✨ Sub-Architectures (#106)

Added functionality for computing sub-architectures for qubit mapping
based on https://arxiv.org/abs/2210.09321.

Signed-off-by: burgholzer <[email protected]>
Co-authored-by: burgholzer <[email protected]>

README.md

@@ -72,4 +72,8 @@ _In Asia and South Pacific Design Automation Conference (ASP-DAC)_, 2021.
 L. Burgholzer, S. Schneider, and R. Wille. Limiting the Search Space in Optimal Quantum Circuit Mapping.
 _In Asia and South Pacific Design Automation Conference (ASP-DAC)_, 2022.
 
+[[5]](https://arxiv.org/pdf/2210.09321.pdf)
+T. Peham, L. Burgholzer, and R. Wille. On Optimal Subarchitectures for Quantum Circuit Mapping.
+_arXiv:2210.09321_, 2022.
+
 [^1]: The Munich Quantum Toolkit was formerly known under the acronym _JKQ_ and developed by the [Institute for Integrated Circuits](https://iic.jku.at/eda/) at the [Johannes Kepler University Linz](https://jku.at)).

docs/source/Publications.rst

@@ -8,6 +8,7 @@ Furthermore, if you use any of the particular algorithms such as
 
 - the heuristic mapping scheme using teleportation :cite:labelpar:`hillmichExlpoitingQuantumTeleportation2021`
 - the search space limitation techniques of the exact mapper (some of which are enabled per default) :cite:labelpar:`burgholzer2022limitingSearchSpace`
+- the method for finding (near-)optimal subarchitectures :cite:labelpar:`peham2022OptimalSubarchitectures`
 
 please consider citing their respective papers as well. A full list of related papers is given below.
 

docs/source/library/Library.rst

@@ -7,3 +7,4 @@ Library
    Mapping
    Architecture
    MappingResults
+   Subarchitectures

docs/source/library/Subarchitectures.rst

@@ -0,0 +1,19 @@
+Optimal Subarchitectures
+========================
+
+To compute (near-)optimal subarchitectures of quantum computing architectures with restricted connectivity as described in :cite:labelpar:`peham2022OptimalSubarchitectures` the :code:`SubarchitectureOrder` class is provided. This class has functionality to compute the quasi-order that allows for fast computation of optimal subarchitectures.
+
+Note that the initial construction of the ordering might take a while for larger architectures.
+
+    .. currentmodule:: mqt.qmap
+    .. autoclass:: SubarchitectureOrder
+       :members:
+
+QMAP also provides precomputed subarchitecture libraries. The available libraries are available via:
+
+    .. autoattribute:: subarchitectures.precomputed_backends
+
+Convenience methods are provided to import these precomputed orderings:
+
+    .. automethod:: subarchitectures.ibm_guadalupe_subarchitectures
+    .. automethod:: subarchitectures.rigetti_16_subarchitectures

docs/source/refs.bib

@@ -50,3 +50,11 @@ @inproceedings{boteaComplexityQuantumCircuit2018
   author = {Botea, A. and Kishimoto, A. and Marinescu, Radu},
   year = {2018},
 }
+
+@inproceedings{peham2022OptimalSubarchitectures,
+  title = {On Optimal Subarchitectures for Quantum Circuit Mapping},
+  author = {Peham, Tom and Burgholzer, Lukas and Wille, Robert},
+  booktitle = {arXiv:2210.09321},
+  year = {2022},
+  url = {https://arxiv.org/pdf/2210.09321.pdf},
+}

mqt/qmap/__init__.py

@@ -28,6 +28,7 @@
     Method,
     SwapReduction,
 )
+from mqt.qmap.subarchitectures import SubarchitectureOrder
 
 __all__ = [
     "compile",
@@ -41,4 +42,5 @@
     "Configuration",
     "MappingResults",
     "Architecture",
+    "SubarchitectureOrder",
 ]

