abp/abp/build_tables.py

"""
This program computes lookup tables and stores them as tables.py and tables.js
# TODO: clifford naming discrepancy
"""

from __future__ import absolute_import
from __future__ import print_function
import numpy as np
import itertools as it
from functools import reduce
from os.path import dirname, join, split
import json
from . import qi, clifford
from six.moves import range


DECOMPOSITIONS = (
    "xxxx", "xx", "zzxx", "zz", "zxx", "z", "zzz", "xxz", "xzx", "xzxxx", "xzzzx",
                  "xxxzx", "xzz", "zzx", "xxx", "x", "zzzx", "xxzx", "zx", "zxxx", "xxxz", "xzzz", "xz", "xzxx")


PY_TEMPLATE = """\
import numpy as np

# Define lookup tables
ir2 = 1/np.sqrt(2)
decompositions = {decompositions}
conjugation_table = np.array({conjugation_table}, dtype=int)
times_table = np.array({times_table}, dtype=int)
cz_table = np.array({cz_table}, dtype=int)
by_name = {by_name}
measurement_table = np.array({measurement_table}, dtype=int)
unitaries_real = np.array({unitaries_real}, dtype=complex)
unitaries_imag = np.array({unitaries_imag}, dtype=complex)

# Reconstruct
unitaries = unitaries_real + 1j*unitaries_imag
"""


def find_clifford(needle, haystack):
    """ Find the index of a given u within a list of unitaries, up to a global phase  """
    needle = qi.normalize_global_phase(needle)
    for i, t in enumerate(haystack):
        if np.allclose(t, needle):
            return i
    raise IndexError


def find_cz(bond, c1, c2, commuters, state_table):
    """ Find the output of a CZ operation """
    # Figure out the target state
    target = qi.cz.dot(state_table[bond, c1, c2])
    target = qi.normalize_global_phase(target)

    # Choose the sets to search over
    s1 = commuters if c1 in commuters else list(range(24))
    s2 = commuters if c2 in commuters else list(range(24))

    # Find a match
    for bondp, c1p, c2p in it.product([0, 1], s1, s2):
        if np.allclose(target, state_table[bondp, c1p, c2p]):
            return bondp, c1p, c2p

    # Didn't find anything - this should never happen
    raise IndexError


def compose_u(decomposition):
    """ Get the unitary representation of a particular decomposition """
    matrices = ({"x": qi.msqx, "z": qi.sqz}[c] for c in decomposition)
    output = reduce(np.dot, matrices, np.eye(2, dtype=complex))
    return qi.normalize_global_phase(output)


def get_unitaries():
    """ The Clifford group """
    return [compose_u(d) for d in DECOMPOSITIONS]


def get_by_name(unitaries, conjugation_table):
    """ Get a lookup table of cliffords by name """
    a = {name: find_clifford(u, unitaries)
         for name, u in list(qi.by_name.items())}
    a.update({key + "_h": conjugation_table[value]
              for key, value in list(a.items())})
    a.update({clifford.get_name(i): i for i in range(24)})
    a.update({i: i for i in range(24)})
    return a


def get_conjugation_table(unitaries):
    """ Construct the conjugation table """
    return np.array([find_clifford(qi.hermitian_conjugate(u), unitaries) for u in unitaries], dtype=int)


def get_times_table(unitaries):
    """ Construct the times-table """
    return np.array([[find_clifford(u.dot(v), unitaries) for v in unitaries]
                     for u in unitaries], dtype=int)


def get_state_table(unitaries):
    """ Cache a table of state to speed up a little bit """
    state_table = np.zeros((2, 24, 24, 4), dtype=complex)
    params = list(it.product([0, 1], list(range(24)), list(range(24))))
    for bond, i, j in params:
        state = qi.bond if bond else qi.nobond
        kp = np.kron(unitaries[i], unitaries[j])
        state_table[bond, i, j, :] = qi.normalize_global_phase(
            np.dot(kp, state).T)
    return state_table


