def phasegate(theta):
"""
Returns quantum object representing the phase shift gate.
Parameters
----------
theta : float
Phase rotation angle.
Returns
-------
phase_gate : qobj
Quantum object representation of phase shift gate.
Examples
--------
>>> phasegate(pi/4)
Quantum object: dims = [[2], [2]], shape = [2, 2], type = oper, isHerm = False
Qobj data =
[[ 1.00000000+0.j 0.00000000+0.j ]
[ 0.00000000+0.j 0.70710678+0.70710678j]]
"""
u = qstate('u')
d = qstate('d')
Q = d * d.dag() + (exp(1.0j * theta) * u * u.dag())
return Qobj(Q)
def cnot():
"""
Quantum object representing the CNOT gate.
Returns
-------
cnot_gate : qobj
Quantum object representation of CNOT gate
Examples
--------
>>> cnot()
Quantum object: dims = [[2, 2], [2, 2]], shape = [4, 4], type = oper, isHerm = True
Qobj data =
[[ 1.+0.j 0.+0.j 0.+0.j 0.+0.j]
[ 0.+0.j 1.+0.j 0.+0.j 0.+0.j]
[ 0.+0.j 0.+0.j 0.+0.j 1.+0.j]
[ 0.+0.j 0.+0.j 1.+0.j 0.+0.j]]
"""
uu = qstate('uu')
ud = qstate('ud')
du = qstate('du')
dd = qstate('dd')
Q = dd * dd.dag() + du * du.dag() + uu * ud.dag() + ud * uu.dag()
return Qobj(Q)
def phasegate(theta):
"""
Returns quantum object representing the phase shift gate.
Parameters
----------
theta : float
Phase rotation angle.
Returns
-------
phase_gate : qobj
Quantum object representation of phase shift gate.
Examples
--------
>>> phasegate(pi/4)
Quantum object: dims = [[2], [2]], \
shape = [2, 2], type = oper, isHerm = False
Qobj data =
[[ 1.00000000+0.j 0.00000000+0.j ]
[ 0.00000000+0.j 0.70710678+0.70710678j]]
"""
u = qstate("u")
d = qstate("d")
Q = d * d.dag() + (exp(1.0j * theta) * u * u.dag())
return Qobj(Q)
def cnot():
"""
Quantum object representing the CNOT gate.
Returns
-------
cnot_gate : qobj
Quantum object representation of CNOT gate
Examples
--------
>>> cnot()
Quantum object: dims = [[2, 2], [2, 2]], \
shape = [4, 4], type = oper, isHerm = True
Qobj data =
[[ 1.+0.j 0.+0.j 0.+0.j 0.+0.j]
[ 0.+0.j 1.+0.j 0.+0.j 0.+0.j]
[ 0.+0.j 0.+0.j 0.+0.j 1.+0.j]
[ 0.+0.j 0.+0.j 1.+0.j 0.+0.j]]
"""
uu = qstate("uu")
ud = qstate("ud")
du = qstate("du")
dd = qstate("dd")
Q = dd * dd.dag() + du * du.dag() + uu * ud.dag() + ud * uu.dag()
return Qobj(Q)
def swap(N=None, control=None, target=None, mask=None):
"""Quantum object representing the SWAP gate.
Returns
-------
swap_gate : qobj
Quantum object representation of SWAP gate
Examples
--------
>>> swap()
Quantum object: dims = [[2, 2], [2, 2]], \
shape = [4, 4], type = oper, isHerm = True
Qobj data =
[[ 1.+0.j 0.+0.j 0.+0.j 0.+0.j]
[ 0.+0.j 0.+0.j 1.+0.j 0.+0.j]
[ 0.+0.j 1.+0.j 0.+0.j 0.+0.j]
[ 0.+0.j 0.+0.j 0.+0.j 1.+0.j]]
"""
if mask:
warnings.warn("The mask argument to iswap is deprecated. " +
"Use the N, control and target arguments instead.")
if sum(mask) != 2:
raise ValueError("mask must only have two ones, rest zeros")
dims = [2] * len(mask)
idx, = where(mask)
N = prod(dims)
data = sp.lil_matrix((N, N))
for s1 in state_number_enumerate(dims):
i1 = state_number_index(dims, s1)
if s1[idx[0]] == s1[idx[1]]:
i2 = i1
else:
s2 = array(s1).copy()
s2[idx[0]], s2[idx[1]] = s2[idx[1]], s2[idx[0]]
i2 = state_number_index(dims, s2)
data[i1, i2] = 1
return Qobj(data, dims=[dims, dims], shape=[N, N])
elif not N is None and not control is None and not target is None:
return gate_expand_2toN(swap(), N, control, target)
else:
uu = qstate('uu')
ud = qstate('ud')
du = qstate('du')
dd = qstate('dd')
Q = uu * uu.dag() + ud * du.dag() + du * ud.dag() + dd * dd.dag()
return Q
def swap(N=None, control=None, target=None, mask=None):
"""Quantum object representing the SWAP gate.
