QuantumWalkP3¶

Method Summary¶

Method Details¶

QuantumWalkP3.destroy()[source]¶

Destroys the 3 particle quantum walk object, and all associated PETSc matrices/vectors.

QuantumWalkP3.exportState(filename, filetype)[source]¶

Exports the final state psi of the quantum walk to a file.

Parameters:	filename (str) – path to desired output file. filetype (str) – the filetype of the exported adjacency matrix. 'txt' - an \(N^3\) element column vector in text format. 'bin' - an \(N^3\) element PETSc binary vector.

QuantumWalkP3.importInitState(filename, filetype)[source]¶

Imports the initial state of the quantum walk from a file.

Parameters:	filename (str) – path to the file containing the input state. filetype (str) – the filetype of the imported adjacency matrix. 'txt' - TODO: not yet implemented! Please use 'bin' for now. 'bin' - an \(N^3\) element PETSc binary vector.
Returns:	: this creates a PETSc vector containing the initial statespace, accessed via self.psi0.
Return type:	petsc4py.PETSc.Vec()

Warning

The number of elements in the imported input statespace must equal \(N^3\) where \(N\) is the number of nodes the 3P CTQW object is initialized with.

QuantumWalkP3.marginal(vec)[source]¶

QuantumWalkP3.plotEntanglement(filename)[source]¶

Creates a plot of the entanglement over time.

Parameters:	filename (str) – the absolute/relative path to the desired output file.

Important

watch() must be called prior to propagation in order for the entanglement to be stored during propagation.

Note

• ensure a file extension is present so that filetype is correctly set (choose one of png, pdf, ps, eps or svg).
• Timesteps are recorded when propagations occur - to increase the number of timesteps, increase the number of propagations prior to plotting.

QuantumWalkP3.plotNode(filename, node, t=None)[source]¶

Creates a plot of the marginal probablities on a specified node over time.

Parameters:	filename (str) – the absolute/relative path to the desired output file. node (int) – the node to plot.

Important

watch() must be called prior to propagation in order for the probabilities at the specified nodes to be stored.

Note

• ensure a file extension is present so that filetype is correctly set (choose one of png, pdf, ps, eps or svg).
• Timesteps are recorded when propagations occur - to increase the number of timesteps, increase the number of propagations.
• See plotNodes() to plot multiple nodes.

QuantumWalkP3.plotNodes(filename, p=1, t=None)[source]¶

Creates a plot of the node probablities over time.

Parameters:	filename (str) – the absolute/relative path to the desired output file. p (int) – (1|2|3) - choose whether to plot the marginal probability of particle 1, 2 or 3.

Important

watch() must be called prior to propagation in order for the probabilities at the specified nodes to be stored.

Note

• if multiple nodes are watched, they will all be plotted.
• if you wish to plot marginal probabilities for all particles, see plotNode().
• ensure a file extension is present so that filetype is correctly set (choose one of png, pdf, ps, eps or svg).
• Timesteps are recorded when propagations occur - to increase the number of timesteps, increase the number of propagations.

QuantumWalkP3.propagate(t, method='expm', **kwargs)[source]¶

Propagates the quantum walk for time t.

