At least we have infinite-size graphs nowmaster
@@ -1,14 +0,0 @@ | |||||
""" This part computes the CZ table """ | |||||
from util import cache_to_disk | |||||
import qi | |||||
import numpy as np | |||||
from tqdm import tqdm | |||||
import clifford | |||||
#@cache_to_disk("cz_table.pkl") | |||||
def construct_table(): | |||||
print "awd" | |||||
return "awd" | |||||
cz_table = construct_table() |
@@ -4,68 +4,75 @@ Provides an extremely basic graph structure, based on neighbour lists | |||||
from collections import defaultdict | from collections import defaultdict | ||||
import itertools as it | import itertools as it | ||||
import clifford | |||||
def graph(): | |||||
""" Generate a graph with Hadamards on each qubit """ | |||||
#return defaultdict(set), defaultdict(lambda: clifford.by_name["hadamard"]) | |||||
return [set() for i in range(100)], [clifford.by_name["hadamard"] for i in range(100)] | |||||
def add_edge(graph, v1, v2): | |||||
""" Add an edge between two vertices in the graph """ | |||||
graph[v1].add(v2) | |||||
graph[v2].add(v1) | |||||
def del_edge(graph, v1, v2): | |||||
""" Delete an edge between two vertices in the graph """ | |||||
graph[v1].remove(v2) | |||||
graph[v2].remove(v1) | |||||
def has_edge(graph, v1, v2): | |||||
""" Test existence of an edge between two vertices in the graph """ | |||||
return v2 in graph[v1] | |||||
def toggle_edge(graph, v1, v2): | |||||
""" Toggle an edge between two vertices in the graph """ | |||||
if has_edge(graph, v1, v2): | |||||
del_edge(graph, v1, v2) | |||||
else: | |||||
add_edge(graph, v1, v2) | |||||
def edgelist(g): | |||||
""" Describe a graph as an edgelist """ | |||||
edges = frozenset(frozenset((i, n)) | |||||
for i, v in enumerate(g) | |||||
for n in v) | |||||
return [tuple(e) for e in edges] | |||||
def cphase(g, vops, a, b): | |||||
""" Act a controlled-phase gate on two qubits """ | |||||
if g[a]-{b}: remove_vop(g, vops, a, b) | |||||
if g[b]-{a}: remove_vop(g, vops, b, a) | |||||
if g[a]-{b}: remove_vop(g, vops, a, b) | |||||
edge = has_edge(g, a, b) | |||||
new_edge, vops[a], vops[b] = cphase_table[edge, vops[a], vops[b]] | |||||
if new_edge != edge: | |||||
toggle_edge(g, a, b) | |||||
def remove_vop(g, vops, a, avoid): | |||||
""" Reduces VOP[a] to the identity, avoiding (if possible) the use of vertex b as a swapping partner """ | |||||
others = g[a] - {avoid} | |||||
swap_qubit = others.pop() if others else avoid | |||||
for v in reversed(clifford.decompositions[vops[a]]): | |||||
local_complementation(g, vops, a if v == "x" else swap_qubit) | |||||
def local_complementation(g, vops, v): | |||||
""" As defined in LISTING 1 of Anders & Briegel """ | |||||
for i, j in it.combinations(g[v], 2): | |||||
toggle_edge(g, i, j) | |||||
# Update VOPs | |||||
vops[v] = clifford.times_table[vops[v]][clifford.by_name["sqx"]] | |||||
for i in g[v]: | |||||
vops[i] = clifford.times_table[vops[i]][clifford.by_name["msqz"]] | |||||
import tables as clifford | |||||
class GraphState(object): | |||||
def __init__(self): | |||||
self.ngbh = defaultdict(set) | |||||
self.vops = defaultdict(int) | |||||
def add_edge(self, v1, v2): | |||||
""" Add an edge between two vertices in the self """ | |||||
if not v1 in self.ngbh: self.vops[v1] = clifford.by_name["hadamard"] | |||||
if not v2 in self.ngbh: self.vops[v2] = clifford.by_name["hadamard"] | |||||
self.ngbh[v1].add(v2) | |||||
self.ngbh[v2].add(v1) | |||||
def del_edge(self, v1, v2): | |||||
""" Delete an edge between two vertices in the self """ | |||||
self.ngbh[v1].remove(v2) | |||||
