerate(real_y_positions):

Things I did in optimization: As we discussed last week, I obtained the initial condition for optimizing the disorder potential from scipy.linalg.lstsq in the following manner: temp_voltages = voltages.copy() tunable_gates_array = np.hstack(tunable_gates.values()) greens_function_matrix = [] for i in range(len(np.hstack(tunable_gates.values()))):

Performance of two dot device in the presence of disorder This time I optimized the gate voltages. I am currently running calculations for 200 disordered samples in io (serial execution) due to the issue in connecting hpc05 using dask_quantumtinkerer. So far gate voltages of 50 samples are optimized and 33 of them have dots formed at expected position in the 2DEG. I had to set a proper initial condition for the optimizer. Otherwise, it gets trapped at a local minima. How do I find the right initial condition? Four dot design also seems to be following the same: need the right initial condition.

Potential with charges underneath the gates and the quantum dot region (gate voltages not tuned yet) Same potental but with gate voltages tuned to have lowest energy at zero eV and tunnel couplings=20microeV Potential for one random state of charge fluctuations (poisson distributed) no_of_charger_per_unit_cell = (charge_density / thickness_Si_dopant) * 5 * 5 * 5 random_nos = stats.poisson.rvs(mu = no_of_charger_per_unit_cell, size = len(chosen_indices), random_state = 1000) random_nos = random_nos / (5 * 5 * 5)