# -*- coding: utf-8 -*-

# Copyright 2018, IBM.
#
# This source code is licensed under the Apache License, Version 2.0 found in
# the LICENSE.txt file in the root directory of this source tree.

"""Tools for compiling a batch of quantum circuits."""
from copy import deepcopy
import logging
import uuid
import numpy as np
import scipy.sparse as sp
import scipy.sparse.csgraph as cs

from qiskit.transpiler._transpilererror import TranspilerError
from qiskit._qiskiterror import QISKitError
from qiskit import QuantumCircuit
from qiskit.dagcircuit import DAGCircuit
from qiskit.unroll import DagUnroller, DAGBackend, JsonBackend
from qiskit.mapper import (Coupling, optimize_1q_gates, coupling_list2dict, swap_mapper,
                           cx_cancellation, direction_mapper,
                           remove_last_measurements, return_last_measurements)
from qiskit.qobj import Qobj, QobjConfig, QobjExperiment, QobjItem, QobjHeader
from ._parallel import parallel_map

logger = logging.getLogger(__name__)


# pylint: disable=redefined-builtin
def compile(circuits, backend,
            config=None, basis_gates=None, coupling_map=None, initial_layout=None,
            shots=1024, max_credits=10, seed=None, qobj_id=None, hpc=None,
            pass_manager=None):
    """Compile a list of circuits into a qobj.

    Args:
        circuits (QuantumCircuit or list[QuantumCircuit]): circuits to compile
        backend (BaseBackend): a backend to compile for
        config (dict): dictionary of parameters (e.g. noise) used by runner
        basis_gates (str): comma-separated basis gate set to compile to
        coupling_map (list): coupling map (perhaps custom) to target in mapping
        initial_layout (list): initial layout of qubits in mapping
        shots (int): number of repetitions of each circuit, for sampling
        max_credits (int): maximum credits to use
        seed (int): random seed for simulators
        qobj_id (int): identifier for the generated qobj
        hpc (dict): HPC simulator parameters
        pass_manager (PassManager): a pass_manager for the transpiler stage

    Returns:
        QobjExperiment: Experiment to be wrapped in a Qobj.

    Raises:
        TranspilerError: in case of bad compile options, e.g. the hpc options.
    """
    if isinstance(circuits, QuantumCircuit):
        circuits = [circuits]

    # FIXME: THIS NEEDS TO BE CLEANED UP -- some things to decide for list of circuits:
    # 1. do all circuits have same coupling map?
    # 2. do all circuit have the same basis set?
    # 3. do they all have same registers etc?
    backend_conf = backend.configuration()
    backend_name = backend_conf['name']
    # Check for valid parameters for the experiments.
    if hpc is not None and \
            not all(key in hpc for key in ('multi_shot_optimization', 'omp_num_threads')):
        raise TranspilerError('Unknown HPC parameter format!')
    basis_gates = basis_gates or backend_conf['basis_gates']
    coupling_map = coupling_map or backend_conf['coupling_map']

    # step 1: Making the list of dag circuits
    dags = _circuits_2_dags(circuits)

    # step 2: Transpile all the dags

    # FIXME: Work-around for transpiling multiple circuits with different qreg names.
    # Make compile take a list of initial_layouts.
    _initial_layout = initial_layout

    # Pick a good initial layout if coupling_map is not already satisfied
    # otherwise keep it as q[i]->q[i].
    # TODO: move this inside mapper pass.
    initial_layouts = []
    for dag in dags:
        if (initial_layout is None and not backend.configuration()['simulator']
                and not _matches_coupling_map(dag, coupling_map)):
            _initial_layout = _pick_best_layout(dag, backend)
        initial_layouts.append(_initial_layout)
    dags = _transpile_dags(dags, basis_gates=basis_gates, coupling_map=coupling_map,
                           initial_layouts=initial_layouts, seed=seed,
                           pass_manager=pass_manager)

    # step 3: Making a qobj
    qobj = _dags_2_qobj(dags, backend_name=backend_name,
                        config=config, shots=shots, max_credits=max_credits,
                        qobj_id=qobj_id, basis_gates=basis_gates,
                        coupling_map=coupling_map, seed=seed)

    return qobj


def _circuits_2_dags(circuits):
    """Convert a list of circuits into a list of dags.

    Args:
        circuits (list[QuantumCircuit]): circuit to compile

    Returns:
        list[DAGCircuit]: the dag representation of the circuits
        to be used in the transpiler
    """
    dags = parallel_map(DAGCircuit.fromQuantumCircuit, circuits)
    return dags


def _transpile_dags(dags, basis_gates='u1,u2,u3,cx,id', coupling_map=None,
                    initial_layouts=None, seed=None, pass_manager=None):
    """Transform multiple dags through a sequence of passes.

