def expT_2order_1D(nbits, dt, hbar, c):
"""
Simulate exp(-i*dt*T/hbar)
error = O(dt^2)
"""
M = c * np.asmatrix([[1, -1], [-1, 1]])
expM = qo.Qoperator(1, qo.matpowerh(np.power(np.e, -1j), (dt / hbar) * M))
expTeven = qo.directopprod(identityop(nbits - 1), expM)
P = cyperm_op(nbits)
Pinv = qo.Qoperator(nbits, P.matrix.H)
U = expTeven.matrix * P.matrix * expTeven.matrix * Pinv.matrix
return qo.Qoperator(nbits, U)
def expH_3order_1D(nbits, dt, hbar, c, expV):
"""
Simulate exp(-i*dt*T/hbar)
error = O(dt^3)
"""
M = c * np.asmatrix([[1, -1], [-1, 1]])
expM = qo.Qoperator(
1, qo.matpowerh(np.power(np.e, -1j), (0.5 * dt / hbar) * M))
expTeven = qo.directopprod(identityop(nbits - 1), expM)
P = cyperm_op(nbits)
Pinv = qo.Qoperator(nbits, P.matrix.H)
U1 = expTeven.matrix * Pinv.matrix * expTeven.matrix * P.matrix
U2 = P.matrix * expTeven.matrix * Pinv.matrix * expTeven.matrix #XXX Check correctness of U1 and U2
U = U1 * expV * U2
return qo.Qoperator(nbits, U)
def wireswitch(wire1, wire2, nbits):
"""
Switch two wires (given by the wire1 and wire2 arguments ) in a n qubit circuit
NUmbering starts from zero
"""
N = np.power(2, nbits)
w1 = np.power(2, wire1)
w2 = np.power(2, wire2)
M = np.asmatrix(np.zeros((N, N), dtype=complex))
for i in range(N):
ev = np.zeros(nbits, dtype=int)
reg1 = qr.getbasis(nbits, i)
binlist = np.array(list(bin(i)[2:]), dtype=int)
ev[nbits - binlist.size:] = binlist
j = i - ev[wire1] * w1 - ev[wire2] * w2 + ev[wire1] * w2 + ev[
wire2] * w1
reg2 = qr.getbasis(nbits, j)
M = M + outerprod(reg2, reg1)
return qo.Qoperator(nbits, M)
def switchop(nxbits, nybits):
"""
Go from row major order to column major order by wire switching
"""
nbits = nxbits + nybits
N = np.power(2, nbits)
arr = np.arange(nbits - 1, -1, -1)
powarr = pow(2, arr)
M = np.asmatrix(np.zeros((N, N), dtype=complex))
for i in range(N):
ev = np.zeros(nbits, dtype=int)
reg1 = qr.getbasis(nbits, i)
binlist = np.array(list(bin(i)[2:]), dtype=int)
ev[nbits - binlist.size:] = binlist
newbin = np.zeros(nbits, dtype=int)
#TODO CHECK CORRECTNESS OF SWAPPINGS
newbin[nxbits:] = ev[:nybits]
newbin[:nxbits] = ev[nybits:]
j = np.inner(powarr, newbin)
reg2 = qr.getbasis(nbits, j)
M = M + qr.outerprod(reg2, reg1)
return qo.Qoperator(nbits, M)
def cyperm_op(nbits):
"""
Constructing a single shift cyclic permuation operator
"""
if nbits == 1:
return qo.Qoperator(1, np.asmatrix([[0, 1], [1, 0]]))
else:
S = qo.Qoperator(1, np.asmatrix([[0, 1], [1, 0]]))
N = np.power(2, nbits)
M1 = np.asmatrix(np.zeros((N / 2, N / 2)))
M1[0, 0] = 1
M2 = np.asmatrix(np.eye(N / 2) - M1)
control0 = qo.Qoperator(nbits - 1, M1)
control1 = qo.Qoperator(nbits - 1, M2)
temp1 = qo.directopprod(S, control0)
temp2 = qo.directopprod(identityop(1), control1)
U2 = qo.Qoperator(nbits, temp1.matrix + temp2.matrix)
U1 = qo.directopprod(identityop(1), cyperm_op(nbits - 1))
U = qo.Qoperator(nbits, U2.matrix * U1.matrix)
return U
def expH_2order_2D(nxbits, nybits, dt, hbar, c, expV):
"""
Simulate exp(-i*dt*H/hbar)
error = O(dt^2)
"""
nbits = nxbits + nybits
M = c * np.asmatrix([[1, -1], [-1, 1]])
expM = qo.Qoperator(1, qo.matpowerh(np.power(np.e, -1j), (dt / hbar) * M))
expTeven = qo.directopprod(identityop(nbits - 1), expM)
P = cyperm_op(nxbits)
P1 = qo.directopprod(identityop(nybits), P)
P1inv = qo.Qoperator(nbits, P1.matrix.H)
expTodd = qo.Qoperator(nbits, P1inv.matrix * expTeven.matrix * P1.matrix)
#TODO Find a linear algebra realization of the switching opeartor
S = switchop(nxbits, nybits)
expTup = qo.Qoperator(nbits, S.matrix.H * expTeven.matrix * S.matrix)
expTdown = qo.Qoperator(nbits, S.matrix.H * expTodd.matrix * S.matrix)
U1 = expTeven.matrix * expTodd.matrix * expTup.matrix * expTdown.matrix
U = U1 * expV
return qo.Qoperator(nbits, U)
def identityop(nbits):
N = np.power(2, nbits)
return qo.Qoperator(nbits, np.asmatrix(np.eye(N)))
