Time-dependent master equations and quantum trajectories

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Table of contents

1. Motivation
2. Code description
3. Tutorial
   • UCL 4 qubit gadgets
   • Single qubit
4. Reference

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Motivation

Simulation codes of time-dependent master equation and quantum trajectories.

Code description

These are the codes of adiabatic master equation (ame.m) and quantum trajectories (aqt.m) used in this paper [1].

The Hamiltonian is a 8-qubit ferromagnetic Ising spin chain in a transverse field, with annealing schedule attached as DW1_parameters.txt. This relatively complex problem illustrates a lot of subtle points in the implementation of ame and aqt, and can be easily reduced to smaller and simpler problems.

The master equation is:

Both ame.m and aqt.m use sparse matrix for computation,

and perform basis rotation for every ode step.

aqt.m uses parallel computation, with sorting of jump operators,

and backtracking for error control.

Tutorial: UCL's 4-qubit gadgets and a single qubit

UCL's 4-qubit gadgets

The folder tutorial_4_qubit_gadget contains a tutorial on how to run the codes of a time-dependent case of the 4-qubit gadgets below.

Single qubit

A onequbit_demo instruction folder was made for how to run codes on various time-dependent single-qubit Hamiltonian simulation. The pdf file kawacode.pdf contains a presentation on excecutions.

Reference

[1] Yip, K.W., Albash, T. and Lidar, D.A., 2018. Quantum trajectories for time-dependent adiabatic master equations. Physical Review A, 97(2), p.022116.