pyCTQW Manual¶

#!/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', 100)
t = OptDB.getReal('t', 20)

# get the MPI rank
rank =  PETSc.Comm.Get_rank(PETSc.COMM_WORLD)

if rank == 0:
	print '1P Line\n'

# initialise an N (default 100) node graph CTQW
walk = qw.Line(N)

# Create a Hamiltonian with defect and amplitude as below.
d = [3,4]
amp = [2.0,1.5]
walk.createH(d,amp)

# create the initial state (1/sqrt(2)) (|0>+|1>)
init_state = [[0.,1.0/np.sqrt(2.0)], [1.,1.0/np.sqrt(2.0)]]
walk.createInitState(init_state)

# set the eigensolver properties.
walk.EigSolver.setEigSolver(tol=1.e-3)

# create a handle to watch the probability at nodes -5,0,1:
walk.watch([0,1,-5])

# Propagate the CTQW using the Chebyshev method
# for t=100s in timesteps of dt=0.01
# Note that psiToInit() is being used rather than global timesteps.
for i in range(int(t/0.01)):
	walk.propagate(0.01,method='chebyshev')
	walk.psiToInit()

# plot the marginal probabilities
# after propagation over all nodes
walk.plot('out/1p_line_plot.png')

# plot the probability over time for the watched nodes
walk.plotNodes('out/1p_line_nodes.png')

# export final state
walk.exportState("out/1p_final_state.txt", "txt")

# destroy the quantum walk
walk.destroy()

#!/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', 100)
t = OptDB.getReal('t', 20)

# get the MPI rank
rank =  PETSc.Comm.Get_rank(PETSc.COMM_WORLD)

if rank == 0:
	print '2P Line\n'

# initialise an N (default 100) node graph CTQW
walk = qw.Line2P(N)

# Create a Hamiltonian with 2P interaction.
walk.createH(interaction=1.)

# create the initial state (1/sqrt(2)) (|0,0>-|1,1>)
init_state = [[0,0,1.0/np.sqrt(2.0)], [1,1,-1.0/np.sqrt(2.0)]]
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)

# create a handle to watch the probability at nodes -5,0,1:
walk.watch([0,1,-5])
# create a handler to watch the entanglement
walk.watch(None,watchtype='entanglement',verbose=False)

# Propagate the CTQW using the Chebyshev method
# for t=100s in timesteps of dt=0.1
for i in np.arange(0.1,t+0.1,0.1):
	walk.propagate(i,method='chebyshev')

# plot the marginal probabilities
# after propagation over all nodes
walk.plot('out/2p_line_plot.png')

# plot the probability over time for the watched nodes
walk.plotNodes('out/2p_line_nodes.png')

# plot the entanglement over time
walk.plotEntanglement('out/2p_line_ent.png')

# export the final state
walk.exportState('out/2p_line_state.bin','bin')

# destroy the quantum walk
walk.destroy()

#!/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()

#!/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', 10)
t = OptDB.getReal('t', 20)

# get the MPI rank
rank =  PETSc.Comm.Get_rank(PETSc.COMM_WORLD)

if rank == 0:
	print '1P 3-cayley Tree CTQW\n'

# initialise a 10 node graph CTQW
walk = qw.Graph(N)

# Create a Hamiltonian from a file.
# A defect of amplitude 3 has been added to node 0
walk.createH('../graphs/cayley/3-cayley.txt','txt',d=[0],amp=[3.])

# create the initial state (1/sqrt(2)) (|0>+i|1>)
init_state = [[0,1.0/np.sqrt(2.0)], [1,1.0j/np.sqrt(2.0)]]
walk.createInitState(init_state)

# set the eigensolver properties. Note that
# Emin is exact, whereas and Emax has been over-estimated.
walk.EigSolver.setEigSolver(tol=1.e-2,verbose=False,emin_estimate=0.,emax_estimate=10.)

# create a handle to watch the probability at nodes 0-4:
walk.watch([0,1,2,3,4])

# Propagate the CTQW using the Chebyshev method
# for t=20s in timesteps of dt=0.01
for dt in np.arange(0.01,t+0.01,0.01):
	walk.propagate(dt,method='chebyshev')

# plot the marginal probabilities
# after propagation over all nodes
walk.plot('out/1p_3cayley_plot.png')

# plot a 3D graph representation with bars
# representing the marginal probabilities
walk.plotGraph(output='out/1p_3cayley_graph.png')

# plot the probability over time for the watched nodes
walk.plotNodes('out/1p_3cayley_nodes.png')

# destroy the quantum walk
walk.destroy()

#!/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', 10)
t = OptDB.getReal('t', 5)

