TN: add build_mpo_propagator_trotterized

jcmgray · Jan 25, 2024 · 777fa75 · 777fa75
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diff --git a/docs/changelog.md b/docs/changelog.md
@@ -7,8 +7,18 @@ Release notes for `quimb`.
 
 **Enhancements:**
 
-- add [TensorNetwork.visualize_tensors](quimb.tensor.drawing.visualize_tensors)
+- add [`TensorNetwork.visualize_tensors`](quimb.tensor.drawing.visualize_tensors)
   for visualizing the actual data entries of an entire tensor network.
+- add [`ham.build_mpo_propagator_trotterized`](quimb.tensor.tensor_1d_tebd.LocalHam1D.build_mpo_propagator_trotterized)
+  for building a trotterized propagator from a local 1D hamiltonian. This
+  also includes updates for creating 'empty' tensor networks using
+  [`TensorNetwork.new`](quimb.tensor.tensor_core.TensorNetwork.new), and
+  building up gates from empty tensor networks using
+  [`TensorNetwork.gate_inds_with_tn`](quimb.tensor.tensor_core.TensorNetwork.gate_inds_with_tn).
+- add more options to [`Tensor.expand_ind`](quimb.tensor.tensor_core.Tensor.expand_ind)
+  and [`Tensor.new_ind`](quimb.tensor.tensor_core.Tensor.new_ind): repeat
+  tiling mode and random padding mode.
+- tensor decomposition: make ``eigh_truncated`` backend agnostic.
 
 **Bug fixes:**
 
@@ -20,7 +30,7 @@ Release notes for `quimb`.
 
 
 (whats-new-1-7-0)=
-## v1.7.0 (12-08-2023)
+## v1.7.0 (2023-12-08)
 
 **Breaking Changes**
 
@@ -178,15 +188,15 @@ Release notes for `quimb`.
   triangular R factors.
 
 (whats-new-1-4-2)=
-## v1.4.2 (28th November 2022)
+## v1.4.2 (2022-11-28)
 
 **Enhancements**
 
 - move from versioneer to to
   [setuptools_scm](https://pypi.org/project/setuptools-scm/) for versioning
 
 (whats-new-1-4-1)=
-## v1.4.1 (28th November 2022)
+## v1.4.1 (2022-11-28)
 
 **Enhancements**
 
@@ -219,7 +229,7 @@ Release notes for `quimb`.
 > - allow unpickling of `PTensor` objects ({issue}`128`, {pull}`131`)
 
 (whats-new-1-4-0)=
-## v1.4.0 (14th June 2022)
+## v1.4.0 (2022-06-14)
 
 **Enhancements**
 
@@ -238,7 +248,7 @@ Release notes for `quimb`.
 - Various graph generators and TN builders
 
 (whats-new-1-3-0)=
-## v1.3.0 (18th Feb 2020)
+## v1.3.0 (2020-02-18)
 
 **Enhancements**
 
@@ -274,7 +284,7 @@ Release notes for `quimb`.
 - Make cache import and initilization of `petsc4py` and `slepc4py` more robust.
 
 (whats-new-1-2-0)=
-## v1.2.0 (6th June 2019)
+## v1.2.0 (2019-06-06)
 
