quimb.tensor.tensor_arbgeom_tebd

Tools for performing TEBD like algorithms on arbitrary lattices.

Classes

LocalHamGen	Representation of a local hamiltonian defined on a general graph. This
TEBDGen	Generic class for performing time evolving block decimation on an
SimpleUpdateGen	Simple update for arbitrary geometry hamiltonians.

Functions

edge_coloring(edges[, strategy, interchange, group])

Generate an edge coloring for the graph given by edges, using

Module Contents

quimb.tensor.tensor_arbgeom_tebd.edge_coloring(edges, strategy='smallest_last', interchange=True, group=True)

Generate an edge coloring for the graph given by edges, using networkx.coloring.greedy_color.

Parameters:

• edges (sequence[tuple[hashable, hashable]]) – The edges of the graph.

• strategy (str or callable, optional) –

  The strategy to use for coloring the edges. Can be:

  • ’largest_first’

  • ’smallest_last’

  • ’random_sequential’

  …

• interchange (bool, optional) – Whether to use the interchange heuristic. Usually generates better colorings but can be slower.

• group (bool, optional) – Whether to group the edges by color or return a flat list.

class quimb.tensor.tensor_arbgeom_tebd.LocalHamGen(H2, H1=None)

Representation of a local hamiltonian defined on a general graph. This combines all two site and one site terms into a single interaction per lattice pair, and caches operations on the terms such as getting their exponential. The sites (nodes) should be hashable and comparable.

Parameters:

• H2 (dict[tuple[node], array_like]) – The interaction terms, with each key being an tuple of nodes defining an edge and each value the local hamilotonian term for those two nodes.

• H1 (array_like or dict[node, array_like], optional) – The one site term(s). If a single array is given, assume to be the default onsite term for all terms. If a dict is supplied, the keys should represent specific coordinates like (i, j) with the values the array representing the local term for that site. A default term for all remaining sites can still be supplied with the key None.

terms

The total effective local term for each interaction (with single site terms appropriately absorbed). Each key is a pair of coordinates site_a, site_b with site_a < site_b.

Type:

dict[tuple, array_like]

_op_cache

terms

sites

_sites_to_covering_terms

property nsites

The number of sites in the system.

items()

Iterate over all terms in the hamiltonian. This is mostly for convenient compatibility with compute_local_expectation.

_convert_from_qarray_cached(x)

_flip_cached(x)

_add_cached(x, y)

_div_cached(x, y)

_op_id_cached(x)

_id_op_cached(x)

_expm_cached(G, x)

get_gate(where)

Get the local term for pair where, cached.

get_gate_expm(where, x)

Get the local term for pair where, matrix exponentiated by x, and cached.

apply_to_arrays(fn)

Apply the function fn to all the arrays representing terms.

get_auto_ordering(order='sort', **kwargs)

Get an ordering of the terms to use with TEBD, for example. The default is to sort the coordinates then greedily group them into commuting sets.

Parameters:

order ({'sort', None, 'random', str}) –

How to order the terms before greedily grouping them into commuting (non-coordinate overlapping) sets:

• 'sort' will sort the coordinate pairs first.

• None will use the current order of terms which should match the order they were supplied to this LocalHam2D instance.

• 'random' will randomly shuffle the coordinate pairs before grouping them - not the same as returning a completely random order.

• 'random-ungrouped' will randomly shuffle the coordinate pairs but not group them at all with respect to commutation.

Any other option will be passed as a strategy to networkx.coloring.greedy_color() to generate the ordering.

Returns:

Sequence of coordinate pairs.

Return type:

list[tuple[node]]

__repr__()

draw(ordering='sort', show_norm=True, figsize=None, fontsize=8, legend=True, ax=None, **kwargs)

Plot this Hamiltonian as a network.

Parameters:

• ordering ({'sort', None, 'random'}, optional) – An ordering of the termns, or an argument to be supplied to quimb.tensor.tensor_arbgeom_tebd.LocalHamGen.get_auto_ordering() to generate this automatically.

• show_norm (bool, optional) – Show the norm of each term as edge labels.

• figsize (None or tuple[int], optional) – Size of the figure, defaults to size of Hamiltonian.

• fontsize (int, optional) – Font size for norm labels.

• legend (bool, optional) – Whether to show the legend of which terms are in which group.

• ax (None or matplotlib.Axes, optional) – Add to a existing set of axes.

graph

class quimb.tensor.tensor_arbgeom_tebd.TEBDGen(psi0, ham, tau=0.01, D=None, cutoff=1e-10, imag=True, gate_opts=None, ordering=None, second_order_reflect=False, compute_energy_every=None, compute_energy_final=True, compute_energy_opts=None, compute_energy_fn=None, compute_energy_per_site=False, tol=None, callback=None, keep_best=False, progbar=True)

Generic class for performing time evolving block decimation on an arbitrary graph, i.e. applying the exponential of a Hamiltonian using a product formula that involves applying local exponentiated gates only.

imag = True

property state

Return a copy of the current state.

ham

progbar = True

callback = None

tau = 0.01

last_tau = 0.0

gate_opts

compute_energy_opts

compute_energy_every = None

compute_energy_final = True

compute_energy_fn = None

compute_energy_per_site = False

tol = None

second_order_reflect = False

_n = 0

its = []

taus = []

energies = []

energy_diffs = []

egrdm

keep_best = False

best

stop = False

sweep(tau)

Perform a full sweep of gates at every pair.

\[\psi \rightarrow \prod_{\{ij\}} \exp(-\tau H_{ij}) \psi\]

_set_progbar_description(pbar)

evolve(steps, tau=None, progbar=None)

Evolve the state with the local Hamiltonian for steps steps with time step tau.

property n

The number of sweeps performed.

property D

The maximum bond dimension.