    Args:
        dags (list[DAGCircuit]): dag circuits to transform
        basis_gates (str): a comma seperated string for the target basis gates
        coupling_map (list): A graph of coupling
        initial_layouts (list[dict]): A mapping of qubit to qubit for each dag
        seed (int): random seed for the swap mapper
        pass_manager (PassManager): pass manager instance for the tranpilation process
            If None, a default set of passes are run.
            Otherwise, the passes defined in it will run.
            If contains no passes in it, no dag transformations occur.

    Returns:
        list[DAGCircuit]: the dag circuits after going through transpilation

    Raises:
        TranspilerError: if the format is not valid.
    """

    index = list(range(len(dags)))
    final_dags = parallel_map(_transpile_dags_parallel, index,
                              task_args=(dags, initial_layouts),
                              task_kwargs={'basis_gates': basis_gates,
                                           'coupling_map': coupling_map,
                                           'seed': seed,
                                           'pass_manager': pass_manager})
    return final_dags


def _transpile_dags_parallel(idx, dags, initial_layouts, basis_gates='u1,u2,u3,cx,id',
                             coupling_map=None, seed=None, pass_manager=None):
    """Helper function for transpiling in parallel (if available).

    Args:
        idx (int): Index for dag of interest
        dags (list): List of dags
        initial_layouts (list): List of initial layouts
        basis_gates (str): a comma seperated string for the target basis gates
        coupling_map (list): A graph of coupling
        seed (int): random seed for the swap mapper
        pass_manager (PassManager): pass manager instance for the tranpilation process
            If None, a default set of passes are run.
            Otherwise, the passes defined in it will run.
            If contains no passes in it, no dag transformations occur.
    Returns:
        DAGCircuit: DAG circuit after going through transpilation.
    """
    dag = dags[idx]
    initial_layout = initial_layouts[idx]
    final_dag, final_layout = transpile(
        dag,
        basis_gates=basis_gates,
        coupling_map=coupling_map,
        initial_layout=initial_layout,
        get_layout=True,
        seed=seed,
        pass_manager=pass_manager)
    final_dag.layout = [[k, v]
                        for k, v in final_layout.items()] if final_layout else None
    return final_dag


def _dags_2_qobj(dags, backend_name, config=None, shots=None,
                 max_credits=None, qobj_id=None, basis_gates=None, coupling_map=None,
                 seed=None):
    """Convert a list of dags into a qobj.

    Args:
        dags (list[DAGCircuit]): dags to compile
        backend_name (str): name of runner backend
        config (dict): dictionary of parameters (e.g. noise) used by runner
        shots (int): number of repetitions of each circuit, for sampling
        max_credits (int): maximum credits to use
        qobj_id (int): identifier for the generated qobj
        basis_gates (list[str])): basis gates for the experiment
        coupling_map (list): coupling map (perhaps custom) to target in mapping
        seed (int): random seed for simulators

    Returns:
        Qobj: the Qobj to be run on the backends
    """
    # TODO: the following will be removed from qobj and thus removed here:
    # `basis_gates`, `coupling_map`

    # Step 1: create the Qobj, with empty experiments.
    # Copy the configuration: the values in `config` have preference
    qobj_config = deepcopy(config or {})
    # TODO: "memory_slots" is required by the qobj schema in the top-level
    # qobj.config, and is user-defined. At the moment is set to the maximum
    # number of *register* slots for the circuits, in order to have `measure`
    # behave properly until the transition is over; and each circuit stores
    # its memory_slots in its configuration.
    qobj_config.update({'shots': shots,
                        'max_credits': max_credits,
                        'memory_slots': 0})

    qobj = Qobj(qobj_id=qobj_id or str(uuid.uuid4()),
                config=QobjConfig(**qobj_config),
                experiments=[],
                header=QobjHeader(backend_name=backend_name))
    if seed:
        qobj.config.seed = seed

    qobj.experiments = parallel_map(_dags_2_qobj_parallel, dags,
                                    task_kwargs={'basis_gates': basis_gates,
                                                 'config': config,
                                                 'coupling_map': coupling_map})

    # Update the `memory_slots` value.
    # TODO: remove when `memory_slots` can be provided by the user.
    qobj.config.memory_slots = max(experiment.config.memory_slots for
                                   experiment in qobj.experiments)

    # Update the `n_qubits` global value.
    # TODO: num_qubits is not part of the qobj specification, but needed
    # for the simulator.
    qobj.config.n_qubits = max(experiment.config.n_qubits for
                               experiment in qobj.experiments)

    return qobj


def _dags_2_qobj_parallel(dag, config=None, basis_gates=None,
                          coupling_map=None):
    """Helper function for dags to qobj in parallel (if available).