Returns
-------
swap_gate : qobj
Quantum object representation of SWAP gate
Examples
--------
>>> swap()
Quantum object: dims = [[2, 2], [2, 2]], \
shape = [4, 4], type = oper, isHerm = True
Qobj data =
[[ 1.+0.j 0.+0.j 0.+0.j 0.+0.j]
[ 0.+0.j 0.+0.j 1.+0.j 0.+0.j]
[ 0.+0.j 1.+0.j 0.+0.j 0.+0.j]
[ 0.+0.j 0.+0.j 0.+0.j 1.+0.j]]
"""
if mask:
warnings.warn("The mask argument to iswap is deprecated. " +
"Use the N, control and target arguments instead.")
if sum(mask) != 2:
raise ValueError("mask must only have two ones, rest zeros")
dims = [2] * len(mask)
idx, = where(mask)
N = prod(dims)
data = sp.lil_matrix((N, N))
for s1 in state_number_enumerate(dims):
i1 = state_number_index(dims, s1)
if s1[idx[0]] == s1[idx[1]]:
i2 = i1
else:
s2 = array(s1).copy()
s2[idx[0]], s2[idx[1]] = s2[idx[1]], s2[idx[0]]
i2 = state_number_index(dims, s2)
data[i1, i2] = 1
return Qobj(data, dims=[dims, dims], shape=[N, N])
elif not N is None and not control is None and not target is None:
return gate_expand_2toN(swap(), N, control, target)
else:
uu = qstate('uu')
ud = qstate('ud')
du = qstate('du')
dd = qstate('dd')
Q = uu * uu.dag() + ud * du.dag() + du * ud.dag() + dd * dd.dag()
return Q
def toffoli():
"""Quantum object representing the Toffoli gate.
Returns
-------
toff_gate : qobj
Quantum object representation of Toffoli gate.
Examples
--------
>>> toffoli()
Quantum object: dims = [[2, 2, 2], [2, 2, 2]], shape = [8, 8], type = oper, isHerm = True
Qobj data =
[[ 1.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j]
[ 0.+0.j 1.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j]
[ 0.+0.j 0.+0.j 1.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j]
[ 0.+0.j 0.+0.j 0.+0.j 1.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j]
[ 0.+0.j 0.+0.j 0.+0.j 0.+0.j 1.+0.j 0.+0.j 0.+0.j 0.+0.j]
[ 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 1.+0.j 0.+0.j 0.+0.j]
[ 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 1.+0.j]
[ 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 1.+0.j 0.+0.j]]
"""
uuu = qstate('uuu')
uud = qstate('uud')
udu = qstate('udu')
udd = qstate('udd')
duu = qstate('duu')
dud = qstate('dud')
ddu = qstate('ddu')
ddd = qstate('ddd')
Q = ddd*ddd.dag() + ddu*ddu.dag() + dud*dud.dag() + duu*duu.dag() + \
udd*udd.dag() + udu*udu.dag() + uuu*uud.dag() + uud*uuu.dag()
return Qobj(Q)
def toffoli():
"""Quantum object representing the Toffoli gate.
Returns
-------
toff_gate : qobj
Quantum object representation of Toffoli gate.
Examples
--------
>>> toffoli()
Quantum object: dims = [[2, 2, 2], [2, 2, 2]], shape = [8, 8], type = oper, isHerm = True
Qobj data =
[[ 1.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j]
[ 0.+0.j 1.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j]
[ 0.+0.j 0.+0.j 1.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j]
[ 0.+0.j 0.+0.j 0.+0.j 1.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j]
[ 0.+0.j 0.+0.j 0.+0.j 0.+0.j 1.+0.j 0.+0.j 0.+0.j 0.+0.j]
[ 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 1.+0.j 0.+0.j 0.+0.j]
[ 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 1.+0.j]
[ 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 1.+0.j 0.+0.j]]
"""
uuu = qstate('uuu')
uud = qstate('uud')
udu = qstate('udu')
udd = qstate('udd')
duu = qstate('duu')
dud = qstate('dud')
ddu = qstate('ddu')
ddd = qstate('ddd')
Q = ddd*ddd.dag() + ddu*ddu.dag() + dud*dud.dag() + duu*duu.dag() + \
udd*udd.dag() + udu*udu.dag() + uuu*uud.dag() + uud*uuu.dag()
return Qobj(Q)
def swap(mask=None):
"""Quantum object representing the SWAP gate.
