QuantumWalkP1¶

Method Summary¶

Method Details¶

QuantumWalkP1.destroy()[source]¶

Destroys the 1 particle quantum walk object, and all associated PETSc matrices/vectors.

QuantumWalkP1.exportState(filename, filetype)[source]¶

Exports the final state 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 \(N\) element column vector in text format. 'bin' - an \(N\) element PETSc binary vector.

QuantumWalkP1.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' - an \(N\) element column vector in text format. 'bin' - an \(N\) element PETSc binary vector.
Returns:	: this creates a PETSc vector containing the initial state, accessed via Graph.psi0.
Return type:	petsc4py.PETSc.Vec()

Warning

The number of elements in the imported input state vector must match the number of nodes the 1P CTQW object is initialized with.

QuantumWalkP1.marginal(vec)[source]¶

QuantumWalkP1.plotNodes(filename, t=None)[source]¶

Creates a plot of the node probablities 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 probabilities at the specified nodes to be stored.

Note

• if multiple nodes are watched, they will all be plotted.
• 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.

QuantumWalkP1.propagate(t, method='chebyshev', **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.

QuantumWalkP1.psiToInit()[source]¶

Copies the state self.psi to self.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()

QuantumWalkP1.watch(nodes)[source]¶

Creates a handle that watches node probability during propagation.

Parameters:	nodes (array of ints) – the nodes to watch (e.g. [0,1,4]).
Returns:	: creates a handle that can be accessed to retrieve node probabilities for various \(t\)
Return type:	pyCTQW.MPI.ctqw.nodeHandle()

Example

>>> walk.watch([0,1,2,3,4])
>>> walk.propagate(5.,method='chebyshev')
>>> timeArray, probArray = walk.handle.getLocalNodes()

Warning

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