    Args:
        dag (DAGCircuit): DAG to compile
        config (dict): dictionary of parameters (e.g. noise) used by runner
        basis_gates (list[str])): basis gates for the experiment
        coupling_map (list): coupling map (perhaps custom) to target in mapping

    Returns:
        Qobj: Qobj to be run on the backends
    """
    json_circuit = DagUnroller(dag, JsonBackend(dag.basis)).execute()
    # Step 3a: create the Experiment based on json_circuit
    experiment = QobjExperiment.from_dict(json_circuit)
    # Step 3b: populate the Experiment configuration and header
    experiment.header.name = dag.name
    # TODO: place in header or config?
    experiment_config = deepcopy(config or {})
    experiment_config.update({
        'coupling_map': coupling_map,
        'basis_gates': basis_gates,
        'layout': dag.layout,
        'memory_slots': sum(dag.cregs.values()),
        # TODO: `n_qubits` is not part of the qobj spec, but needed for the simulator.
        'n_qubits': sum(dag.qregs.values())})
    experiment.config = QobjItem(**experiment_config)

    # set eval_symbols=True to evaluate each symbolic expression
    # TODO: after transition to qobj, we can drop this
    experiment.header.compiled_circuit_qasm = dag.qasm(
        qeflag=True, eval_symbols=True)
    # Step 3c: add the Experiment to the Qobj
    return experiment


def transpile(dag, basis_gates='u1,u2,u3,cx,id', coupling_map=None,
              initial_layout=None, get_layout=False,
              format='dag', seed=None, pass_manager=None):
    """Transform a dag circuit into another dag circuit (transpile), through
    consecutive passes on the dag.

    Args:
        dag (DAGCircuit): dag circuit to transform via transpilation
        basis_gates (str): a comma seperated string for the target basis gates
        coupling_map (list): A graph of coupling::

            [
             [control0(int), target0(int)],
             [control1(int), target1(int)],
            ]

            eg. [[0, 2], [1, 2], [1, 3], [3, 4]}

        initial_layout (dict): A mapping of qubit to qubit::

                              {
                                ("q", start(int)): ("q", final(int)),
                                ...
                              }
                              eg.
                              {
                                ("q", 0): ("q", 0),
                                ("q", 1): ("q", 1),
                                ("q", 2): ("q", 2),
                                ("q", 3): ("q", 3)
                              }
        get_layout (bool): flag for returning the final layout after mapping
        format (str): The target format of the compilation:
            {'dag', 'json', 'qasm'}
        seed (int): random seed for the swap mapper
        pass_manager (PassManager): pass manager instance for the tranpilation process
            If None, a default set of passes are run.
            Otherwise, the passes defined in it will run.
            If contains no passes in it, no dag transformations occur.

    Returns:
        DAGCircuit: transformed dag
        DAGCircuit, dict: transformed dag along with the final layout on backend qubits

    Raises:
        TranspilerError: if the format is not valid.
    """
    # TODO: `basis_gates` will be removed after we have the unroller pass.
    # TODO: `coupling_map`, `initial_layout`, `get_layout`, `seed` removed after mapper pass.

    # TODO: move this to the mapper pass
    num_qubits = sum(dag.qregs.values())
    if num_qubits == 1 or coupling_map == "all-to-all":
        coupling_map = None

    final_layout = None

    if pass_manager:
        # run the passes specified by the pass manager
        for pass_ in pass_manager.passes():
            pass_.run(dag)
    else:
        # default set of passes
        # TODO: move each step here to a pass, and use a default passmanager below
        basis = basis_gates.split(',') if basis_gates else []
        dag_unroller = DagUnroller(dag, DAGBackend(basis))
        dag = dag_unroller.expand_gates()
        # if a coupling map is given compile to the map
        if coupling_map:
            logger.info("pre-mapping properties: %s",
                        dag.property_summary())
            # Insert swap gates
            coupling = Coupling(coupling_list2dict(coupling_map))
            removed_meas = remove_last_measurements(dag)
            logger.info("measurements moved: %s", removed_meas)
            logger.info("initial layout: %s", initial_layout)
            dag, final_layout, last_layout = swap_mapper(
                dag, coupling, initial_layout, trials=20, seed=seed)
            logger.info("final layout: %s", final_layout)
            # Expand swaps
            dag_unroller = DagUnroller(dag, DAGBackend(basis))
            dag = dag_unroller.expand_gates()
            # Change cx directions
            dag = direction_mapper(dag, coupling)
            # Simplify cx gates
            cx_cancellation(dag)
            # Simplify single qubit gates
            dag = optimize_1q_gates(dag)
            return_last_measurements(dag, removed_meas,
                                     last_layout)
            logger.info("post-mapping properties: %s",
                        dag.property_summary())