Returns
-------
swap_gate : qobj
Quantum object representation of SWAP gate
Examples
--------
>>> swap()
Quantum object: dims = [[2, 2], [2, 2]], \
shape = [4, 4], type = oper, isHerm = True
Qobj data =
[[ 1.+0.j 0.+0.j 0.+0.j 0.+0.j]
[ 0.+0.j 0.+0.j 1.+0.j 0.+0.j]
[ 0.+0.j 1.+0.j 0.+0.j 0.+0.j]
[ 0.+0.j 0.+0.j 0.+0.j 1.+0.j]]
"""
if mask is None:
uu = qstate('uu')
ud = qstate('ud')
du = qstate('du')
dd = qstate('dd')
Q = uu * uu.dag() + ud * du.dag() + du * ud.dag() + dd * dd.dag()
return Qobj(Q)
else:
if sum(mask) != 2:
raise ValueError("mask must only have two ones, rest zeros")
dims = [2] * len(mask)
idx, = where(mask)
N = prod(dims)
data = sp.lil_matrix((N, N))
for s1 in state_number_enumerate(dims):
i1 = state_number_index(dims, s1)
if s1[idx[0]] == s1[idx[1]]:
i2 = i1
else:
s2 = array(s1).copy()
s2[idx[0]], s2[idx[1]] = s2[idx[1]], s2[idx[0]]
i2 = state_number_index(dims, s2)
data[i1, i2] = 1
return Qobj(data, dims=[dims, dims], shape=[N, N])
def swap(mask=None):
"""Quantum object representing the SWAP gate.
Returns
-------
swap_gate : qobj
Quantum object representation of SWAP gate
Examples
--------
>>> swap()
Quantum object: dims = [[2, 2], [2, 2]], \
shape = [4, 4], type = oper, isHerm = True
Qobj data =
[[ 1.+0.j 0.+0.j 0.+0.j 0.+0.j]
[ 0.+0.j 0.+0.j 1.+0.j 0.+0.j]
[ 0.+0.j 1.+0.j 0.+0.j 0.+0.j]
[ 0.+0.j 0.+0.j 0.+0.j 1.+0.j]]
"""
if mask is None:
uu = qstate('uu')
ud = qstate('ud')
du = qstate('du')
dd = qstate('dd')
Q = uu * uu.dag() + ud * du.dag() + du * ud.dag() + dd * dd.dag()
return Qobj(Q)
else:
if sum(mask) != 2:
raise ValueError("mask must only have two ones, rest zeros")
dims = [2] * len(mask)
idx, = where(mask)
N = prod(dims)
data = sp.lil_matrix((N, N))
for s1 in state_number_enumerate(dims):
i1 = state_number_index(dims, s1)
if s1[idx[0]] == s1[idx[1]]:
i2 = i1
else:
s2 = array(s1).copy()
s2[idx[0]], s2[idx[1]] = s2[idx[1]], s2[idx[0]]
i2 = state_number_index(dims, s2)
data[i1, i2] = 1
return Qobj(data, dims=[dims, dims], shape=[N, N])
def snot():
"""Quantum object representing the SNOT (Hadamard) gate.
Returns
-------
snot_gate : qobj
Quantum object representation of SNOT (Hadamard) gate.
Examples
--------
>>> snot()
Quantum object: dims = [[2], [2]], shape = [2, 2], type = oper, isHerm = True
Qobj data =
[[ 0.70710678+0.j 0.70710678+0.j]
[ 0.70710678+0.j -0.70710678+0.j]]
"""
u=qstate('u')
d=qstate('d')
Q=1.0/sqrt(2.0)*(d*d.dag()+u*d.dag()+d*u.dag()-u*u.dag())
return Qobj(Q)
def snot():
"""Quantum object representing the SNOT (Hadamard) gate.
Returns
-------
snot_gate : qobj
Quantum object representation of SNOT (Hadamard) gate.
Examples
--------
>>> snot()
Quantum object: dims = [[2], [2]], shape = [2, 2], type = oper, isHerm = True
Qobj data =
[[ 0.70710678+0.j 0.70710678+0.j]
[ 0.70710678+0.j -0.70710678+0.j]]
"""
u = qstate('u')
d = qstate('d')
Q = 1.0 / sqrt(2.0) * (d * d.dag() + u * d.dag() + d * u.dag() -
u * u.dag())
return Qobj(Q)
def fredkin():
"""Quantum object representing the Fredkin gate.