def get_measurement_entry(operator, unitary):
    """
    Any Clifford group unitary will map an operator A in {I, X, Y, Z}
    to an operator B in +-{I, X, Y, Z}. This finds that mapping.
    """
    matrices = ({"x": qi.msqx, "z": qi.sqz}[c]
                for c in DECOMPOSITIONS[unitary])
    unitary = reduce(np.dot, matrices, np.eye(2, dtype=complex))
    operator = qi.operators[operator]
    new_operator = reduce(np.dot,
                          (unitary, operator, qi.hermitian_conjugate(unitary)))

    for i, o in enumerate(qi.operators):
        if np.allclose(o, new_operator):
            return i, 1
        elif np.allclose(o, -new_operator):
            return i, -1

    raise IndexError


def get_measurement_table():
    """
    Compute a table of transform * operation * transform^dagger
    This is pretty unintelligible right now, we should probably compute the phase from unitaries instead
    """
    measurement_table = np.zeros((4, 24, 2), dtype=int)
    for operator, unitary in it.product(list(range(4)), list(range(24))):
        measurement_table[operator, unitary] = get_measurement_entry(
            operator, unitary)
    return measurement_table


def get_commuters(unitaries):
    """ Get the indeces of gates which commute with CZ """
    commuters = (qi.id, qi.pz, qi.ph, qi.hermitian_conjugate(qi.ph))
    return [find_clifford(u, unitaries) for u in commuters]


def get_cz_table(unitaries):
    """ Compute the lookup table for the CZ (A&B eq. 9) """
    # Get a cached state table and a list of gates which commute with CZ
    commuters = get_commuters(unitaries)
    state_table = get_state_table(unitaries)

    # And now build the CZ table
    cz_table = np.zeros((2, 24, 24, 3), dtype=int)
    rows = list(
        it.product([0, 1], it.combinations_with_replacement(list(range(24)), 2)))
    # CZ is symmetric so we only need combinations
    for bond, (c1, c2) in rows:
        newbond, c1p, c2p = find_cz(
            bond, c1, c2, commuters, state_table)
        cz_table[bond, c1, c2] = [newbond, c1p, c2p]
        cz_table[bond, c2, c1] = [newbond, c2p, c1p]
    return cz_table


def get_display_table(unitaries):
    """ Used to display VOPs in a human readable style """
    for u in unitaries:
        c = qi.CircuitModel(1)
        c.act_local_rotation(0, u)
        state = c.state.round(2)
        print(("{:.2f}, {:.2f}".format(state[0][0], state[1][0])))


def compute_everything():
    """ Compute all lookup tables """
    unitaries = get_unitaries()
    conjugation_table = get_conjugation_table(unitaries)
    return {"decompositions": DECOMPOSITIONS,
            "unitaries": unitaries,
            "by_name": get_by_name(unitaries, conjugation_table),
            "conjugation_table": conjugation_table,
            "times_table": get_times_table(unitaries),
            "cz_table": get_cz_table(unitaries),
            "measurement_table": get_measurement_table()}


def human_readable(data):
    """ Format the data """
    unitaries = np.array(data["unitaries"])
    return {"decompositions": json.dumps(DECOMPOSITIONS),
            "unitaries_real": json.dumps(unitaries.real.round(5).tolist()).replace("0.70711", "ir2"),
            "unitaries_imag": json.dumps(unitaries.imag.round(5).tolist()).replace("0.70711", "ir2"),
            "conjugation_table": json.dumps(data["conjugation_table"].tolist()),
            "times_table": json.dumps(data["times_table"].tolist()),
            "cz_table": json.dumps(data["cz_table"].tolist()),
            "by_name": json.dumps(data["by_name"]),
            "measurement_table": json.dumps(data["measurement_table"].tolist())}


def write_python(data):
    """ Write the tables to a python module """
    path = join(dirname(__file__), "tables.py")
    content = PY_TEMPLATE.format(**data)
    with open(path, "w") as f:
        f.write(content)


if __name__ == '__main__':
    get_display_table(get_unitaries())
    data = compute_everything()
    data = human_readable(data)
    write_python(data)