# get the MPI rank
rank =  PETSc.Comm.Get_rank(PETSc.COMM_WORLD)

if rank == 0:
	print '2P 3-cayley Tree CTQW\n'

# initialise a 10 node graph CTQW
walk = qw.Graph2P(N)

# Create a 2 particle interacting Hamiltonian from a file.
# A defect of amplitude 2 and 0.5 has
# been added to nodes 3 and 4 respectively.
d = [3,4]
amp = [2.0,1.5]
walk.createH('../graphs/cayley/3-cayley.txt','txt',d=d,amp=amp,layout='spring',interaction=0.5)

# create the initial state (1/sqrt(2)) (|0,1>+i|1,1>)
init_state = [[0,1,1.0/np.sqrt(2.0)], [1,1,1.0j/np.sqrt(2.0)]]
walk.createInitState(init_state)

# set the eigensolver properties.
#Note that Emin has been set exactly.
walk.EigSolver.setEigSolver(tol=1.e-2,verbose=False,emin_estimate=0.)

# create a handle to watch the probability at nodes 0-4,9:
walk.watch([0,1,2,3,4,9])
# create a handle to watch the entanglement
walk.watch(None,watchtype='entanglement',verbose=False,esolver='lapack',max_it=100)

# Propagate the CTQW using the Chebyshev method
# for t=5s in timesteps of dt=0.01
for dt in np.arange(0.01,t+0.01,0.01):
	walk.propagate(dt,method='chebyshev')

# plot the p1 and p2 marginal probabilities
# after propagation over all nodes
walk.plot('out/2p_3cayley_plot.png')

# plot a 3D graph representation with bars
# representing the p1 and p2 marginal probabilities
walk.plotGraph(output='out/2p_3cayley_graph.png')

# plot the p1 and p2 probability over time for watched node1
walk.plotNode('out/2p_3cayley_node1.png',1)
# plot the particle 1 probability over all watched nodes
walk.plotNodes('out/2p_3cayley_nodes_particle1.png',p=1)
# plot the particle 2 probability over all watched nodes
walk.plotNodes('out/2p_3cayley_nodes_particle2.png',p=2)

# plot the entanglement vs. time
walk.plotEntanglement('out/2p_3cayley_ent.png')

# export the partial trace
walk.exportPartialTrace('out/3-cayley-2p-rhoX.txt','txt',p=1)

# destroy the quantum walk
walk.destroy()

#!/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', 10)
t = OptDB.getReal('t', 5)

# get the MPI rank
rank =  PETSc.Comm.Get_rank(PETSc.COMM_WORLD)

if rank == 0:
	print '3P 3-cayley Tree CTQW\n'

# initialise a 10 node graph CTQW
walk = qw.Graph3P(N)

# Create a 3 particle interacting Hamiltonian from a file.
# A defect of amplitude 2 and 0.5 has
# been added to nodes 3 and 4 respectively.
d = [3,4]
amp = [2.0,1.5]
walk.createH('../graphs/cayley/3-cayley.txt','txt',d=d,amp=amp,layout='spring',interaction=1.5)

# create the initial state (1/sqrt(2)) (|0,1,4>+i|1,1,4>)
init_state = [[0,1,4,1.0/np.sqrt(2.0)], [1,1,4,1.j/np.sqrt(2.0)]]
walk.createInitState(init_state)

# set the eigensolver properties.
#Note that Emin has been set exactly.
walk.EigSolver.setEigSolver(tol=1.e-2,verbose=False,emin_estimate=0.)

# create a handle to watch the probability at nodes 0-4,9:
walk.watch([0,1,2,3,4,9])

# Propagate the CTQW using the Chebyshev method
# for t=5s in timesteps of dt=0.01
for dt in np.arange(0.01,t+0.01,0.01):
	walk.propagate(dt,method='chebyshev')

# plot the p1, p2, p3 marginal probabilities
# after propagation over all nodes
walk.plot('out/3p_3cayley_plot.png')

# plot the p1, p2, p3 probability over time for watched node1
walk.plotNode('out/3p_3cayley_node1.png',1)
# plot the particle 1 probability over all watched nodes
walk.plotNodes('out/3p_3cayley_nodes_particle1.png',p=1)
# plot the particle 2 probability over all watched nodes
walk.plotNodes('out/2p_3cayley_nodes_particle2.png',p=2)
# plot the particle 3 probability over all watched nodes
walk.plotNodes('out/3p_3cayley_nodes_particle3.png',p=3)