Parameters:	t (float) – the timestep over which to propagate the state walk.psi0 via the relationship \(\left|\psi\right\rangle = e^{-iHt}\left|\psi0\right\rangle\). method (str) – the propagation algorithm to use ('chebyshev' (default) or 'krylov').
Keyword Arguments:
	esolver (str) – the eigensolver algorithm to use. 'krylovschur' (default) - Krylov-Schur 'arnoldi' - Arnoldi Method 'lanczos' - Lanczos Method 'power' - Power Iteration/Rayleigh Quotient Iteration 'gd' - Generalized Davidson 'jd' - Jacobi-Davidson, 'lapack' - Uses LAPACK eigenvalue solver routines 'arpack' - only available if SLEPc is compiled with ARPACK linking workType (str) – can be used to set the eigensolver worktype (either 'ncv' or 'mpd'). The default is to let SLEPc decide. workSize (int) – sets the work size if workType is set. tolIn (float) – tolerance of the eigenvalue solver (default 0. (SLEPc decides)). maxIt (int) – maximum number of iterations of the eigenvalue solver (default 0 (SLEPc decides)). verbose (bool) – if True, writes eigensolver information to the console emax_estimate (float) – used to override the calculation of the graphs maximum eigenvalue. emin_estimate (float) – used to override the calculation of the graphs minimum eigenvalue. For a finite graph, emin_estimate=0 is set by default. Caution If supplied, the value of emax_estimate (\(\hat{\lambda}_{\max}\)) must satisfy \(\hat{\lambda}_{\max}\geq\lambda_{\max}\), where \(\lambda_{\max}\) is the actual maximum eigenvalue of the graph. Similarly, the value of emin_estimate (\(\hat{\lambda}_{\min}\)) must satisfy \(\hat{\lambda}_{\min}\leq\lambda_{\min}\), where \(\lambda_{\min}\) is the actual minimum eigenvalue of the graph. The greater the difference value of \(|\hat{\lambda}_{\max} -\lambda_{\max}|\) and \(|\hat{\lambda}_{\min} -\lambda_{\min}|\), the longer the convergence time of the chebyshev propagator. Note The keyword arguments properties only apply if propagator='chebyshev' For more information regarding these properties,refer to the SLEPc documentation
Returns:	: this creates a PETSc vector containing the propagated state, accessed via the attribute psi, as well as a PETSc vector containing the marginal probabilities, prob.
Return type:	petsc4py.PETSc.Vec()

Note

The EigSolver properties only take effect if method=’chebyshev’.

Fortran interface

This function calls the Fortran function expm(). for the Krylov method, and the function qw_cheby() for the Chebyshev method.

QuantumWalkP3.psiToInit()[source]¶

Copies the state psi to psi0.

Example

This can be used to iterate the propagation over discrete timesteps:

for i in range(10):
        walk.propagate(0.01,method='chebyshev')
        walk.psiToInit()

QuantumWalkP3.watch(nodes, watchtype='prob', **kwargs)[source]¶

Creates a handle that watches either marginal probability or walker entanglement during propagation.

Parameters:	nodes (array of ints) – the nodes to watch marginal probability (e.g. [0,1,4]). watchtype (str) – (‘prob’ , ‘entanglement’). the type of watch handle to produce.
Keyword Arguments:
	: If ``watchtype=’entanglement’``, EigSolver keywords can also be passed; – for more details of the available EigSolver properties, see propagate().
Returns:	: * if watchtype='prob', creates a handle that can be accessed to retrieve marginal node probabilities for various \(t\) * if watchtype='entanglment', creates a handle that can be accessed to retrieve entanglement values for various \(t\)
Return type:	if watchtype='prob': pyCTQW.MPI.ctqw.nodeHandle() if watchtype='entanglement': pyCTQW.MPI.ctqw.entanglementHandle()

Examples

To watch the entanglement,

>>> walk.watch(None,watchtype='entanglement')
>>> walk.propagate(5.,method='chebyshev')
>>> timeArray, entArray = walk.entanglementHandle.getEntanglement()

Note

• The entanglement measure used in Von Neumann entropy, calculated via \(S=-\sum_{i}\lambda_i\log_{2}\lambda_i\), where \(\lambda_i\) are the eigenvalues of the reduced density matrix \(\rho_2 = \text{Tr}_1(|\psi(t)\rangle\langle\psi(t)|)\)
• Nodes do not need to be specified, as entanglement is a global measurement.
• As it is a global measurement, there is a large amount of node communication which may increase overall program run time.

To watch the probabilities,

>>> walk.watch([0,1,4])
>>> walk.propagate(2.,method='chebyshev')
>>> timeArray, probXArray, probYArray, probZArray = walk.handle.getLocalNodes(p=2)

Warning

Note that walk.handle attributes are not collective; if running on multiple nodes, only local values will be returned.