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Remove unused sympletic functions, remove numpy import *
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@chriseclectic
chriseclectic committed Mar 19, 2020
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Showing 1 changed file with 129 additions and 203 deletions.
332 changes: 129 additions & 203 deletions qiskit/quantum_info/operators/symplectic/symplectic_utils.py
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Original file line number Diff line number Diff line change
@@ -1,111 +1,27 @@
# -*- coding: utf-8 -*-

# Copyright 2019, IBM.
# Copyright 2017, 2020 BM.
#
# 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.

# This code is licensed under the Apache License, Version 2.0. You may
# obtain a copy of this license in the LICENSE.txt file in the root directory
# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
#
# Any modifications or derivative works of this code must retain this
# copyright notice, and modified files need to carry a notice indicating
# that they have been altered from the originals.
"""
canonical ordering of symplectic group elements
from "How to efficiently select an arbitrary clifford group element"
by Robert Koenig and John A. Smolin
Symplectic matrix group utilities.
"""

from numpy import *

def directsum(m1, m2):
""" direct sum """
n1 = len(m1[0])
n2 = len(m2[0])
output = zeros((n1+n2, n1+n2), dtype=int8)
for i in range(0, n1):
for j in range(0, n1):
output[i, j] = m1[i, j]
for i in range(0, n2):
for j in range(0, n2):
output[i+n1, j+n1] = m2[i, j]
return output

def inner(v, w):
""" symplectic inner product """
t = 0
for i in range(0, size(v)>>1):
t += v[2*i]*w[2*i+1]
t += w[2*i]*v[2*i+1]
return t%2

def transvection(k, v):
""" applies transvection Z_k to v """
return (v+inner(k, v)*k)%2

def int2bits(i, n):
""" converts integer i to an length n array of bits """
output = zeros(n, dtype=int8)
for j in range(0, n):
output[j] = i&1
i >>= 1
return output

import numpy as np

def findtransvection(x, y):
"""
finds h1,h2 such that y = Z_h1 Z_h2 x
Lemma 2 in the text
Note that if only one transvection is required output[1] will be
zero and applying the all-zero transvection does nothing.
"""
output = zeros((2, size(x)), dtype=int8)
if array_equal(x, y):
return output
if inner(x, y) == 1:
output[0] = (x+y)%2
return output
#
# find a pair where they are both not 00
z = zeros(size(x))
for i in range(0, size(x)>>1):
ii = 2*i
if ((x[ii]+x[ii+1]) != 0) and ((y[ii]+y[ii+1]) != 0): # found the pair
z[ii] = (x[ii]+y[ii])%2
z[ii+1] = (x[ii+1]+y[ii+1])%2
if (z[ii]+z[ii+1]) == 0: # they were the same so they added to 00
z[ii+1] = 1
if x[ii] != x[ii+1]:
z[ii] = 1
output[0] = (x+z)%2
output[1] = (y+z)%2
return output
# didn't find a pair
# so look for two places where x has 00 and y doesn't, and vice versa

# first y==00 and x doesn't
for i in range(0, size(x)>>1):
ii = 2*i
if ((x[ii]+x[ii+1]) != 0) and ((y[ii]+y[ii+1]) == 0): # found the pair
if x[ii] == x[ii+1]:
z[ii+1] = 1
else:
z[ii+1] = x[ii]
z[ii] = x[ii+1]
break
# NOTE: Following code needs to be heavily optimized and should probably
# be moved to a symplectic_utils.py file.

# finally x==00 and y doesn't
for i in range(0, size(x)>>1):
ii = 2*i
if ((x[ii]+x[ii+1]) == 0) and ((y[ii]+y[ii+1]) != 0): # found the pair
if y[ii] == y[ii+1]:
z[ii+1] = 1
else:
z[ii+1] = y[ii]
z[ii] = y[ii+1]
break
output[0] = (x+z)%2
output[1] = (y+z)%2
return output
###################### end findtransvction
def symplectic(i, n):
"""Output symplectic canonical matrix i of size 2nX2n
def symplectic(i, n): # output symplectic canonical matrix i of size 2nX2n
"""
Note, compared to the text the transpose of the symplectic matrix
is returned. This is not particularly important since
Transpose(g in Sp(2n)) is in Sp(2n)
Expand All @@ -118,141 +34,151 @@ def symplectic(i, n): # output symplectic canonical matrix i of size 2nX2n
as the algorithm recurses.
"""

nn = 2*n # this is convenient to have
# step 1
s = ((1<<nn)-1)
k = (i%s)+1
nn = 2 * n # this is convenient to have
# Step 1
s = ((1 << nn) - 1)
k = (i % s) + 1
i //= s
#
# step 2