mqt/qmap/subarchitectures.py

@@ -0,0 +1,323 @@
+"""
+Functionality for computing good subarchitectures for quantum circuit mapping.
+
+This file implements the methods presented in https://arxiv.org/abs/2210.09321.
+"""
+
+from __future__ import annotations
+
+import sys
+
+if sys.version_info < (3, 10, 0):
+    import importlib_resources as resources
+else:
+    from importlib import resources
+
+import pickle
+from itertools import combinations
+from pathlib import Path
+from typing import Dict, NewType, Set, Tuple
+
+import retworkx as rx
+from matplotlib import figure
+from mqt.qmap import Architecture
+
+from qiskit.providers import Backend
+
+PartialOrder = NewType("PartialOrder", Dict[Tuple[int, int], Set[Tuple[int, int]]])
+
+#: Architectures for which precomputed orderings are available
+precomputed_backends = ["rigetti_16", "ibm_guadalupe_16"]
+
+
+class SubarchitectureOrder:
+    """Class representing partial order of Subarchitectures."""
+
+    __inactive_color: str = "#1f78b4"
+    __active_color: str = "#faf18e"
+
+    def __init__(self) -> None:
+        """Construct SubarchitectureOrder with default fields."""
+        self.arch: rx.PyGraph = rx.PyGraph()
+        self.subarch_order: PartialOrder = PartialOrder({})
+        self.desirable_subarchitectures: PartialOrder = PartialOrder({})
+        self.__isomorphisms: dict[tuple[int, int], dict[tuple[int, int], dict[int, int]]] = {}
+
+        self.__compute_subarchs()
+        self.__compute_subarch_order()
+        self.__compute_desirable_subarchitectures()
+        return
+
+    @classmethod
+    def from_retworkx_graph(cls, graph: rx.PyGraph) -> SubarchitectureOrder:
+        """Construct SubarchitectureOrder from retworkx graph."""
+        so = SubarchitectureOrder()
+        so.arch = graph
+
+        so.__compute_subarchs()
+        so.__compute_subarch_order()
+        so.__compute_desirable_subarchitectures()
+        return so
+
+    @classmethod
+    def from_coupling_map(cls, coupling_map: set[tuple[int, int]] | list[tuple[int, int]]) -> SubarchitectureOrder:
+        """Construct SubarchitectureOrder from coupling map defined as set of tuples of connected qubits."""
+        num_nodes = max(max(int(u), int(v)) for u, v in coupling_map)
+        graph = rx.PyGraph()
+        graph.add_nodes_from(list(range(num_nodes + 1)))
+        graph.add_edges_from_no_data([tuple(edge) for edge in coupling_map])
+
+        return cls.from_retworkx_graph(graph)
+
+    @classmethod
+    def from_backend(cls, backend: Backend) -> SubarchitectureOrder:
+        """Construct SubarchitectureOrder from coupling map defined by qiskit backend."""
+        coupling_map = {(a, b) for a, b in backend.configuration().coupling_map}
+        return cls.from_coupling_map(coupling_map)
+
+    @classmethod
+    def from_qmap_architecture(cls, arch: Architecture) -> SubarchitectureOrder:
+        """Construct SubarchitectureOrder from qmap Architecture object."""
+        return cls.from_coupling_map(arch.coupling_map)
+
+    @classmethod
+    def from_library(cls, lib_name: str | Path) -> SubarchitectureOrder:
+        """Construct SubarchitectureOrder from stored library."""
+        path = Path(lib_name).with_suffix(".pickle")
+        with path.open("rb") as f:
+            temp = pickle.load(f)
+
+        so = SubarchitectureOrder()
+        so.__dict__.update(temp.__dict__)
+
+        return so
+
+    @classmethod
+    def from_string(cls, path: str) -> SubarchitectureOrder:
+        """Construct SubarchitectureOrder from library name."""
+        if path in precomputed_backends:
+            ref = resources.files("mqt.qmap") / "libs" / (path + ".pickle")
+            with resources.as_file(ref) as lib_path:
+                return cls.from_library(lib_path)
+        return SubarchitectureOrder()
+
+    def optimal_candidates(self, nqubits: int) -> list[rx.PyGraph]:
+        """Return optimal subarchitecture candidate.
+
+        nqubits : int
+            size of circuit for which the optimal candidate should be given.
+        """
+        if nqubits <= 0 or nqubits > self.arch.num_nodes():
+            raise ValueError(
+                "Number of qubits must not be smaller or equal 0 or larger then number of physical qubits of architecture."
+            )
+
+        if nqubits == self.arch.num_nodes():
+            return [self.arch]
+
+        cands = self.__cand(nqubits)
+        trans_ord = self.__transitive_closure(self.subarch_order)
+        ref_ord = self.__reflexive_closure(trans_ord)
+
+        opt_cands = set(ref_ord[next(iter(cands))])
