def S2Proj(Quket, Q, threshold=1e-8):
"""Function
Perform spin-projection to QuantumState |Q>
|Q'> = Ps |Q>
where Ps is a spin-projection operator (non-unitary).
Ps = \sum_i^ng wg[i] Ug[i]
This function provides a shortcut to |Q'>, which is unreal.
One actually needs to develop a quantum circuit for this
(See PRR 2, 043142 (2020)).
Author(s): Takashi Tsuchimochi
"""
spin = Quket.projection.spin
s = (spin - 1) / 2
Ms = Quket.projection.Ms / 2
n_qubits = Q.get_qubit_count()
state_P = QuantumState(n_qubits)
state_P.multiply_coef(0)
nalpha = max(Quket.projection.euler_ngrids[0], 1)
nbeta = max(Quket.projection.euler_ngrids[1], 1)
ngamma = max(Quket.projection.euler_ngrids[2], 1)
for ialpha in range(nalpha):
alpha = Quket.projection.sp_angle[0][ialpha]
alpha_coef = Quket.projection.sp_weight[0][ialpha] * np.exp(
1j * alpha * Ms)
for ibeta in range(nbeta):
beta = Quket.projection.sp_angle[1][ibeta]
beta_coef = (Quket.projection.sp_weight[1][ibeta] *
Quket.projection.dmm[ibeta])
for igamma in range(ngamma):
gamma = Quket.projection.sp_angle[2][igamma]
gamma_coef = (Quket.projection.sp_weight[2][igamma] *
np.exp(1j * gamma * Ms))
# Total Weight
coef = (2 * s + 1) / (8 * np.pi) * (alpha_coef * beta_coef *
gamma_coef)
state_g = QuantumState(n_qubits)
state_g.load(Q)
circuit_Rg = QuantumCircuit(n_qubits)
set_circuit_Rg(circuit_Rg, n_qubits, alpha, beta, gamma)
circuit_Rg.update_quantum_state(state_g)
state_g.multiply_coef(coef)
state_P.add_state(state_g)
# Normalize
norm2 = state_P.get_squared_norm()
if norm2 < threshold:
error(
"Norm of spin-projected state is too small!\n",
"This usually means the broken-symmetry state has NO component ",
"of the target spin.")
state_P.normalize(norm2)
# print_state(state_P,name="P|Q>",threshold=1e-6)
return state_P
def NProj(Quket, Q, threshold=1e-8):
"""Function
Perform number-projection to QuantumState |Q>
|Q'> = PN |Q>
where PN is a number-projection operator (non-unitary).
PN = \sum_i^ng wg[i] Ug[i]
This function provides a shortcut to |Q'>, which is unreal.
One actually needs to develop a quantum circuit for this
(See QST 6, 014004 (2021)).
Author(s): Takashi Tsuchimochi
"""
n_qubits = Q.get_qubit_count()
state_P = QuantumState(n_qubits)
state_P.multiply_coef(0)
state_g = QuantumState(n_qubits)
nphi = max(Quket.projection.number_ngrids, 1)
#print_state(Q)
for iphi in range(nphi):
coef = (Quket.projection.np_weight[iphi] *
np.exp(1j * Quket.projection.np_angle[iphi] *
(Quket.projection.n_active_electrons -
Quket.projection.n_active_orbitals)))
state_g = Q.copy()
circuit = QuantumCircuit(n_qubits)
set_circuit_ExpNa(circuit, n_qubits, Quket.projection.np_angle[iphi])
set_circuit_ExpNb(circuit, n_qubits, Quket.projection.np_angle[iphi])
circuit.update_quantum_state(state_g)
state_g.multiply_coef(coef)
state_P.add_state(state_g)
norm2 = state_P.get_squared_norm()
if norm2 < threshold:
error(
"Norm of number-projected state is too small!\n",
"This usually means the broken-symmetry state has NO component ",
"of the target number.")
state_P.normalize(norm2)
return state_P