    # choose output format
    # TODO: do we need all of these formats, or just the dag?
    if format == 'dag':
        compiled_circuit = dag
    elif format == 'json':
        # FIXME: JsonBackend is wrongly taking an ordered dict as basis, not list
        dag_unroller = DagUnroller(dag, JsonBackend(dag.basis))
        compiled_circuit = dag_unroller.execute()
    elif format == 'qasm':
        compiled_circuit = dag.qasm()
    else:
        raise TranspilerError('unrecognized circuit format')

    if get_layout:
        return compiled_circuit, final_layout
    return compiled_circuit


def _best_subset(backend, n_qubits):
    """Computes the qubit mapping with the best
    connectivity.

    Parameters:
        backend (Qiskit.BaseBackend): A QISKit backend instance.
        n_qubits (int): Number of subset qubits to consider.

    Returns:
        ndarray: Array of qubits to use for best
                connectivity mapping.

    Raises:
        QISKitError: Wrong number of qubits given.
    """
    if n_qubits == 1:
        return np.array([0])
    elif n_qubits <= 0:
        raise QISKitError('Number of qubits <= 0.')

    device_qubits = backend.configuration()['n_qubits']
    if n_qubits > device_qubits:
        raise QISKitError('Number of qubits greater than device.')

    cmap = np.asarray(backend.configuration()['coupling_map'])
    data = np.ones_like(cmap[:, 0])
    sp_cmap = sp.coo_matrix((data, (cmap[:, 0], cmap[:, 1])),
                            shape=(device_qubits, device_qubits)).tocsr()
    best = 0
    best_map = None
    # do bfs with each node as starting point
    for k in range(sp_cmap.shape[0]):
        bfs = cs.breadth_first_order(sp_cmap, i_start=k, directed=False,
                                     return_predecessors=False)

        connection_count = 0
        for i in range(n_qubits):
            node_idx = bfs[i]
            for j in range(sp_cmap.indptr[node_idx],
                           sp_cmap.indptr[node_idx + 1]):
                node = sp_cmap.indices[j]
                for counter in range(n_qubits):
                    if node == bfs[counter]:
                        connection_count += 1
                        break

        if connection_count > best:
            best = connection_count
            best_map = bfs[0:n_qubits]
    return best_map


def _matches_coupling_map(dag, coupling_map):
    """Iterate over circuit gates to check if all multi-qubit couplings
    match the qubit coupling graph in the backend.

    Parameters:
            dag (DAGCircuit): DAG representation of circuit.
            coupling_map (list): Backend coupling map, represented as an adjacency list.

    Returns:
            bool: True if all gates readily fit the backend coupling graph.
                  False if there's at least one gate that uses multiple qubits
                  which does not match the backend couplings.
    """
    match = True
    for _, data in dag.multi_graph.nodes(data=True):
        if data['type'] == 'op':
            gate_map = [qr[1] for qr in data['qargs']]
            if gate_map not in coupling_map:
                match = False
                break
    return match


def _pick_best_layout(dag, backend):
    """Pick a convenient layout depending on the best matching qubit connectivity

    Parameters:
        dag (DAGCircuit): DAG representation of circuit.
        backend (BaseBackend) : The backend with the coupling_map for searching

    Returns:
        dict: A special ordered initial_layout

    """
    num_qubits = sum(dag.qregs.values())
    best_sub = _best_subset(backend, num_qubits)
    layout = {}
    map_iter = 0
    for key, value in dag.qregs.items():
        for i in range(value):
            layout[(key, i)] = ('q', best_sub[map_iter])
            map_iter += 1
    return layout

qiskit/transpiler/_transpiler.py
# -*- coding: utf-8 -*-

# Copyright 2018, IBM.
#
# This source code is licensed under the Apache License, Version 2.0 found in
# the LICENSE.txt file in the root directory of this source tree.

