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import numpy as np
import warnings
from qutip import tensor, identity, destroy, sigmax, sigmaz, basis
from qutip.qip.circuit import QubitCircuit, Gate
from qutip.qip.models.circuitprocessor import CircuitProcessor
[docs]class DispersivecQED(CircuitProcessor):
"""
Representation of the physical implementation of a quantum
program/algorithm on a dispersive cavity-QED system.
"""
def __init__(self, N, correct_global_phase=True, Nres=None, deltamax=None,
epsmax=None, w0=None, wq=None, eps=None, delta=None, g=None):
"""
Parameters
----------
Nres: Integer
The number of energy levels in the resonator.
deltamax: Integer/List
The sigma-x coefficient for each of the qubits in the system.
epsmax: Integer/List
The sigma-z coefficient for each of the qubits in the system.
wo: Integer
The base frequency of the resonator.
wq: Integer/List
The frequency of the qubits.
eps: Integer/List
The epsilon for each of the qubits in the system.
delta: Integer/List
The epsilon for each of the qubits in the system.
g: Integer/List
The interaction strength for each of the qubit with the resonator.
"""
super(DispersivecQED, self).__init__(N, correct_global_phase)
# user definable
if Nres is None:
self.Nres = 10
else:
self.Nres = Nres
if deltamax is None:
self.sx_coeff = np.array([1.0 * 2 * np.pi] * N)
elif not isinstance(deltamax, list):
self.sx_coeff = np.array([deltamax * 2 * np.pi] * N)
else:
self.sx_coeff = np.array(deltamax)
if epsmax is None:
self.sz_coeff = np.array([9.5 * 2 * np.pi] * N)
elif not isinstance(epsmax, list):
self.sz_coeff = np.array([epsmax * 2 * np.pi] * N)
else:
self.sz_coeff = np.array(epsmax)
if w0 is None:
self.w0 = 10 * 2 * np.pi
else:
self.w0 = w0
if eps is None:
self.eps = np.array([9.5 * 2 * np.pi] * N)
elif not isinstance(eps, list):
self.eps = np.array([eps * 2 * np.pi] * N)
else:
self.eps = np.array(eps)
if delta is None:
self.delta = np.array([0.0 * 2 * np.pi] * N)
elif not isinstance(delta, list):
self.delta = np.array([delta * 2 * np.pi] * N)
else:
self.delta = np.array(delta)
if g is None:
self.g = np.array([0.01 * 2 * np.pi] * N)
elif not isinstance(g, list):
self.g = np.array([g * 2 * np.pi] * N)
else:
self.g = np.array(g)
if wq is not None:
if not isinstance(wq, list):
self.wq = np.array([wq] * N)
else:
self.wq = np.array(wq)
if wq is None:
if eps is None:
self.eps = np.array([9.5 * 2 * np.pi] * N)
elif not isinstance(eps, list):
self.eps = np.array([eps] * N)
else:
self.eps = np.array(eps)
if delta is None:
self.delta = np.array([0.0 * 2 * np.pi] * N)
elif not isinstance(delta, list):
self.delta = np.array([delta] * N)
else:
self.delta = np.array(delta)
# computed
self.wq = np.sqrt(self.eps ** 2 + self.delta ** 2)
self.Delta = self.wq - self.w0
# rwa/dispersive regime tests
if any(self.g / (self.w0 - self.wq) > 0.05):
warnings.warn("Not in the dispersive regime")
if any((self.w0 - self.wq) / (self.w0 + self.wq) > 0.05):
warnings.warn(
"The rotating-wave approximation might not be valid.")