+        for cand in cands:
+            opt_cands = opt_cands.intersection(set(ref_ord[cand]))
+
+        ordered_cands = list(opt_cands)
+        ordered_cands.sort()
+        for cand in ordered_cands:
+            opt_cands = opt_cands.difference(trans_ord[cand])
+
+        return [self.sgs[n][i] for (n, i) in opt_cands]
+
+    def covering(self, nqubits: int, size: int) -> list[rx.PyGraph]:
+        """
+        Return covering for nqubit circuits.
+
+        The size of the covering is limited by size.
+        Note that a smaller covering might be found.
+        """
+        cov = self.__cand(nqubits)
+        po_trans = self.__transitive_closure(self.subarch_order)
+        ref_trans_po = self.__reflexive_closure(po_trans)
+        queue = list({el for cand in cov for el in ref_trans_po[cand]})
+        queue.sort(reverse=True)
+
+        po_inv = self.__inverse_relation(po_trans)
+
+        while len(cov) > size:
+            d = queue.pop()
+            cov_d = cov.intersection(po_inv[d])
+            if len(cov_d) > 1:
+                cov = cov.difference(cov_d)
+                cov.add(d)
+
+        return [self.sgs[n][i] for n, i in cov]
+
+    def store_library(self, lib_name: str | Path) -> None:
+        """Store ordering."""
+        path = Path(lib_name).with_suffix(".pickle")
+        with path.open("wb") as f:
+            pickle.dump(self, f)
+
+    def draw_subarchitecture(self, subarchitecture: rx.PyGraph | tuple[int, int]) -> figure.Figure:
+        """Return matplotlib figure showing subarchitecture within the entire architecture.
+
+        Nodes that are part of the subarchitecture are drawn yellow.
+        Nodes that are not part of the subarchitecture are drawn blue.
+        """
+        if isinstance(subarchitecture, tuple):
+            subarchitecture = self.sgs[subarchitecture[0]][subarchitecture[1]]
+        colors = [SubarchitectureOrder.__inactive_color for node in range(self.arch.num_nodes())]
+        for node in subarchitecture.nodes():
+            colors[node] = SubarchitectureOrder.__active_color
+        return rx.visualization.mpl_draw(subarchitecture, node_color=colors)
+
+    def draw_subarchitectures(self, subarchitectures: list[rx.PyGraph] | list[tuple[int, int]]) -> list[figure.Figure]:
+        """Return matplotlib figures showing subarchitectures within the entire architecture.
+
+        For each subarchitecture one figure is drawn.
+        Nodes that are part of the subarchitecture are drawn yellow.
+        Nodes that are not part of the subarchitecture are drawn blue.
+        """
+        return [self.draw_subarchitecture(subarchitecture) for subarchitecture in subarchitectures]
+
+    def __compute_subarchs(self) -> None:
+        self.sgs: list[list[rx.PyGraph]] = [[] for i in range(self.arch.num_nodes() + 1)]
+
+        for i in range(1, self.arch.num_nodes() + 1):
+            node_combinations = combinations(range(self.arch.num_nodes()), i)
+            for sg in (self.arch.subgraph(selected_nodes) for selected_nodes in node_combinations):
+                if rx.is_connected(sg):
+                    new_class = True
+                    for g in self.sgs[i]:
+                        if rx.is_isomorphic(g, sg):
+                            new_class = False
+                            break
+                    if new_class:
+                        self.sgs[i].append(sg)
+        # init orders
+        for n in range(self.arch.num_nodes() + 1):
+            for i in range(len(self.sgs[n])):
+                self.subarch_order[(n, i)] = set()
+                self.desirable_subarchitectures[(n, i)] = set()
+                self.__isomorphisms[(n, i)] = {}
+
+    def __compute_subarch_order(self) -> None:
+        for n, sgs_n in enumerate(self.sgs[:-1]):
+            for i, sg in enumerate(sgs_n):
+                for j, parent_sg in enumerate(self.sgs[n + 1]):
+                    matcher = rx.graph_vf2_mapping(parent_sg, sg, subgraph=True)
+                    for iso in matcher:
+                        self.subarch_order[(n, i)].add((n + 1, j))
+                        iso_rev = {}
+                        for key, val in iso.items():
+                            iso_rev[val] = key
+                        self.__isomorphisms[(n, i)][(n + 1, j)] = iso_rev
+                        break  # One isomorphism suffices
+
+    def __complete_isos(self) -> None:
+        for n in reversed(range(1, len(self.sgs[:-1]))):
+            for i in range(len(self.sgs[n])):
+                for _, i_prime in self.subarch_order[(n, i)]:
