# 3P_line.py¶

## Description¶

This example propagates a 3 particle continuous-time quantum walk on an infinite line

Amongst the features used, it illustrates:
• recieving command line options using PETSc

• the use of the chebyshev algorithm
• setting the EigSolver tolerance, as well as the minimum eigenvalue
• adding a diagonal defects to various nodes

• same-node interactions between particles

• probability vs node plot

• Exporting the final state to a PETSc binary vector file

## Source Code¶

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 #!/usr/bin/env python2.7 # initialize PETSc import sys, petsc4py petsc4py.init(sys.argv) from petsc4py import PETSc import numpy as np # import pyCTQW as qw import pyCTQW.MPI as qw # enable command line arguments -t and -N OptDB = PETSc.Options() N = OptDB.getInt('N', 20) t = OptDB.getReal('t', 2) # get the MPI rank rank = PETSc.Comm.Get_rank(PETSc.COMM_WORLD) if rank == 0: print '3P Line\n' # initialise an N (default 20) node graph CTQW walk = qw.Line3P(N) # Create a Hamiltonian with 2P very strong interaction. walk.createH(interaction=10.) # create the initial state |0,4,4> init_state = [[0,4,4,1.0]] walk.createInitState(init_state) # set the eigensolver properties. walk.EigSolver.setEigSolver(tol=1.e-2) # underestimate the minimum eigenvalue walk.EigSolver.setEigSolver(emin_estimate=0) # Propagate the CTQW using the Chebyshev method for t=2s walk.propagate(t,method='chebyshev') # plot the marginal probabilities # after propagation over all nodes walk.plot('out/3p_line_plot.png') # destroy the quantum walk walk.destroy()