"""Tools for compiling a batch of quantum circuits."""
from copy import deepcopy
import logging
import uuid
import numpy as np
import scipy.sparse as sp
import scipy.sparse.csgraph as cs

from qiskit.transpiler._transpilererror import TranspilerError
from qiskit._qiskiterror import QISKitError
from qiskit import QuantumCircuit
from qiskit.dagcircuit import DAGCircuit
from qiskit.unroll import DagUnroller, DAGBackend, JsonBackend
from qiskit.mapper import (Coupling, optimize_1q_gates, coupling_list2dict, swap_mapper,
                           cx_cancellation, direction_mapper,
                           remove_last_measurements, return_last_measurements)
from qiskit.qobj import Qobj, QobjConfig, QobjExperiment, QobjItem, QobjHeader
from ._parallel import parallel_map

logger = logging.getLogger(__name__)


# pylint: disable=redefined-builtin
def compile(circuits, backend,
            config=None, basis_gates=None, coupling_map=None, initial_layout=None,
            shots=1024, max_credits=10, seed=None, qobj_id=None, hpc=None,
            pass_manager=None):
    """Compile a list of circuits into a qobj.

    Args:
        circuits (QuantumCircuit or list[QuantumCircuit]): circuits to compile
        backend (BaseBackend): a backend to compile for
        config (dict): dictionary of parameters (e.g. noise) used by runner
        basis_gates (str): comma-separated basis gate set to compile to
        coupling_map (list): coupling map (perhaps custom) to target in mapping
        initial_layout (list): initial layout of qubits in mapping
        shots (int): number of repetitions of each circuit, for sampling
        max_credits (int): maximum credits to use
        seed (int): random seed for simulators
        qobj_id (int): identifier for the generated qobj
        hpc (dict): HPC simulator parameters
        pass_manager (PassManager): a pass_manager for the transpiler stage

    Returns:
        QobjExperiment: Experiment to be wrapped in a Qobj.

    Raises:
        TranspilerError: in case of bad compile options, e.g. the hpc options.
    """
    if isinstance(circuits, QuantumCircuit):
        circuits = [circuits]

    # FIXME: THIS NEEDS TO BE CLEANED UP -- some things to decide for list of circuits:
    # 1. do all circuits have same coupling map?
    # 2. do all circuit have the same basis set?
    # 3. do they all have same registers etc?
    backend_conf = backend.configuration()
    backend_name = backend_conf['name']
    # Check for valid parameters for the experiments.
    if hpc is not None and \
            not all(key in hpc for key in ('multi_shot_optimization', 'omp_num_threads')):
        raise TranspilerError('Unknown HPC parameter format!')
    basis_gates = basis_gates or backend_conf['basis_gates']
    coupling_map = coupling_map or backend_conf['coupling_map']

    # step 1: Making the list of dag circuits
    dags = _circuits_2_dags(circuits)

    # step 2: Transpile all the dags

    # FIXME: Work-around for transpiling multiple circuits with different qreg names.
    # Make compile take a list of initial_layouts.
    _initial_layout = initial_layout

    # Pick a good initial layout if coupling_map is not already satisfied
    # otherwise keep it as q[i]->q[i].
    # TODO: move this inside mapper pass.
    initial_layouts = []
    for dag in dags:
        if (initial_layout is None and not backend.configuration()['simulator']
                and not _matches_coupling_map(dag, coupling_map)):
            _initial_layout = _pick_best_layout(dag, backend)
        initial_layouts.append(_initial_layout)
    dags = _transpile_dags(dags, basis_gates=basis_gates, coupling_map=coupling_map,
                           initial_layouts=initial_layouts, seed=seed,
                           pass_manager=pass_manager)

    # step 3: Making a qobj
    qobj = _dags_2_qobj(dags, backend_name=backend_name,
                        config=config, shots=shots, max_credits=max_credits,
                        qobj_id=qobj_id, basis_gates=basis_gates,
                        coupling_map=coupling_map, seed=seed)

    return qobj


def _circuits_2_dags(circuits):
    """Convert a list of circuits into a list of dags.

    Args:
        circuits (list[QuantumCircuit]): circuit to compile

    Returns:
        list[DAGCircuit]: the dag representation of the circuits
        to be used in the transpiler
    """
    dags = parallel_map(DAGCircuit.fromQuantumCircuit, circuits)
    return dags


def _transpile_dags(dags, basis_gates='u1,u2,u3,cx,id', coupling_map=None,
                    initial_layouts=None, seed=None, pass_manager=None):
    """Transform multiple dags through a sequence of passes.

    Args:
        dags (list[DAGCircuit]): dag circuits to transform
        basis_gates (str): a comma seperated string for the target basis gates
        coupling_map (list): A graph of coupling
        initial_layouts (list[dict]): A mapping of qubit to qubit for each dag
        seed (int): random seed for the swap mapper
        pass_manager (PassManager): pass manager instance for the tranpilation process
            If None, a default set of passes are run.
            Otherwise, the passes defined in it will run.
            If contains no passes in it, no dag transformations occur.