 **Enhancements**
 

diff --git a/docs/examples/schematic-demo.ipynb b/docs/examples/schematic-demo.ipynb
@@ -5,7 +5,7 @@
    "metadata": {},
    "source": [
     "(schematic)=\n",
-    "## `schematic` - manual drawing\n",
+    "# `schematic` - manual drawing\n",
     "\n",
     "This example demonstrates the basic functionality of the `schematic` module.\n",
     "The schematic module is a simple wrapper around `matplotlib` that allows \n",
@@ -16,13 +16,13 @@
     "is the [`Drawing`](quimb.schematic.Drawing) class.\n",
     "\n",
     "\n",
-    "### Illustrative full examples\n",
+    "## Illustrative full examples\n",
     "\n",
     "The following examples are intended to be illustrative of a full drawing.\n",
     "If you supply a dict of `presets` to `Drawing`, then you can provide default\n",
     "styling for various elements simply by name.\n",
     "\n",
-    "#### 2D example"
+    "### 2D example"
    ]
   },
   {
@@ -744,7 +744,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "#### Pseudo-3D example\n",
+    "### Pseudo-3D example\n",
     "\n",
     "If you supply 3D coordinates to `Drawing` methods then the objects will be \n",
     "mapped by the axonometric projection to 2D and given appropriate z-ordering.\n",
@@ -8172,7 +8172,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Individual elements:\n",
+    "## Individual elements:\n",
     "\n",
     "Here we demonstrate the different types of individual element that can be placed.\n",
     "The `hash_to_color` function is useful way to deterministically generate colors\n",
@@ -8194,7 +8194,7 @@
    "metadata": {},
    "source": [
     "\n",
-    "#### Circles\n",
+    "### Circles\n",
     "\n",
     "[Drawing.circle](quimb.schematic.Drawing.circle) draws a circle with a given\n",
     "radius and center coordinates."
@@ -8506,7 +8506,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "#### Cubes\n",
+    "### Cubes\n",
     "\n",
     "[Drawing.cube](quimb.schematic.Drawing.cube) draws a cube with a given\n",
     "'radius' and center coordinates, only for 3D coordinates."
@@ -9362,10 +9362,10 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "#### Text\n",
+    "### Text\n",
     "\n",
     "[Drawing.text](quimb.schematic.Drawing.cube) places text in data coordinates \n",
-    "(including 3D). [Drawing.label_axes](quimb.schematic.Drawing.label_axes) and\n",
+    "(including 3D). [Drawing.label_ax](quimb.schematic.Drawing.label_ax) and\n",
     "[Drawing.label_fig](quimb.schematic.Drawing.label_fig) are the same but default\n",
     "to axis and figure coordinates respectively."
    ]
@@ -9944,7 +9944,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "#### General shapes\n",
+    "### General shapes\n",
     "\n",
     "[Drawing.shape](quimb.schematic.Drawing.shape) draws a general filled shape \n",
     "given a sequence of 2D or 3D coordinates."
@@ -10723,7 +10723,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "#### Markers\n",
+    "### Markers\n",
     "\n",
     "[Drawing.marker](quimb.schematic.Drawing.marker) is a convenience method for\n",
     "specifying the shape of a patch using a single string or integer, to yield\n",
@@ -11221,9 +11221,9 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Lines and curves\n",
+    "## Lines and curves\n",
     "\n",
-    "#### Lines\n",
+    "### Lines\n",
     "\n",
     "The basic method for drawing lines between a pair of 2D or 3d points is \n",
     "[Drawing.line](quimb.schematic.Drawing.line)."
@@ -11329,7 +11329,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "#### Arrows and labels\n",
+    "### Arrows and labels\n",
     "\n",
     "You can easily add text and arrows along lines:"
    ]
@@ -11838,7 +11838,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "#### Curves\n",
+    "### Curves\n",
     "\n",
     "If you want a line to pass through multiple points, you can use\n",
     "[Drawing.curve](quimb.schematic.Drawing.curve) to draw a smooth curve."
@@ -12862,7 +12862,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "#### Multi-edges\n",
+    "### Multi-edges\n",
     "\n",
     "If you want to programmatically draw multiple lines from one place to the other ('multi-edges') you can use `line_offset`:"
    ]
@@ -13375,9 +13375,9 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Highlighting areas and groups of objects\n",
+    "## Highlighting areas and groups of objects\n",
     "\n",
-    "#### Patches around general areas\n",
+    "### Patches around general areas\n",
     "\n",
     "In technical drawings it is often useful to highlight areas. The \n",
     "[Drawing.patch](quimb.schematic.Drawing.patch) method does this by filling in\n",
@@ -13486,7 +13486,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "#### Patches around two circles\n",
+    "### Patches around two circles\n",
     "\n",
     "If you want to specifically highlight two circles, you can use\n",
     "[Drawing.patch_around_circles](quimb.schematic.Drawing.patch_around_circles),\n",
@@ -13613,7 +13613,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "#### Patches around arbitrary collections of objects\n",
+    "### Patches around arbitrary collections of objects\n",
     "\n",
     "If you want to highlight an arbitrary collection of objects, you can call\n",
     "[Drawing.patch_around](quimb.schematic.Drawing.patch_around), this computes\n",
@@ -14701,9 +14701,9 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Python [conda env:py311]",
+   "display_name": "py311",
    "language": "python",
-   "name": "conda-env-py311-py"
+   "name": "python3"
   },
   "language_info": {
    "codemirror_mode": {

diff --git a/quimb/tensor/tensor_1d_tebd.py b/quimb/tensor/tensor_1d_tebd.py
@@ -1,7 +1,9 @@
 """Tools for performing TEBD like algorithms in 1D.
 """
+import itertools
 
 import numpy as np
+from autoray import do
 
 from ..utils import ensure_dict, continuous_progbar, deprecated
 from ..utils import progbar as Progbar
@@ -99,6 +101,117 @@ def mean_norm(self):
             for h in self.terms.values()
         ) / len(self.terms)
 
