DISCLAMER: this code is still in development and not finished yet. For any problem open an issue or email directly the author. If you want to contribute see the Contributing section below.

This project gathers the code I'm using for my masther thesis on quantum computing.

The goal is to understand and better describe the thermalization process of a quantum annealer, a D-Wave QPU made of superconducting qubits (https://www.dwavesys.com).

All the experiments so far run through Leap cloud service. The code is based on the D-Wave Ocean Software, documentation available here.

The code, presented in Usage, follows the chronological order of writing, to help me keep track of the meeting with my supervisors. A more integral structure of the project will be available at the time of writing of the thesis (mid-August).

Steps to set up your project locally

• Python 3

1. Clone this repo on your computer

   $ git clone https://github.com/federicovisintini/Dwave2000q.git

2. (optional) Create a virtual enviroment

   $ cd Dwave2000q
   $ python3 -m venv myvenv

   and activate it

   $ source myvenv/bin/activate

   N.B. the virtual enviroment should be activated every time

3. Install the requirements

   $ pip install -r requirements.txt

4. (recommended) Set up the D-Wave environment following the official documentation here.

5. Create a Leap account to have access to D-Wave QPUs.

6. Configure Access to D-Wave Solvers connect to your Leap account using the D-Wave’s Solver API (SAPI), documentation available here.

Description of the notebook and scripts in the code/ folder.

Code which uses QPU time is commented so whole scrips / notebooks can be run whithout worrying. Code which takes a long time to execute is decleared in comments / md.

To run the notebooks (*.ipynb) you will need to use jupyter; open the terminal (activate the venv if you created it) and type:

$ jupyter notebook

This first notebook introduces the machine hamiltonian, plotting the annealing functions A(s) and B(s).

We try to evaluate the thermalisazion of a single qubit in two different methods:

1. We let the spin evolve in the idling channel in the final state of the annealling, or said another way we initialise the spin in the first excited state and let it decay (this method fails);

2. Taking inspiration from the official documentation we measure the temperature assuming classical Boltzamnn distribution as final state (good result but using perhabs an oversimplifing assumption)

Finally, we inquire the presence of entanglement for some two-qubit state that could be created in the machine.

In this notebook we focus our effort to find a microscopic model that can describe the spin-enviroment interaction through a Lindblad Master Equation.

A Python script has been introduced to parallelise and speed up computation. We introduce also QuTiP a python module to simulate quantum systems.

We then start focusing on the two-qubit thermalization, performing an experiment and numerically computing the concurrece (entanglement measure) at all points during the annealling.

First thing we convert the result of two-qubit experiment to a more usable form using 2_save_results.py

Then we focus on generalizing the single spin Lindblad Master Equation to a general case of n-qubits interacting, in 2_two_temperature_simulation.py.

Finally, the script 2_two_temperatures_simulation.py plot said results.

This work takes inspiration from:

• Authors: Tameem Albash and Jeffrey Marshall
  Title: “Comparing Relaxation Mechanisms in Quantum and Classical Transverse-Field Annealing”
  In: Phys. Rev. Applied 15 (Jan. 2021), p. 014029
  DOI: 10.1103/PhysRevApplied.15.014029

• Authors: Lorenzo Buffoni and Michele Campisi
  Title: "Thermodynamics of a quantum annealer"
  In: IOP Publishing, Quantum Science and Technology 5 (Jun. 2020), p. 035013
  DOI: 10.1088/2058-9565/ab9755

• Authors: Jeffrey Marshall et al.
  Title: “Power of Pausing: Advancing Understanding of Thermalization in Experimental Quantum Annealers”
  In: Phys. Rev. Applied 11 (Apr. 2019), p. 044083
  DOI: 10.1103/PhysRevApplied.11.044083

• Authors: Tameem Albash et al.
  Title: “Quantum adiabatic Markovian master equations”
  In: New Journal of Physics 14.12 (Dec. 2012), p. 123016
  DOI: 10.1088/1367-2630/14/12/123016

I would like to thank my thesis advisors Vittorio Giovannetti and Michele Campisi for the guidance and motivation through this project.

Pull requests are welcome.

For major changes, please open an issue first to discuss what you would like to change.

Distributed under the GNU GPLv3 by Federico Visintini.

See LICENSE for more information.