Pete Shadbolt
8 years ago
2 changed files with 138 additions and 139 deletions
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+138 -10abp/clifford.py
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+0 -129abp/make_tables.py
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- 10
abp/clifford.py
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| @@ -1,18 +1,146 @@ | |||||
| import numpy as np | |||||
| #!/usr/bin/python | |||||
| # -*- coding: utf-8 -*- | |||||
| """ | |||||
| This program generates lookup tables | |||||
| """ | |||||
| import os, json | import os, json | ||||
| from functools import reduce | |||||
| import itertools as it | |||||
| from . import qi | |||||
| import numpy as np | |||||
| import tempfile | |||||
| from tqdm import tqdm | |||||
| decompositions = ("xxxx", "xx", "zzxx", "zz", "zxx", "z", "zzz", "xxz", | decompositions = ("xxxx", "xx", "zzxx", "zz", "zxx", "z", "zzz", "xxz", | ||||
| "xzx", "xzxxx", "xzzzx", "xxxzx", "xzz", "zzx", "xxx", "x", | "xzx", "xzxxx", "xzzzx", "xxxzx", "xzz", "zzx", "xxx", "x", | ||||
| "zzzx", "xxzx", "zx", "zxxx", "xxxz", "xzzz", "xz", "xzxx") | "zzzx", "xxzx", "zx", "zxxx", "xxxz", "xzzz", "xz", "xzxx") | ||||
| directory = os.path.dirname(os.path.abspath(__file__)) | |||||
| where = os.path.join(directory, "tables/") | |||||
| os.chdir(where) | |||||
| unitaries = np.load("unitaries.npy") | |||||
| conjugation_table = np.load("conjugation_table.npy") | |||||
| times_table = np.load("times_table.npy") | |||||
| cz_table = np.load("cz_table.npy") | |||||
| with open("by_name.json") as f: | |||||
| by_name = json.load(f) | |||||
| def find_clifford(needle, haystack): | |||||
| """ Find the index of a given u within a list of unitaries, up to a global phase """ | |||||
| needle = normalize_global_phase(needle) | |||||
| for i, t in enumerate(haystack): | |||||
| if np.allclose(t, needle): | |||||
| return i | |||||
| raise IndexError | |||||
| def normalize_global_phase(m): | |||||
| """ Normalize the global phase of a matrix """ | |||||
| v = (x for x in m.flatten() if np.abs(x) > 0.001).next() | |||||
| phase = np.arctan2(v.imag, v.real) % np.pi | |||||
| rot = np.exp(-1j * phase) | |||||
| return rot * m if rot * v > 0 else -rot * m | |||||
| 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 = normalize_global_phase(target) | |||||
| # Choose the sets to search over | |||||
| s1 = commuters if c1 in commuters else xrange(24) | |||||
| s2 = commuters if c2 in commuters else xrange(24) | |||||
| # Find a match | |||||
| for bond, c1p, c2p in it.product([0, 1], s1, s2): | |||||
| if np.allclose(target, state_table[bond, c1p, c2p]): | |||||
| return bond, 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.sqx, "z": qi.msqz}[c] for c in decomposition) | |||||
| output = reduce(np.dot, matrices, np.eye(2, dtype=complex)) | |||||
| return normalize_global_phase(output) | |||||
| def get_unitaries(): | |||||
| """ The Clifford group """ | |||||
| return [compose_u(d) for d in decompositions] | |||||
| def get_by_name(unitaries): | |||||
| """ Get a lookup table of cliffords by name """ | |||||
| return {name: find_clifford(u, unitaries) | |||||
| for name, u in qi.by_name.items()} | |||||
| def get_conjugation_table(unitaries): | |||||
| """ Construct the conjugation table """ | |||||
| return np.array([find_clifford(qi.hermitian_conjugate(u), unitaries) for u in unitaries]) | |||||
| 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 tqdm(unitaries, desc="Building times-table")]) | |||||
| 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], range(24), range(24))) | |||||
| for bond, i, j in tqdm(params, desc="Building state table"): | |||||
| state = qi.bond if bond else qi.nobond | |||||
| kp = np.kron(unitaries[i], unitaries[j]) | |||||
| state_table[bond, i, j, :] = normalize_global_phase( | |||||
| np.dot(kp, state).T) | |||||
| return state_table | |||||
| def get_cz_table(unitaries): | |||||
| """ Compute the lookup table for the CZ (A&B eq. 9) """ | |||||
| # This is the set of Cliffords which commute with CZ | |||||
| commuters = (qi.id, qi.px, qi.pz, qi.ph, qi.hermitian_conjugate(qi.ph)) | |||||
| commuters = [find_clifford(u, unitaries) for u in commuters] | |||||
| # Get a cached state table | |||||
| state_table = get_state_table(unitaries) | |||||
| # And now build the CZ table | |||||
| cz_table = np.zeros((2, 24, 24, 3)) | |||||
| rows = list(it.product([0, 1], it.combinations(range(24), 2))) | |||||
| # CZ is symmetric so we only need combinations | |||||
| for bond, (c1, c2) in tqdm(rows, desc="Building CZ table"): | |||||
| 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 | |||||
| # First try to load tables from cache. If that fails, build them from | |||||
| # scratch and store | |||||
| os.chdir(tempfile.gettempdir()) | |||||
| try: | |||||
| unitaries = np.load("unitaries.npy") | |||||
| conjugation_table = np.load("conjugation_table.npy") | |||||
| times_table = np.load("times_table.npy") | |||||