# destroy the quantum walk
walk.destroy()

#!/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

# get the MPI rank
rank =  PETSc.Comm.Get_rank(PETSc.COMM_WORLD)

if rank == 0:
	print '1P Strong Regular\n'

# initialise a 25 node graph CTQW, 
# and create a Hamiltonian from a file.
walk = qw.Graph(25)
walk.createH('../graphs/strong-regular-25-12-5-6/1.txt','txt',layout='circle')

# create the initial state |0,1>
init_state = [[0,1]]
walk.createInitState(init_state)

# Propagate the CTQW using Krylov subspace methods for t=100s
walk.propagate(100,method='krylov')

# plot the marginal probabilities
# after propagation over all nodes
walk.plot('out/1p_sr_plot.png')

# plot a 3D graph representation with bars
# representing the marginal probabilities
walk.plotGraph(output='out/1p_sr_graph.png')

# destroy the quantum walk
walk.destroy()

#!/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

# get the MPI rank
rank =  PETSc.Comm.Get_rank(PETSc.COMM_WORLD)

if rank == 0:
	print '2P Strong Regular CTQW'

# initialise a 25 node 2P graph CTQW, 
# and create a Hamiltonian from a file.
walk = qw.Graph2P(25)
walk.createH('../graphs/strong-regular-25-12-5-6/1.txt','txt',layout='circle')

# create the initial state (1/sqrt(2)) (|0,1>+i|1,1>)
init_state = [[0,1,1.0/np.sqrt(2.0)], [1,1,1.0j/np.sqrt(2.0)]]
walk.createInitState(init_state)

# Propagate the CTQW using Krylov subspace methods
walk.propagate(100,method='krylov')

# plot the p1 and p2 marginal probabilities
# after propagation over all nodes
walk.plot('out/2p_sr_plot.png')

# plot a 3D graph representation with bars
# representing p1 and p2 marginal probabilities
walk.plotGraph(output='out/2p_sr_graph.png')

# destroy the quantum walk
walk.destroy()

#!/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

# get the MPI rank
rank =  PETSc.Comm.Get_rank(PETSc.COMM_WORLD)

# create a graph isomorphism object
gi = qw.GraphISO()

# create a comparison table of two 3-cayley permutations
# present in the '../graphs/cayley/3-cayley-permutations'
# folder. As they are permutations, they are isomorphic,
# so the result should be a 2x2 matrix composed of 1.
comparisonTable = gi.AllIsomorphicQ('../graphs/cayley/3-cayley-permutations',info=False)

if rank==0:
	print '1) Testing isomorphism of all pairings:'
	print comparisonTable


# create a comparison table of a 3-cayley graph, and a
# a 3-cayley graph with an additional edge added.
# These are *not* isomorphic,
# so the result should be a 2x2 matrix identity matrix.
comparisonTable = gi.AllIsomorphicQ('../graphs/cayley/3-cayley-variant',info=False)

if rank==0:
	print '\n2) Testing isomorphism of all pairings:'
	print comparisonTable

#!/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

# get the MPI rank
rank =  PETSc.Comm.Get_rank(PETSc.COMM_WORLD)

# create a graph isomorphism object
gi = qw.GraphISO()

#=========================
#  Two Isomorphic Graphs
#=========================
# import two adjacency matrices; these are permutations
# of the first graph in the SR-25-12-5-6, and thus are isomorphic
adj1 = np.genfromtxt('../graphs/strong-regular-25-12-5-6/1-permutations/SR1_perm_1.txt')
adj2 = np.genfromtxt('../graphs/strong-regular-25-12-5-6/1-permutations/SR1_perm_3.txt')

# generate certificates for these two graphs
cert1 = gi.GIcert(adj1)
cert2 = gi.GIcert(adj2)

# print the certificates side by side;
# they should be identical
if rank == 0:
	print 'The GI certificates of two permutations of SR(25,12,5,6) graph 1:'
	for i in range(len(cert1)):
		print cert1[i], cert2[i]

if rank == 0:
	print '\nTesting isomorphism of the two permutations of SR(25,12,5,6) graph 1:'
# verify using the inbuilt checking method
checkISO = gi.isomorphicQ(adj1,adj2)
if rank == 0: print checkISO

#=========================
#Two Non-Isomorphic Graphs
#=========================
if rank == 0:
	print '\nTesting isomorphism of graphs 1 and 11 of the SR(25,12,5,6) family:'

adj1 = np.genfromtxt('../graphs/strong-regular-25-12-5-6/1.txt')
adj2 = np.genfromtxt('../graphs/strong-regular-25-12-5-6/11.txt')

checkISO = gi.isomorphicQ(adj1,adj2)
if rank == 0: print checkISO