self.ngbh[v2].remove(v1) | |||||
def has_edge(self, v1, v2): | |||||
""" Test existence of an edge between two vertices in the self """ | |||||
return v2 in self.ngbh[v1] | |||||
def toggle_edge(self, v1, v2): | |||||
""" Toggle an edge between two vertices in the self """ | |||||
if self.has_edge(v1, v2): | |||||
self.del_edge(v1, v2) | |||||
else: | |||||
self.add_edge(v1, v2) | |||||
def edgelist(self): | |||||
""" Describe a graph as an edgelist """ | |||||
edges = frozenset(frozenset((i, n)) | |||||
for i, v in enumerate(self.ngbh.values()) | |||||
for n in v) | |||||
return [tuple(e) for e in edges] | |||||
def remove_vop(self, a, avoid): | |||||
""" Reduces VOP[a] to the identity, avoiding (if possible) the use of vertex b as a swapping partner """ | |||||
others = self.ngbh[a] - {avoid} | |||||
swap_qubit = others.pop() if others else avoid | |||||
for v in reversed(clifford.decompositions[self.vops[a]]): | |||||
self.local_complementation(a if v == "x" else swap_qubit) | |||||
def cphase(self, a, b): | |||||
""" Act a controlled-phase gate on two qubits """ | |||||
if self.ngbh[a] - {b}: | |||||
self.remove_vop(a, b) | |||||
if self.ngbh[b] - {a}: | |||||
self.remove_vop(b, a) | |||||
if self.ngbh[a] - {b}: | |||||
self.remove_vop(a, b) | |||||
edge = self.has_edge(a, b) | |||||
new_edge, vops[a], vops[b] = cphase_table[edge, vops[a], vops[b]] | |||||
if new_edge != edge: | |||||
self.toggle_edge(a, b) | |||||
def local_complementation(self, v): | |||||
""" As defined in LISTING 1 of Anders & Briegel """ | |||||
for i, j in it.combinations(self.ngbh[v], 2): | |||||
self.toggle_edge(i, j) | |||||
# Update VOPs | |||||
self.vops[v] = clifford.times_table[self.vops[v]][clifford.by_name["sqx"]] | |||||
for i in self.ngbh[v]: | |||||
self.vops[i] = clifford.times_table[self.vops[i]][clifford.by_name["msqz"]] | |||||
@@ -9,7 +9,21 @@ import numpy as np | |||||
from tqdm import tqdm | from tqdm import tqdm | ||||
import qi | import qi | ||||
from functools import reduce | from functools import reduce | ||||
from util import cache_to_disk | |||||
import cPickle | |||||
def cache_to_disk(file_name): | |||||
""" A decorator to cache the output of a function to disk """ | |||||
def wrap(func): | |||||
def modified(*args, **kwargs): | |||||
try: | |||||
output = cPickle.load(open(file_name, "r")) | |||||
except (IOError, ValueError): | |||||
output = func(*args, **kwargs) | |||||
with open(file_name, "w") as f: | |||||
cPickle.dump(output, f) | |||||
return output | |||||
return modified | |||||
return wrap | |||||
# TODO: make this more efficient / shorter | # TODO: make this more efficient / shorter | ||||
@@ -27,12 +41,13 @@ def compose_u(decomposition): | |||||
us = (elements[c] for c in decomposition) | us = (elements[c] for c in decomposition) | ||||
return np.matrix(reduce(np.dot, us), dtype=complex) | return np.matrix(reduce(np.dot, us), dtype=complex) | ||||
def name_of(vop): | def name_of(vop): | ||||
""" Get the formatted name of a VOP """ | """ Get the formatted name of a VOP """ | ||||
return "%s" % get_name[vop] if vop in get_name else "VOP%d" % vop | return "%s" % get_name[vop] if vop in get_name else "VOP%d" % vop | ||||
@cache_to_disk("clifford_tables.pkl") | |||||
@cache_to_disk("tables.cache") | |||||
def construct_tables(): | def construct_tables(): | ||||
""" Constructs / caches multiplication and conjugation tables """ | """ Constructs / caches multiplication and conjugation tables """ | ||||