Returns
-------
fred_gate : qobj
Quantum object representation of Fredkin gate.
Examples
--------
>>> fredkin()
Quantum object: dims = [[2, 2, 2], [2, 2, 2]], \
shape = [8, 8], type = oper, isHerm = True
Qobj data =
[[ 1.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j]
[ 0.+0.j 1.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j]
[ 0.+0.j 0.+0.j 1.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j]
[ 0.+0.j 0.+0.j 0.+0.j 1.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j]
[ 0.+0.j 0.+0.j 0.+0.j 0.+0.j 1.+0.j 0.+0.j 0.+0.j 0.+0.j]
[ 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 1.+0.j 0.+0.j]
[ 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 1.+0.j 0.+0.j 0.+0.j]
[ 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 1.+0.j]]
"""
uuu = qstate("uuu")
uud = qstate("uud")
udu = qstate("udu")
udd = qstate("udd")
duu = qstate("duu")
dud = qstate("dud")
ddu = qstate("ddu")
ddd = qstate("ddd")
Q = (
ddd * ddd.dag()
+ ddu * ddu.dag()
+ dud * dud.dag()
+ duu * duu.dag()
+ udd * udd.dag()
+ uud * udu.dag()
+ udu * uud.dag()
+ uuu * uuu.dag()
)
return Qobj(Q)
def toffoli(N=None, control1=None, control2=None, target=None):
"""Quantum object representing the Toffoli gate.
Returns
-------
toff_gate : qobj
Quantum object representation of Toffoli gate.
Examples
--------
>>> toffoli()
Quantum object: dims = [[2, 2, 2], [2, 2, 2]], \
shape = [8, 8], type = oper, isHerm = True
Qobj data =
[[ 1.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j]
[ 0.+0.j 1.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j]
[ 0.+0.j 0.+0.j 1.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j]
[ 0.+0.j 0.+0.j 0.+0.j 1.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j]
[ 0.+0.j 0.+0.j 0.+0.j 0.+0.j 1.+0.j 0.+0.j 0.+0.j 0.+0.j]
[ 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 1.+0.j 0.+0.j 0.+0.j]
[ 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 1.+0.j]
[ 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 1.+0.j 0.+0.j]]
"""
if (not N is None and not control1 is None and not control2 is None
and not target is None):
return gate_expand_3toN(toffoli(), N, control1, control2, target)
else:
uuu = qstate('uuu')
uud = qstate('uud')
udu = qstate('udu')
udd = qstate('udd')
duu = qstate('duu')
dud = qstate('dud')
ddu = qstate('ddu')
ddd = qstate('ddd')
Q = ddd * ddd.dag() + ddu * ddu.dag() + dud * dud.dag() + \
duu * duu.dag() + udd * udd.dag() + udu * udu.dag() + \
uuu * uud.dag() + uud * uuu.dag()
return Qobj(Q)
def toffoli(N=None, control1=None, control2=None, target=None):
"""Quantum object representing the Toffoli gate.
Returns
-------
toff_gate : qobj
Quantum object representation of Toffoli gate.
Examples
--------
>>> toffoli()
Quantum object: dims = [[2, 2, 2], [2, 2, 2]], \
shape = [8, 8], type = oper, isHerm = True
Qobj data =
[[ 1.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j]
[ 0.+0.j 1.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j]
[ 0.+0.j 0.+0.j 1.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j]
[ 0.+0.j 0.+0.j 0.+0.j 1.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j]
[ 0.+0.j 0.+0.j 0.+0.j 0.+0.j 1.+0.j 0.+0.j 0.+0.j 0.+0.j]
[ 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 1.+0.j 0.+0.j 0.+0.j]
[ 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 1.+0.j]
[ 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j 1.+0.j 0.+0.j]]
"""
if (not N is None and not control1 is None
and not control2 is None and not target is None):
return gate_expand_3toN(toffoli(), N, control1, control2, target)
else:
uuu = qstate('uuu')
uud = qstate('uud')
udu = qstate('udu')
udd = qstate('udd')
duu = qstate('duu')
dud = qstate('dud')
ddu = qstate('ddu')
ddd = qstate('ddd')
Q = ddd * ddd.dag() + ddu * ddu.dag() + dud * dud.dag() + \
duu * duu.dag() + udd * udd.dag() + udu * udu.dag() + \
uuu * uud.dag() + uud * uuu.dag()
return Qobj(Q)