    Returns:
        list[DAGCircuit]: the dag circuits after going through transpilation

    Raises:
        TranspilerError: if the format is not valid.
    """

    index = list(range(len(dags)))
    final_dags = parallel_map(_transpile_dags_parallel, index,
                              task_args=(dags, initial_layouts),
                              task_kwargs={'basis_gates': basis_gates,
                                           'coupling_map': coupling_map,
                                           'seed': seed,
                                           'pass_manager': pass_manager})
    return final_dags


def _transpile_dags_parallel(idx, dags, initial_layouts, basis_gates='u1,u2,u3,cx,id',
                             coupling_map=None, seed=None, pass_manager=None):
    """Helper function for transpiling in parallel (if available).

    Args:
        idx (int): Index for dag of interest
        dags (list): List of dags
        initial_layouts (list): List of initial layouts
        basis_gates (str): a comma seperated string for the target basis gates
        coupling_map (list): A graph of coupling
        seed (int): random seed for the swap mapper
        pass_manager (PassManager): pass manager instance for the tranpilation process
            If None, a default set of passes are run.
            Otherwise, the passes defined in it will run.
            If contains no passes in it, no dag transformations occur.
    Returns:
        DAGCircuit: DAG circuit after going through transpilation.
    """
    dag = dags[idx]
    initial_layout = initial_layouts[idx]
    final_dag, final_layout = transpile(
        dag,
        basis_gates=basis_gates,
        coupling_map=coupling_map,
        initial_layout=initial_layout,
        get_layout=True,
        seed=seed,
        pass_manager=pass_manager)
    final_dag.layout = [[k, v]
                        for k, v in final_layout.items()] if final_layout else None
    return final_dag


def _dags_2_qobj(dags, backend_name, config=None, shots=None,
                 max_credits=None, qobj_id=None, basis_gates=None, coupling_map=None,
                 seed=None):
    """Convert a list of dags into a qobj.

    Args:
        dags (list[DAGCircuit]): dags to compile
        backend_name (str): name of runner backend
        config (dict): dictionary of parameters (e.g. noise) used by runner
        shots (int): number of repetitions of each circuit, for sampling
        max_credits (int): maximum credits to use
        qobj_id (int): identifier for the generated qobj
        basis_gates (list[str])): basis gates for the experiment
        coupling_map (list): coupling map (perhaps custom) to target in mapping
        seed (int): random seed for simulators

    Returns:
        Qobj: the Qobj to be run on the backends
    """
    # TODO: the following will be removed from qobj and thus removed here:
    # `basis_gates`, `coupling_map`

    # Step 1: create the Qobj, with empty experiments.
    # Copy the configuration: the values in `config` have preference
    qobj_config = deepcopy(config or {})
    # TODO: "memory_slots" is required by the qobj schema in the top-level
    # qobj.config, and is user-defined. At the moment is set to the maximum
    # number of *register* slots for the circuits, in order to have `measure`
    # behave properly until the transition is over; and each circuit stores
    # its memory_slots in its configuration.
    qobj_config.update({'shots': shots,
                        'max_credits': max_credits,
                        'memory_slots': 0})

    qobj = Qobj(qobj_id=qobj_id or str(uuid.uuid4()),
                config=QobjConfig(**qobj_config),
                experiments=[],
                header=QobjHeader(backend_name=backend_name))
    if seed:
        qobj.config.seed = seed

    qobj.experiments = parallel_map(_dags_2_qobj_parallel, dags,
                                    task_kwargs={'basis_gates': basis_gates,
                                                 'config': config,
                                                 'coupling_map': coupling_map})

    # Update the `memory_slots` value.
    # TODO: remove when `memory_slots` can be provided by the user.
    qobj.config.memory_slots = max(experiment.config.memory_slots for
                                   experiment in qobj.experiments)

    # Update the `n_qubits` global value.
    # TODO: num_qubits is not part of the qobj specification, but needed
    # for the simulator.
    qobj.config.n_qubits = max(experiment.config.n_qubits for
                               experiment in qobj.experiments)

    return qobj


def _dags_2_qobj_parallel(dag, config=None, basis_gates=None,
                          coupling_map=None):
    """Helper function for dags to qobj in parallel (if available).