+                    self.__combine_iso_with_parent(n, i, i_prime)
+
+    def __combine_iso_with_parent(self, n: int, i: int, j: int) -> None:
+        """Combine all isomorphisms from sgs[n][i] with those from sgs[n+1][j]."""
+        first = self.__isomorphisms[(n, i)][(n + 1, j)]
+        for (row, k), second in self.__isomorphisms[(n + 1, j)].items():
+            self.__isomorphisms[(n, i)][(row, k)] = SubarchitectureOrder.__combine_isos(first, second)
+
+    @staticmethod
+    def __combine_isos(first: dict[int, int], second: dict[int, int]) -> dict[int, int]:
+        combined = {}
+        for src, img in first.items():
+            combined[src] = second[img]
+        return combined
+
+    def __transitive_closure(self, po: PartialOrder) -> PartialOrder:
+        po_trans: PartialOrder = PartialOrder({})
+        po_trans[self.arch.num_nodes(), 0] = set()
+
+        for n in reversed(range(1, len(self.sgs[:-1]))):
+            for i in range(len(self.sgs[n])):
+                new_rel = set(po[(n, i)])
+                po_trans[(n, i)] = new_rel.copy()
+                for n_prime, i_prime in po_trans[(n, i)]:
+                    new_rel = new_rel.union(po_trans[(n_prime, i_prime)])
+                po_trans[(n, i)] = new_rel
+
+        return po_trans
+
+    def __reflexive_closure(self, po: PartialOrder) -> PartialOrder:
+        po_ref = PartialOrder({})
+        for k, v in po.items():
+            v_copy = v.copy()
+            v_copy.add(k)
+            po_ref[k] = v_copy
+        return po_ref
+
+    def __inverse_relation(self, po: PartialOrder) -> PartialOrder:
+        po_inv = PartialOrder({})
+        for n in range(self.arch.num_nodes() + 1):
+            for i in range(len(self.sgs[n])):
+                po_inv[(n, i)] = set()
+        for k, v in po.items():
+            for e in v:
+                po_inv[e].add(k)
+        return po_inv
+
+    def __path_order_less(self, n: int, i: int, n_prime: int, i_prime: int) -> bool:
+        lhs = self.sgs[n][i]
+        rhs = self.sgs[n_prime][i_prime]
+        iso = self.__isomorphisms[(n, i)][(n_prime, i_prime)]
+        for v in range(lhs.num_nodes()):
+            for w in range(lhs.num_nodes()):
+                if v is w:
+                    continue
+                if (
+                    rx.dijkstra_shortest_path_lengths(lhs, v, lambda x: 1, goal=w)[w]
+                    > rx.dijkstra_shortest_path_lengths(rhs, iso[v], lambda x: 1, goal=iso[w])[iso[w]]
+                ):
+                    return True
+        return False
+
+    def __compute_desirable_subarchitectures(self) -> None:
+        self.__complete_isos()
+        for n in reversed(range(1, len(self.sgs[:-1]))):
+            for i in range(len(self.sgs[n])):
+                val = self.__isomorphisms[(n, i)]
+                for n_prime, i_prime in val.keys():
+                    if self.__path_order_less(n, i, n_prime, i_prime):
+                        self.desirable_subarchitectures[(n, i)].add((n_prime, i_prime))
+                des = list(self.desirable_subarchitectures[(n, i)])
+                des.sort()
+                new_des: set[tuple[int, int]] = set()
+                for j, (n_prime, i_prime) in enumerate(reversed(des)):
+                    j = len(des) - j - 1
+                    if not any([(n_prime, i_prime) in self.subarch_order[k] for k in des[:j]]):
+                        new_des.add((n_prime, i_prime))
+
+                self.desirable_subarchitectures[(n, i)] = new_des
+                if len(self.desirable_subarchitectures[(n, i)]) == 0:
+                    self.desirable_subarchitectures[(n, i)].add((n, i))
+        self.desirable_subarchitectures[self.arch.num_nodes(), 0] = {(self.arch.num_nodes(), 0)}
+
+    def __cand(self, nqubits: int) -> set[tuple[int, int]]:
+        return {
+            des for (n, i), desirables in self.desirable_subarchitectures.items() if n == nqubits for des in desirables
+        }
+
+
+def ibm_guadalupe_subarchitectures() -> SubarchitectureOrder:
+    """Load the precomputed ibm guadalupe subarchitectures."""
+    ref = resources.files("mqt.qmap") / "libs" / "ibm_guadalupe_16.pickle"
+    with resources.as_file(ref) as path:
+        return SubarchitectureOrder.from_library(path)
+
+
+def rigetti_16_subarchitectures() -> SubarchitectureOrder:
+    """Load the precomputed rigetti subarchitectures."""
+    ref = resources.files("mqt.qmap") / "libs" / "rigetti_16.pickle"
+    with resources.as_file(ref) as path:
+        return SubarchitectureOrder.from_library(path)