_check_energy()

Logic for maybe computing the energy if needed.

property energy

Return the energy of current state, computing it only if necessary.

get_state()

The default method for retrieving the current state - simply a copy. Subclasses can override this to perform additional transformations.

set_state(psi)

The default method for setting the current state - simply a copy. Subclasses can override this to perform additional transformations.

presweep(i)

Perform any computations required before the sweep (and energy computation). For the basic TEBD update is nothing.

postlayer()

Perform any computations required after each layer of commuting gates. For the basic update this is nothing.

postsweep(i)

Perform any computations required after the sweep (but before the energy computation). For the basic update this is nothing.

gate(U, where)

Perform single gate U at coordinate pair where. This is the the most common method to override.

compute_energy()

Compute and return the energy of the current state. Subclasses can override this with a custom method to compute the energy.

plot(zoom='auto', xscale='symlog', xscale_linthresh=20, color_energy=(0.0, 0.5, 1.0), color_gauge_diff=(1.0, 0.5, 0.0), hlines=(), figsize=(8, 4))

Plot an overview of the evolution of the energy and gauge diffs.

Parameters:

• zoom (int or 'auto', optional) – The number of iterations to zoom in on, or ‘auto’ to automatically choose a reasonable zoom level.

• xscale ({'linear', 'log', 'symlog'}, optional) – The x-axis scale, for the upper plot of the entire evolution.

• xscale_linthresh (float, optional) – The linear threshold for the upper symlog scale.

• color_energy (str or tuple, optional) – The color to use for the energy plot.

• color_gauge_diff (str or tuple, optional) – The color to use for the gauge diff plot.

• hlines (dict, optional) – Add horizontal lines to the plot, with keys as labels and values as the y-values.

• figsize (tuple, optional) – The size of the figure.

Returns:

fig, axs

Return type:

matplotlib.Figure, tuple[matplotlib.Axes]

__repr__()

class quimb.tensor.tensor_arbgeom_tebd.SimpleUpdateGen(psi0, ham, tau=0.01, D=None, cutoff=1e-10, imag=True, gate_opts=None, ordering=None, second_order_reflect=False, compute_energy_every=None, compute_energy_final=True, compute_energy_opts=None, compute_energy_fn=None, compute_energy_per_site=False, tol=None, equilibrate_every=0, equilibrate_start=True, equilibrate_opts=None, callback=None, keep_best=False, progbar=True)

Bases: TEBDGen

Simple update for arbitrary geometry hamiltonians.

Parameters:

• psi0 (TensorNetworkGenVector) – The initial state.

• ham (LocalHamGen) – The local hamiltonian.

• tau (float, optional) – The default time step to use.

• D (int, optional) – The maximum bond dimension, by default the current maximum bond of psi0.

• cutoff (float, optional) – The singular value cutoff to use when applying gates.

• imag (bool, optional) – Whether to evolve in imaginary time (default) or real time.

• gate_opts (dict, optional) – Other options to supply to the gate application method, quimb.tensor.tensor_arbgeom.TensorNetworkGenVector.gate_simple_().

• ordering (None, str or callable, optional) – The ordering of the terms to apply, by default this will be determined automatically.

• second_order_reflect (bool, optional) – Whether to use a second order Trotter decomposition by reflecting the ordering.

• compute_energy_every (int, optional) – Compute the energy every this many steps.

• compute_energy_final (bool, optional) – Whether to compute the energy at the end.

• compute_energy_opts (dict, optional) – Options to supply to the energy computation method, quimb.tensor.tensor_arbgeom.TensorNetworkGenVector.compute_local_expectation_cluster().

• compute_energy_fn (callable, optional) – A custom function to compute the energy, with signature fn(su), where su is this instance.

• compute_energy_per_site (bool, optional) – Whether to compute the energy per site.

• tol (float, optional) – If not None, stop when either energy difference falls below this value, or maximum singluar value changes fall below this value.

• equilibrate_every (int, optional) – Equilibrate the gauges every this many steps.

• equilibrate_start (bool, optional) – Whether to equilibrate the gauges at the start, regardless of equilibrate_every.

• equilibrate_opts (dict, optional) – Default options to supply to the gauge equilibration method, see quimb.tensor.tensor_core.TensorNetwork.gauge_all_simple(). By default max_iterations is set to 100 and tol to 1e-3.

• callback (callable, optional) – A function to call after each step, with signature fn(su).

• keep_best (bool, optional) – Whether to keep track of the best state and energy.

• progbar (bool, optional) – Whether to show a progress bar during evolution.

equilibrate_every = 0

equilibrate_start = True

equilibrate_opts

gauges_prev = None

gauge_diffs = []

gate(G, where)

Application of a single gate G at where.

equilibrate(**kwargs)

Equilibrate the gauges with the current state (like evolving with tau=0).

postlayer()

Performed after each layer of commuting gates.

postsweep(i)

Performed after every full sweep.

normalize()

Normalize the state and simple gauges.

compute_energy()

Default estimate of the energy.

get_state(absorb_gauges=True)

Return the current state, possibly absorbing the gauges.

Parameters:

absorb_gauges (bool or "return", optional) – Whether to absorb the gauges into the state or not. If True, a standard PEPS is returned with the gauges absorbed. If False`, the gauges are added to the tensor network but uncontracted. If “return”, the gauges are returned separately.

Returns:

• psi (TensorNetwork) – The current state.

• gauges (dict) – The current gauges, if absorb_gauges == "return".

set_state(psi, gauges=None)

Set the current state and possibly the gauges.