    Args:
        dag (DAGCircuit): DAG to compile
        config (dict): dictionary of parameters (e.g. noise) used by runner
        basis_gates (list[str])): basis gates for the experiment
        coupling_map (list): coupling map (perhaps custom) to target in mapping

    Returns:
        Qobj: Qobj to be run on the backends
    """
    json_circuit = DagUnroller(dag, JsonBackend(dag.basis)).execute()
    # Step 3a: create the Experiment based on json_circuit
    experiment = QobjExperiment.from_dict(json_circuit)
    # Step 3b: populate the Experiment configuration and header
    experiment.header.name = dag.name
    # TODO: place in header or config?
    experiment_config = deepcopy(config or {})
    experiment_config.update({
        'coupling_map': coupling_map,
        'basis_gates': basis_gates,
        'layout': dag.layout,
        'memory_slots': sum(dag.cregs.values()),
        # TODO: `n_qubits` is not part of the qobj spec, but needed for the simulator.
        'n_qubits': sum(dag.qregs.values())})
    experiment.config = QobjItem(**experiment_config)

    # set eval_symbols=True to evaluate each symbolic expression
    # TODO: after transition to qobj, we can drop this
    experiment.header.compiled_circuit_qasm = dag.qasm(
        qeflag=True, eval_symbols=True)
    # Step 3c: add the Experiment to the Qobj
    return experiment


def transpile(dag, basis_gates='u1,u2,u3,cx,id', coupling_map=None,
              initial_layout=None, get_layout=False,
              format='dag', seed=None, pass_manager=None):
    """Transform a dag circuit into another dag circuit (transpile), through
    consecutive passes on the dag.

    Args:
        dag (DAGCircuit): dag circuit to transform via transpilation
        basis_gates (str): a comma seperated string for the target basis gates
        coupling_map (list): A graph of coupling::

            [
             [control0(int), target0(int)],
             [control1(int), target1(int)],
            ]

            eg. [[0, 2], [1, 2], [1, 3], [3, 4]}

        initial_layout (dict): A mapping of qubit to qubit::

                              {
                                ("q", start(int)): ("q", final(int)),
                                ...
                              }
                              eg.
                              {
                                ("q", 0): ("q", 0),
                                ("q", 1): ("q", 1),
                                ("q", 2): ("q", 2),
                                ("q", 3): ("q", 3)
                              }
        get_layout (bool): flag for returning the final layout after mapping
        format (str): The target format of the compilation:
            {'dag', 'json', 'qasm'}
        seed (int): random seed for the swap mapper
        pass_manager (PassManager): pass manager instance for the tranpilation process
            If None, a default set of passes are run.
            Otherwise, the passes defined in it will run.
            If contains no passes in it, no dag transformations occur.

    Returns:
        DAGCircuit: transformed dag
        DAGCircuit, dict: transformed dag along with the final layout on backend qubits

    Raises:
        TranspilerError: if the format is not valid.
    """
    # TODO: `basis_gates` will be removed after we have the unroller pass.
    # TODO: `coupling_map`, `initial_layout`, `get_layout`, `seed` removed after mapper pass.

    # TODO: move this to the mapper pass
    num_qubits = sum(dag.qregs.values())
    if num_qubits == 1 or coupling_map == "all-to-all":
        coupling_map = None

    final_layout = None

    if pass_manager:
        # run the passes specified by the pass manager
        for pass_ in pass_manager.passes():
            pass_.run(dag)
    else:
        # default set of passes
        # TODO: move each step here to a pass, and use a default passmanager below
        basis = basis_gates.split(',') if basis_gates else []
        dag_unroller = DagUnroller(dag, DAGBackend(basis))
        dag = dag_unroller.expand_gates()
        # if a coupling map is given compile to the map
        if coupling_map:
            logger.info("pre-mapping properties: %s",
                        dag.property_summary())
            # Insert swap gates
            coupling = Coupling(coupling_list2dict(coupling_map))
            removed_meas = remove_last_measurements(dag)
            logger.info("measurements moved: %s", removed_meas)
            logger.info("initial layout: %s", initial_layout)
            dag, final_layout, last_layout = swap_mapper(
                dag, coupling, initial_layout, trials=20, seed=seed)
            logger.info("final layout: %s", final_layout)
            # Expand swaps
            dag_unroller = DagUnroller(dag, DAGBackend(basis))
            dag = dag_unroller.expand_gates()
            # Change cx directions
            dag = direction_mapper(dag, coupling)
            # Simplify cx gates
            cx_cancellation(dag)
            # Simplify single qubit gates
            dag = optimize_1q_gates(dag)
            return_last_measurements(dag, removed_meas,
                                     last_layout)
            logger.info("post-mapping properties: %s",
                        dag.property_summary())

    # choose output format
    # TODO: do we need all of these formats, or just the dag?
    if format == 'dag':
        compiled_circuit = dag
    elif format == 'json':
        # FIXME: JsonBackend is wrongly taking an ordered dict as basis, not list
        dag_unroller = DagUnroller(dag, JsonBackend(dag.basis))
        compiled_circuit = dag_unroller.execute()
    elif format == 'qasm':
        compiled_circuit = dag.qasm()
    else:
        raise TranspilerError('unrecognized circuit format')

    if get_layout:
        return compiled_circuit, final_layout
    return compiled_circuit


def _best_subset(backend, n_qubits):
    """Computes the qubit mapping with the best
    connectivity.