# Step 2
f1 = int2bits(k, nn)
#
# step 3
e1 = zeros(nn, dtype=int8) # define first basis vectors

# Step 3
e1 = np.zeros(nn, dtype=np.int8) # define first basis vectors
e1[0] = 1
T = findtransvection(e1, f1) # use Lemma 2 to compute T
#
# step 4
T = findtransvection(e1, f1) # use Lemma 2 to compute T

# Step 4
# b[0]=b in the text, b[1]...b[2n-2] are b_3...b_2n in the text
bits = int2bits(i%(1<<(nn-1)), nn-1)
#
# step 5
eprime = copy(e1)
bits = int2bits(i % (1 << (nn - 1)), nn - 1)

# Step 5
eprime = np.copy(e1)
for j in range(2, nn):
eprime[j] = bits[j-1]
eprime[j] = bits[j - 1]
h0 = transvection(T[0], eprime)
h0 = transvection(T[1], h0)
#
# step 6

# Step 6
if bits[0] == 1:
f1 *= 0
# T' from the text will be Z_f1 Z_h0. If f1 has been set to zero
# it doesn't do anything
# We could now compute f2 as said in the text but step 7 is slightly
# changed and will recompute f1,f2 for us anyway
#
# step 7
# define the 2x2 identity matrix
id2 = zeros((2, 2), dtype=int8)
# T' from the text will be Z_f1 Z_h0. If f1 has been set to zero
# it doesn't do anything
# We could now compute f2 as said in the text but step 7 is slightly
# changed and will recompute f1,f2 for us anyway

# Step 7
# define the 2x2 identity matrix
id2 = np.zeros((2, 2), dtype=np.int8)
id2[0, 0] = 1
id2[1, 1] = 1
#

if n != 1:
g = directsum(id2, symplectic(i>>(nn-1), n-1))
g = directsum(id2, symplectic(i >> (nn - 1), n - 1))
else:
g = id2
#

for j in range(0, nn):
g[j] = transvection(T[0], g[j])
g[j] = transvection(T[1], g[j])
g[j] = transvection(h0, g[j])
g[j] = transvection(f1, g[j])
#
return g
############# end symplectic

def bits2int(b, nn):
""" converts an nn-bit string b to an integer between 0 and 2^n-1 """
output = 0
tmp = 1
for j in range(0, nn):
if b[j] == 1:
output = output+tmp
tmp = tmp*2
return output

def numberofcosets(n):
""" returns the number of different cosets """
x = power(2, 2*n-1)*(power(2, 2*n)-1)
return x

def numberofsymplectic(n):
""" returns the number of symplectic group elements """
x = 1
for j in range(1, n+1):
x = x*numberofcosets(j)
return x
return g


def symplecticinverse(n, gn):
""" produce an index associated with group element gn """
def directsum(m1, m2):
""" direct sum """
rows1, cols1 = np.shape(m1)
rows2, cols2 = np.shape(m2)
ret = np.zeros((rows1 + rows2, cols1 + cols2), dtype=m1.dtype)
ret[0:rows1, 0:cols1] = m1.copy()
ret[rows1:rows1+rows2, cols1:cols1+cols2] = m2.copy()
return ret

nn = 2*n # this is convenient to have

# step 1
v = gn[0]
w = gn[1]
def inner(v, w):
""" symplectic inner product """
# TODO: UPDATE
t = 0
for i in range(0, np.size(v) >> 1):
t += v[2 * i] * w[2 * i + 1]
t += w[2 * i] * v[2 * i + 1]
return t % 2

