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@@ -1,15 +1,22 @@ |
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""" |
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Enumerates the 24 elements of the local Clifford group, providing multiplication and conjugation tables |
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permutations = (id, ha, ph, ha*ph, ha*ph*ha, ha*ph*ha*ph) |
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signs = (id, px, py, pz) |
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unitaries = [p*s for p in permutations for s in signs] |
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""" |
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import numpy as np |
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from tqdm import tqdm |
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import os |
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from qi import * |
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import cPickle |
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from functools import reduce |
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from util import cache_to_disk |
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def find_up_to_phase(u): |
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""" Find the index of a given u within a list of unitaries, up to a global phase """ |
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global unitaries |
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for i, t in enumerate(unitaries): |
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for phase in range(8): |
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if np.allclose(t, np.exp(1j*phase*np.pi/4.)*u): |
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if np.allclose(t, np.exp(1j * phase * np.pi / 4.) * u): |
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return i, phase |
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raise IndexError |
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@@ -20,30 +27,20 @@ def compose_u(decomposition): |
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return np.matrix(reduce(np.dot, us), dtype=complex) |
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@cache_to_disk("tables.pkl") |
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def construct_tables(): |
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""" Constructs multiplication and conjugation tables """ |
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conjugation_table = [find_up_to_phase(u.H)[0] for i, u in enumerate(unitaries)] |
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times_table = [[find_up_to_phase(u*v)[0] for v in unitaries] |
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for u in tqdm(unitaries, "Building times-table")] |
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with open("tables.pkl", "w") as f: |
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cPickle.dump((conjugation_table, times_table), f) |
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#permutations = (id, ha, ph, ha*ph, ha*ph*ha, ha*ph*ha*ph) |
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#signs = (id, px, py, pz) |
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#unitaries = [p*s for p in permutations for s in signs] |
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decompositions = \ |
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("xxxx", "xx", "zzxx", "zz", "zxx", "z", "zzz", "xxz", |
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"xzx", "xzxxx", "xzzzx", "xxxzx", "xzz", "zzx", "xxx", "x", |
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"zzzx", "xxzx", "zx", "zxxx", "xxxz", "xzzz", "xz", "xzxx") |
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""" Constructs / caches multiplication and conjugation tables """ |
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conjugation_table = [find_up_to_phase(u.H)[0] |
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for i, u in enumerate(unitaries)] |
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times_table = [[find_up_to_phase(u * v)[0] for v in unitaries] |
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for u in tqdm(unitaries)] |
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return conjugation_table, times_table |
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# Various useful tables |
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decompositions = ("xxxx", "xx", "zzxx", "zz", "zxx", "z", "zzz", "xxz", |
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"xzx", "xzxxx", "xzzzx", "xxxzx", "xzz", "zzx", "xxx", "x", |
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"zzzx", "xxzx", "zx", "zxxx", "xxxz", "xzzz", "xz", "xzxx") |
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elements = {"x": sqx, "z": msqz} |
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unitaries = [compose_u(d) for d in decompositions] |
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# Build / reload lookup tables |
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if not os.path.exists("tables.pkl"): |
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construct_tables() |
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with open("tables.pkl") as f: |
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conjugation_table, times_table = cPickle.load(f) |
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if __name__ == '__main__': |
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pass |
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conjugation_table, times_table = construct_tables() |