    Parameters:
        backend (Qiskit.BaseBackend): A QISKit backend instance.
        n_qubits (int): Number of subset qubits to consider.

    Returns:
        ndarray: Array of qubits to use for best
                connectivity mapping.

    Raises:
        QISKitError: Wrong number of qubits given.
    """
    if n_qubits == 1:
        return np.array([0])
    elif n_qubits <= 0:
        raise QISKitError('Number of qubits <= 0.')

    device_qubits = backend.configuration()['n_qubits']
    if n_qubits > device_qubits:
        raise QISKitError('Number of qubits greater than device.')

    cmap = np.asarray(backend.configuration()['coupling_map'])
    data = np.ones_like(cmap[:, 0])
    sp_cmap = sp.coo_matrix((data, (cmap[:, 0], cmap[:, 1])),
                            shape=(device_qubits, device_qubits)).tocsr()
    best = 0
    best_map = None
    # do bfs with each node as starting point
    for k in range(sp_cmap.shape[0]):
        bfs = cs.breadth_first_order(sp_cmap, i_start=k, directed=False,
                                     return_predecessors=False)

        connection_count = 0
        for i in range(n_qubits):
            node_idx = bfs[i]
            for j in range(sp_cmap.indptr[node_idx],
                           sp_cmap.indptr[node_idx + 1]):
                node = sp_cmap.indices[j]
                for counter in range(n_qubits):
                    if node == bfs[counter]:
                        connection_count += 1
                        break

        if connection_count > best:
            best = connection_count
            best_map = bfs[0:n_qubits]
    return best_map


def _matches_coupling_map(dag, coupling_map):
    """Iterate over circuit gates to check if all multi-qubit couplings
    match the qubit coupling graph in the backend.

    Parameters:
            dag (DAGCircuit): DAG representation of circuit.
            coupling_map (list): Backend coupling map, represented as an adjacency list.

    Returns:
            bool: True if all gates readily fit the backend coupling graph.
                  False if there's at least one gate that uses multiple qubits
                  which does not match the backend couplings.
    """
    match = True
    for _, data in dag.multi_graph.nodes(data=True):
        if data['type'] == 'op':
            gate_map = [qr[1] for qr in data['qargs']]
            if len(gate_map) > 1:
                if gate_map not in coupling_map:
                    match = False
                    break
    return match


def _pick_best_layout(dag, backend):
    """Pick a convenient layout depending on the best matching qubit connectivity

    Parameters:
        dag (DAGCircuit): DAG representation of circuit.
        backend (BaseBackend) : The backend with the coupling_map for searching

    Returns:
        dict: A special ordered initial_layout

    """
    num_qubits = sum(dag.qregs.values())
    best_sub = _best_subset(backend, num_qubits)
    layout = {}
    map_iter = 0
    for key, value in dag.qregs.items():
        for i in range(value):
            layout[(key, i)] = ('q', best_sub[map_iter])
            map_iter += 1
    return layout

qiskit/transpiler/_transpiler.py
diff --git a/qiskit/transpiler/_transpiler.py b/qiskit/transpiler/_transpiler.py
index 4479b35b6706..7f6c68392af2 100644
--- a/qiskit/transpiler/_transpiler.py
+++ b/qiskit/transpiler/_transpiler.py
@@ -457,9 +457,10 @@ def _matches_coupling_map(dag, coupling_map):
     for _, data in dag.multi_graph.nodes(data=True):
         if data['type'] == 'op':
             gate_map = [qr[1] for qr in data['qargs']]
-            if gate_map not in coupling_map:
-                match = False
-                break
+            if len(gate_map) > 1:
+                if gate_map not in coupling_map:
+                    match = False
+                    break
     return match
 
 

_matches_coupling_map seems to check single qubit ops too and fails
<!-- ⚠️ If you do not respect this template, your issue will be closed -->
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### Informations

- **Qiskit Terra version**: 0.6.0
- **Python version**: 3.6
- **Operating system**: macos

### What is the current behavior?

Using _matches_coupling_map breaks and returns false at first single qubit op as single qubits are not in the coupling map

### Steps to reproduce the problem

Run the function on a dag 

### What is the expected behavior?

Ignore single qubits ops

### Suggested solutions
Check no of qubits. Have fixed and pull request ready to go if ok. 👍 