+    def build_mpo_propagator_trotterized(
+        self,
+        x,
+        site_tag_id="I{}",
+        tags=None,
+        upper_ind_id="k{}",
+        lower_ind_id="b{}",
+        shape="lrud",
+        contract_sites=True,
+        **split_opts,
+    ):
+        """Build an MPO representation of ``expm(H * x)``, i.e. the imaginary
+        or real time propagator of this local 1D hamiltonian, using a first
+        order trotterized decomposition.
+
+        Parameters
+        ----------
+        x : float
+            The time to evolve for. Note this does **not** include the
+            imaginary prefactor of the Schrodinger equation, so real ``x``
+            corresponds to imaginary time evolution, and vice versa.
+        site_tag_id : str
+            A string specifiying how to tag the tensors at each site. Should
+            contain a ``'{}'`` placeholder. It is used to generate the actual tags
+            like: ``map(site_tag_id.format, range(len(arrays)))``.
+        tags : str or sequence of str, optional
+            Global tags to attach to all tensors.
+        upper_ind_id : str
+            A string specifiying how to label the upper physical site indices.
+            Should contain a ``'{}'`` placeholder. It is used to generate the
+            actual indices like:
+            ``map(upper_ind_id.format, range(len(arrays)))``.
+        lower_ind_id : str
+            A string specifiying how to label the lower physical site indices.
+            Should contain a ``'{}'`` placeholder. It is used to generate the
+            actual indices like:
+            ``map(lower_ind_id.format, range(len(arrays)))``.
+        shape : str, optional
+            String specifying layout of the tensors. E.g. 'lrud' (the default)
+            indicates the shape corresponds left-bond, right-bond, 'up'
+            physical index, 'down' physical index.
+            End tensors have either 'l' or 'r' dropped from the string if not
+            periodic.
+        contract_sites : bool, optional
+            Whether to contract all the decomposed factors at each site to
+            yield a single tensor per site, by default True.
+        split_opts
+            Supplied to :func:`~quimb.tensor.tensor_core.tensor_split`.
+        """
+        from .tensor_core import Tensor
+        from .tensor_1d import MatrixProductOperator
+
+        mpo = MatrixProductOperator.new(
+            L=self.L,
+            site_tag_id=site_tag_id,
+            upper_ind_id=upper_ind_id,
+            lower_ind_id=lower_ind_id,
+            cyclic=self.cyclic,
+        )
+        imax = self.L - (not self.cyclic)
+
+        # process even bonds then odd bonds
+        layered_sites = itertools.chain(range(0, imax, 2), range(1, imax, 2))
+
+        # process even bonds
+        for i in layered_sites:
+            j = (i + 1) % self.L
+
+            # get a tensor of the local exponentiated term
+            U = self.get_gate_expm((i, j), x)
+            U = do("reshape", U, (2, 2, 2, 2))
+
+            ki = upper_ind_id.format(i)
+            kj = upper_ind_id.format(j)
+            bi = lower_ind_id.format(i)
+            bj = lower_ind_id.format(j)
+
+            # split spatially
+            tnU = Tensor(
+                data=U,
+                inds=(ki, kj, bi, bj),
+            ).split(
+                left_inds=(ki, bi),
+                ltags=site_tag_id.format(i),
+                rtags=site_tag_id.format(j),
+                **split_opts,
+            )
+            # add tensors to mpo
+            mpo.gate_inds_with_tn_(
+                inds=(ki, kj),
+                gate=tnU,
+                gate_inds_inner=(bi, bj),
+                gate_inds_outer=(ki, kj),
+            )
+
+        if contract_sites:
+            # combine site groups into single tensors
+            for st in mpo.site_tags:
+                mpo ^= st
+
+        if tags is not None:
+            # global tags
+            mpo.add_tag(tags)
+
+        if shape is not None:
+            # enforce a canonical ordering of indices within each tensor
+            mpo.permute_arrays(shape)
+
+        return mpo
+
+
     def __repr__(self):
         return f"<LocalHam1D(L={self.L}, cyclic={self.cyclic})>"
 

diff --git a/quimb/tensor/tensor_arbgeom.py b/quimb/tensor/tensor_arbgeom.py
@@ -132,6 +132,14 @@ def tensor_network_apply_op_vec(
     A, x = tn_op.copy(), tn_vec.copy()
 
     # align the indices
+    #
+    #     |       <- upper_ind_id to be site_ind_id (outerid)
+    #    -A- ...
+    #     |       <- lower_ind_id to be innerid
+    #     :
+    #     |       <- site_ind_id to be innerid
+    #    -x- ...
+    #
     coordinate_formatter = get_coordinate_formatter(A._NDIMS)
     A.lower_ind_id = f"__tmp{coordinate_formatter}__"
     A.upper_ind_id = x.site_ind_id