# step 2
e1 = zeros(nn, dtype=int8) # define first basis vectors
e1[0] = 1
T = findtransvection(v, e1) # use Lemma 2 to compute T

# step 3
tw = copy(w)
tw = transvection(T[0], tw)
tw = transvection(T[1], tw)
b = tw[0]
h0 = zeros(nn, dtype=int8)
h0[0] = 1
h0[1] = 0
for j in range(2, nn):
h0[j] = tw[j]
def transvection(k, v):
""" applies transvection Z_k to v """
return (v + inner(k, v) * k) % 2


# step 4
bb = zeros(nn-1, dtype=int8)
bb[0] = b
for j in range(2, nn):
bb[j-1] = tw[j]
zv = bits2int(v, nn)-1 # number between 0...2^(2n)-2
# indexing non-zero bitstring v of length 2n
def int2bits(i, n):
""" converts integer i to an length n array of bits """
# TODO: UPDATE
output = np.zeros(n, dtype=np.int8)
for j in range(0, n):
output[j] = i & 1
i >>= 1
return output

zw = bits2int(bb, nn-1) # number between 0..2^(2n-1)-1
#indexing w (such that v,w is symplectic pair)
cvw = zw*(power(2, 2*n)-1)+zv
# cvw is a number indexing the unique coset specified by (v,w)
# it is between 0...2^(2n-1)*(2^(2n)-1)-1=numberofcosets(n)-1

def findtransvection(x, y):
"""
finds h1,h2 such that y = Z_h1 Z_h2 x
Lemma 2 in the text
Note that if only one transvection is required output[1] will be
zero and applying the all-zero transvection does nothing.
"""
# TODO: UPDATE
output = np.zeros((2, np.size(x)), dtype=np.int8)
if np.array_equal(x, y):
return output
if inner(x, y) == 1:
output[0] = (x + y) % 2
return output

#step 5
if n == 1:
return cvw
# find a pair where they are both not 00
z = np.zeros(np.size(x))
for i in range(0, np.size(x) >> 1):
ii = 2 * i
if ((x[ii] + x[ii + 1]) != 0) and ((y[ii] + y[ii + 1]) != 0):
# found the pair
z[ii] = (x[ii] + y[ii]) % 2
z[ii + 1] = (x[ii + 1] + y[ii + 1]) % 2
if (z[ii] + z[ii + 1]) == 0:
# they were the same so they added to 00
z[ii + 1] = 1
if x[ii] != x[ii + 1]:
z[ii] = 1
output[0] = (x + z) % 2
output[1] = (y + z) % 2
return output
# didn't find a pair
# so look for two places where x has 00 and y doesn't, and vice versa

#step 6
gprime = copy(gn)
if b == 0:
for j in range(0, nn):
gprime[j] = transvection(T[1], transvection(T[0], gn[j]))
gprime[j] = transvection(h0, gprime[j])
gprime[j] = transvection(e1, gprime[j])
else:
for j in range(0, nn):
gprime[j] = transvection(T[1], transvection(T[0], gn[j]))
gprime[j] = transvection(h0, gprime[j])
# first y==00 and x doesn't
for i in range(0, np.size(x) >> 1):
ii = 2 * i
if ((x[ii] + x[ii + 1]) != 0) and ((y[ii] +
y[ii + 1]) == 0): # found the pair
if x[ii] == x[ii + 1]:
z[ii + 1] = 1
else:
z[ii + 1] = x[ii]
z[ii] = x[ii + 1]
break

# step 7
gnew = gprime[2:nn, 2:nn] # take submatrix
gnidx = symplecticinverse(n-1, gnew)*numberofcosets(n)+cvw
return gnidx
####### end symplecticinverse
# finally x==00 and y doesn't
for i in range(0, np.size(x) >> 1):
ii = 2 * i
if ((x[ii] +
x[ii + 1]) == 0) and ((y[ii] + y[ii + 1]) != 0): # found the pair
if y[ii] == y[ii + 1]:
z[ii + 1] = 1
else:
z[ii + 1] = y[ii]
z[ii] = y[ii + 1]
break
output[0] = (x + z) % 2
output[1] = (y + z) % 2
return output

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