by_name = {name: find_up_to_phase(u)[0] for name, u in qi.by_name.items()} | by_name = {name: find_up_to_phase(u)[0] for name, u in qi.by_name.items()} | ||||
@@ -41,13 +56,14 @@ def construct_tables(): | |||||
for i, u in enumerate(unitaries)] | for i, u in enumerate(unitaries)] | ||||
times_table = [[find_up_to_phase(u * v)[0] for v in unitaries] | times_table = [[find_up_to_phase(u * v)[0] for v in unitaries] | ||||
for u in tqdm(unitaries)] | for u in tqdm(unitaries)] | ||||
return by_name, get_name, conjugation_table, times_table | |||||
cz_table = None | |||||
return by_name, get_name, conjugation_table, times_table, cz_table | |||||
# Various useful tables | |||||
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") | ||||
elements = {"x": qi.sqx, "z": qi.msqz} | elements = {"x": qi.sqx, "z": qi.msqz} | ||||
unitaries = [compose_u(d) for d in decompositions] | unitaries = [compose_u(d) for d in decompositions] | ||||
by_name, get_name, conjugation_table, times_table = construct_tables() | |||||
by_name, get_name, conjugation_table, times_table, cz_table = construct_tables() | |||||
@@ -1,4 +1,4 @@ | |||||
import clifford as lc | |||||
import tables as lc | |||||
from numpy import * | from numpy import * | ||||
from scipy.linalg import sqrtm | from scipy.linalg import sqrtm | ||||
import qi | import qi | ||||
@@ -1,51 +1,52 @@ | |||||
from graph import * | |||||
from graph import GraphState | |||||
import tables as lc | |||||
def test_graph(): | def test_graph(): | ||||
g, v = graph() | |||||
add_edge(g, 0,1) | |||||
add_edge(g, 1,2) | |||||
add_edge(g, 2,0) | |||||
assert g[0]==set([1,2]) | |||||
g = GraphState() | |||||
g.add_edge(0,1) | |||||
g.add_edge(1,2) | |||||
g.add_edge(2,0) | |||||
assert g.ngbh[0]==set([1,2]) | |||||
del_edge(g, 0,1) | |||||
assert g[0]==set([2]) | |||||
el = edgelist(g) | |||||
g.del_edge(0,1) | |||||
assert g.ngbh[0]==set([2]) | |||||
el = g.edgelist() | |||||
assert (1,2) in el | assert (1,2) in el | ||||
assert not (0,1) in el | assert not (0,1) in el | ||||
assert len(el)==2 | assert len(el)==2 | ||||
assert has_edge(g, 1,2) | |||||
assert not has_edge(g, 0,1) | |||||
assert g.has_edge(1,2) | |||||
assert not g.has_edge(0,1) | |||||
def test_local_complementation(): | def test_local_complementation(): | ||||
""" Test that local complementation works as expected """ | """ Test that local complementation works as expected """ | ||||
g, vops = graph() | |||||
add_edge(g, 0, 1) | |||||
add_edge(g, 0, 2) | |||||
add_edge(g, 1, 2) | |||||
add_edge(g, 0, 3) | |||||
local_complementation(g, vops, 0) | |||||
assert has_edge(g, 0, 1) | |||||
assert has_edge(g, 0, 2) | |||||
assert not has_edge(g, 1, 2) | |||||
assert has_edge(g, 3, 2) | |||||
assert has_edge(g, 3, 1) | |||||
g = GraphState() | |||||
g.add_edge(0,1) | |||||
g.add_edge(1,2) | |||||
g.add_edge(2,0) | |||||
g.add_edge(0,3) | |||||
g.local_complementation(0) | |||||
assert g.has_edge(0, 1) | |||||
assert g.has_edge(0, 2) | |||||
assert not g.has_edge(1, 2) | |||||
assert g.has_edge(3, 2) | |||||
assert g.has_edge(3, 1) | |||||
# TODO: test VOP conditions | # TODO: test VOP conditions | ||||
def test_remove_vop(): | def test_remove_vop(): | ||||
""" Test that removing VOPs really works """ | """ Test that removing VOPs really works """ | ||||
g, vops = graph() | |||||
add_edge(g, 0, 1) | |||||
add_edge(g, 0, 2) | |||||
add_edge(g, 1, 2) | |||||
add_edge(g, 0, 3) | |||||
remove_vop(g, vops, 0, 1) | |||||
assert vops[0] == clifford.by_name["identity"] | |||||
remove_vop(g, vops, 1, 1) | |||||
assert vops[1] == clifford.by_name["identity"] | |||||
remove_vop(g, vops, 2, 1) | |||||