| cz_table = np.load("cz_table.npy") | |||||
| with open("by_name.json") as f: | |||||
| by_name = json.load(f) | |||||
| print "Loaded tables from cache" | |||||
| except IOError: | |||||
| # Spend time building the tables | |||||
| unitaries = get_unitaries() | |||||
| by_name = get_by_name(unitaries) | |||||
| conjugation_table = get_conjugation_table(unitaries) | |||||
| times_table = get_times_table(unitaries) | |||||
| cz_table = get_cz_table(unitaries) | |||||
| # Write it all to disk | |||||
| np.save("unitaries.npy", unitaries) | |||||
| np.save("conjugation_table.npy", conjugation_table) | |||||
| np.save("times_table.npy", times_table) | |||||
| np.save("cz_table.npy", cz_table) | |||||
| with open("by_name.json", "wb") as f: | |||||
| json.dump(by_name, f) | |||||
+ 0
- 129
abp/make_tables.py
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| @@ -1,129 +0,0 @@ | |||||
| #!/usr/bin/python | |||||
| # -*- coding: utf-8 -*- | |||||
| """ | |||||
| This program generates lookup tables | |||||
| """ | |||||
| import os, json | |||||
| from functools import reduce | |||||
| import itertools as it | |||||
| import qi | |||||
| import numpy as np | |||||
| import tempfile | |||||
| from tqdm import tqdm | |||||
| from clifford import decompositions | |||||
| def find_clifford(needle, haystack): | |||||
| """ Find the index of a given u within a list of unitaries, up to a global phase """ | |||||
| needle = normalize_global_phase(needle) | |||||
| for i, t in enumerate(haystack): | |||||
| if np.allclose(t, needle): | |||||
| return i | |||||
| raise IndexError | |||||
| def normalize_global_phase(m): | |||||
| """ Normalize the global phase of a matrix """ | |||||
| v = (x for x in m.flatten() if np.abs(x)>0.001).next() | |||||
| phase = np.arctan2(v.imag, v.real) % np.pi | |||||
| rot = np.exp(-1j*phase) | |||||
| return rot * m if rot * v > 0 else -rot*m | |||||
| 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 = normalize_global_phase(target) | |||||
| # Choose the sets to search over | |||||
| s1 = commuters if c1 in commuters else xrange(24) | |||||
| s2 = commuters if c2 in commuters else xrange(24) | |||||
| # Find a match | |||||
| for bond, c1p, c2p in it.product([0, 1], s1, s2): | |||||
| if np.allclose(target, state_table[bond, c1p, c2p]): | |||||
| return bond, 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.sqx, "z": qi.msqz}[c] for c in decomposition) | |||||
| output = reduce(np.dot, matrices, np.eye(2, dtype=complex)) | |||||
| return normalize_global_phase(output) | |||||
| def get_unitaries(): | |||||
| """ The Clifford group """ | |||||
| return [compose_u(d) for d in decompositions] | |||||
| def get_by_name(unitaries): | |||||
| """ Get a lookup table of cliffords by name """ | |||||
| return {name: find_clifford(u, unitaries) | |||||
| for name, u in qi.by_name.items()} | |||||
| def get_conjugation_table(unitaries): | |||||
| """ Construct the conjugation table """ | |||||
| return np.array([find_clifford(qi.hermitian_conjugate(u), unitaries) for u in unitaries]) | |||||
| 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 tqdm(unitaries, desc="Building times-table")]) | |||||
| 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], range(24), range(24))) | |||||
| for bond, i, j in tqdm(params, desc="Building state table"): | |||||
| state = qi.bond if bond else qi.nobond | |||||
| kp = np.kron(unitaries[i], unitaries[j]) | |||||
| state_table[bond, i, j, :] = normalize_global_phase(np.dot(kp, state).T) | |||||
| return state_table | |||||
| def get_cz_table(unitaries): | |||||
| """ Compute the lookup table for the CZ (A&B eq. 9) """ | |||||
| # This is the set of Cliffords which commute with CZ | |||||
| commuters = (qi.id, qi.px, qi.pz, qi.ph, qi.hermitian_conjugate(qi.ph)) | |||||
| commuters = [find_clifford(u, unitaries) for u in commuters] | |||||
| # Get a cached state table | |||||
| state_table = get_state_table(unitaries) | |||||
| # And now build the CZ table | |||||
| cz_table = np.zeros((2, 24, 24, 3)) | |||||
| rows = list(it.product([0, 1], it.combinations(range(24), 2))) # CZ is symmetric so we only need combinations | |||||
| for bond, (c1, c2) in tqdm(rows, desc="Building CZ table"): | |||||
| 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 | |||||
| if __name__ == "__main__": | |||||
| # Spend time building the tables | |||||
| unitaries = get_unitaries() | |||||
| by_name = get_by_name(unitaries) | |||||
| conjugation_table = get_conjugation_table(unitaries) | |||||
| times_table = get_times_table(unitaries) | |||||
| cz_table = get_cz_table(unitaries) | |||||
| # Write it all to disk | |||||
| where = tempfile.gettempdir() | |||||
| np.save("unitaries.npy", unitaries) | |||||
| np.save("conjugation_table.npy", conjugation_table) | |||||
| np.save("times_table.npy", times_table) | |||||
| np.save("cz_table.npy", cz_table) | |||||
| with open("by_name.json", "wb") as f: | |||||
| json.dump(by_name, f) | |||||