QbitControl

A simple framework to simulate and control few-level quantum systems.

Description

This package allows the propagation of pure and mixed quantum states according to Schrödinger and von-Neumann equations, respectively. The embedding system is represented by a time-dependent Hamiltonian and the state by a complex vector or density matrix. The aim is to study (super-)adiabatic control protocols that may allow for efficient state manipulation at the quantum speed limit. It comes with a set of templates implementing common few-level quantum systems:

• Landau-Zener (LZ)
• Carroll-Hioe (CH)
• Sequential Crossings

Installation

pip install git+https://github.com/EmCeeEs/QbitControl.git@master

Example

Let us examine the LZ problem. It regards a time-dependent system, where two states change their characteristics in the course of time. In the case of non-zero interaction the states do not cross (avoided crossing) resulting in a non-zero transition probability. The LZ formula gives this transition probability in the asymptotic limit. We can simulate this behaviour as follows:

from qbitcontrol.templates import LZ

# model parameters
alpha = 1       # sweep velocity
delta = 0.5     # interaction strength

# numeric parameters
tstart = -100
tend = 100
Nsteps = 1000

# init model
qsys = LZ(alpha, delta)
qsys.state = qsys.eigenstates(tstart)[0]   # start in eigenstate

# init simulation
times, states, _ = qsys.propagate(tstart, tend, Nsteps)

# final state is superposition of eigenstates
print(states[-1])

# make transitionless (super-adiabatic)
qsys2 = qsys.make_transitionless()
qsys2.state = qsys.eigenstates(tstart)[0]   # start in original eigenstate

# init simulation
times, states, _ = qsys2.propagate(tstart, tend, Nsteps)

# final state is eigenstate
print(states[-1])

API

The main component is the QuantumSystem object. It's important attributes are:

• N

  • dimensionality of the problem

• H

  • the system's Hamiltonian

• state

  • the current state of the system

• eigenstates(time)

  • compute eigenstates at specified time

• eigenenergies(time)

  • compute eigenenergies at specified time

• makes_transitionless()

  • compute super-adiabatic version of system

• propagate(tstart, tend, Nsteps)

  • propagate system in time; from tstart to tend with Nsteps
  • return times, states and errors

• spectrum()

  • compute energy spectrum