assert vops[2] == clifford.by_name["identity"] | |||||
remove_vop(g, vops, 0, 1) | |||||
assert vops[0] == clifford.by_name["identity"] | |||||
g = GraphState() | |||||
g.add_edge(0,1) | |||||
g.add_edge(1,2) | |||||
g.add_edge(2,0) | |||||
g.add_edge(0,3) | |||||
g.remove_vop(0, 1) | |||||
assert g.vops[0] == lc.by_name["identity"] | |||||
g.remove_vop(1, 1) | |||||
assert g.vops[1] == lc.by_name["identity"] | |||||
g.remove_vop(2, 1) | |||||
assert g.vops[2] == lc.by_name["identity"] | |||||
g.remove_vop(0, 1) | |||||
assert g.vops[0] == lc.by_name["identity"] | |||||
@@ -0,0 +1,11 @@ | |||||
from graph import GraphState | |||||
import viz | |||||
def test_viz(): | |||||
g = GraphState() | |||||
g.add_edge(0,1) | |||||
g.add_edge(1,2) | |||||
g.add_edge(2,0) | |||||
g.add_edge(0,3) | |||||
print g.vops | |||||
viz.draw(g) |
@@ -1,14 +1,7 @@ | |||||
""" | """ | ||||
Useful but messy crap | Useful but messy crap | ||||
""" | """ | ||||
import cPickle | |||||
import networkx as nx | |||||
from matplotlib import pyplot as plt | |||||
from graph import * | |||||
import clifford | |||||
import numpy as np | |||||
VOP_COLORS = ["red", "green", "blue", "orange", "yellow", "purple", "black", "white"] | |||||
def cache_to_disk(file_name): | def cache_to_disk(file_name): | ||||
""" A decorator to cache the output of a function to disk """ | """ A decorator to cache the output of a function to disk """ | ||||
@@ -25,21 +18,3 @@ def cache_to_disk(file_name): | |||||
return wrap | return wrap | ||||
def draw(graph, vops, filename="out.pdf", pos=None, ns=500): | |||||
""" Draw a graph with networkx layout """ | |||||
plt.clf() | |||||
g = nx.from_edgelist(edgelist(graph)) | |||||
pos = nx.spring_layout(g) if pos==None else pos | |||||
colors = [VOP_COLORS[vop % len(VOP_COLORS)] for vop in vops] | |||||
nx.draw_networkx_nodes(g, pos, node_color="white", node_size=ns) | |||||
nx.draw_networkx_nodes(g, pos, node_color=colors, node_size=ns, alpha=.4) | |||||
nx.draw_networkx_edges(g, pos, edge_color="gray") | |||||
nx.draw_networkx_labels(g, pos, font_family="FreeSans") | |||||
labels = {i: clifford.name_of(vops[i]) for i in g.nodes()} | |||||
pos = {k: v + np.array([0, -.1]) for k, v in pos.items()} | |||||
nx.draw_networkx_labels(g, pos, labels, font_family="FreeSans") | |||||
plt.axis('off') | |||||
plt.savefig(filename) | |||||
return pos | |||||
@@ -0,0 +1,25 @@ | |||||
import networkx as nx | |||||
from matplotlib import pyplot as plt | |||||
import tables | |||||
import numpy as np | |||||
from graph import GraphState | |||||
VOP_COLORS = ["red", "green", "blue", "orange", "yellow", "purple", "black", "white"] | |||||
def draw(state, filename="out.pdf", pos=None, ns=500): | |||||
""" Draw a graph with networkx layout """ | |||||
plt.clf() | |||||
graph = nx.from_edgelist(state.edgelist()) | |||||
pos = nx.spring_layout(graph) if pos==None else pos | |||||
colors = [VOP_COLORS[vop % len(VOP_COLORS)] for vop in state.vops.values()] | |||||
nx.draw_networkx_nodes(graph, pos, node_color="white", node_size=ns) | |||||
nx.draw_networkx_nodes(graph, pos, node_color=colors, node_size=ns, alpha=.4) | |||||
nx.draw_networkx_edges(graph, pos, edge_color="gray") | |||||
nx.draw_networkx_labels(graph, pos, font_family="FreeSans") | |||||
labels = {i: tables.name_of(v) for i, v in state.vops.items()} | |||||
pos = {k: v + np.array([0, -.1]) for k, v in pos.items()} | |||||
nx.draw_networkx_labels(graph, pos, labels, font_family="FreeSans") | |||||
plt.axis('off') | |||||
plt.savefig(filename) | |||||
return pos |