self.sx_ops = [tensor([identity(self.Nres)] +
[sigmax() if m == n else identity(2)
for n in range(N)])
for m in range(N)]
self.sz_ops = [tensor([identity(self.Nres)] +
[sigmaz() if m == n else identity(2)
for n in range(N)])
for m in range(N)]
self.a = tensor([destroy(self.Nres)] + [identity(2) for n in range(N)])
self.cavityqubit_ops = []
for n in range(N):
sm = tensor([identity(self.Nres)] +
[destroy(2) if m == n else identity(2)
for m in range(N)])
self.cavityqubit_ops.append(self.a.dag() * sm + self.a * sm.dag())
self.psi_proj = tensor([basis(self.Nres, 0)] +
[identity(2) for n in range(N)])
[docs] def get_ops_and_u(self):
H0 = self.a.dag() * self.a
return ([H0] + self.sx_ops + self.sz_ops + self.cavityqubit_ops,
np.hstack((self.w0 * np.zeros((self.sx_u.shape[0], 1)),
self.sx_u, self.sz_u, self.g_u)))
[docs] def get_ops_labels(self):
return ([r"$a^\dagger a$"] +
[r"$\sigma_x^%d$" % n for n in range(self.N)] +
[r"$\sigma_z^%d$" % n for n in range(self.N)] +
[r"$g_{%d}$" % (n) for n in range(self.N)])
[docs] def optimize_circuit(self, qc):
self.qc0 = qc
self.qc1 = self.qc0.resolve_gates(basis=["ISWAP", "RX", "RZ"])
self.qc2 = self.dispersive_gate_correction(self.qc1)
return self.qc2
def eliminate_auxillary_modes(self, U):
return self.psi_proj.dag() * U * self.psi_proj
[docs] def dispersive_gate_correction(self, qc1, rwa=True):
"""
Method to resolve ISWAP and SQRTISWAP gates in a cQED system by adding
single qubit gates to get the correct output matrix.
Parameters
----------
qc: Qobj
The circular spin chain circuit to be resolved
rwa: Boolean
Specify if RWA is used or not.
Returns
----------
qc: QubitCircuit
Returns QubitCircuit of resolved gates for the qubit circuit in the
desired basis.
"""
qc = QubitCircuit(qc1.N, qc1.reverse_states)
for gate in qc1.gates:
qc.gates.append(gate)
if rwa:
if gate.name == "SQRTISWAP":
qc.gates.append(Gate("RZ", [gate.targets[0]], None,
arg_value=-np.pi / 4,
arg_label=r"-\pi/4"))
qc.gates.append(Gate("RZ", [gate.targets[1]], None,
arg_value=-np.pi / 4,
arg_label=r"-\pi/4"))
qc.gates.append(Gate("GLOBALPHASE", None, None,
arg_value=-np.pi / 4,
arg_label=r"-\pi/4"))
elif gate.name == "ISWAP":
qc.gates.append(Gate("RZ", [gate.targets[0]], None,
arg_value=-np.pi / 2,
arg_label=r"-\pi/2"))
qc.gates.append(Gate("RZ", [gate.targets[1]], None,
arg_value=-np.pi / 2,
arg_label=r"-\pi/2"))
qc.gates.append(Gate("GLOBALPHASE", None, None,
arg_value=-np.pi / 2,
arg_label=r"-\pi/2"))
return qc
[docs] def load_circuit(self, qc):
gates = self.optimize_circuit(qc).gates
self.global_phase = 0
self.sx_u = np.zeros((len(gates), len(self.sx_ops)))
self.sz_u = np.zeros((len(gates), len(self.sz_ops)))
self.g_u = np.zeros((len(gates), len(self.cavityqubit_ops)))
self.T_list = []
n = 0
for gate in gates:
if gate.name == "ISWAP":
t0, t1 = gate.targets[0], gate.targets[1]
self.sz_u[n, t0] = self.wq[t0] - self.w0
self.sz_u[n, t1] = self.wq[t1] - self.w0
self.g_u[n, t0] = self.g[t0]
self.g_u[n, t1] = self.g[t1]
J = self.g[t0] * self.g[t1] * (1 / self.Delta[t0] +
1 / self.Delta[t1]) / 2
T = (4 * np.pi / abs(J)) / 4
self.T_list.append(T)
n += 1
elif gate.name == "SQRTISWAP":
t0, t1 = gate.targets[0], gate.targets[1]
self.sz_u[n, t0] = self.wq[t0] - self.w0
self.sz_u[n, t1] = self.wq[t1] - self.w0
self.g_u[n, t0] = self.g[t0]
self.g_u[n, t1] = self.g[t1]
J = self.g[t0] * self.g[t1] * (1 / self.Delta[t0] +
1 / self.Delta[t1]) / 2
T = (4 * np.pi / abs(J)) / 8
self.T_list.append(T)
n += 1
elif gate.name == "RZ":
g = self.sz_coeff[gate.targets[0]]
self.sz_u[n, gate.targets[0]] = np.sign(gate.arg_value) * g
T = abs(gate.arg_value) / (2 * g)
self.T_list.append(T)
n += 1
elif gate.name == "RX":
g = self.sx_coeff[gate.targets[0]]
self.sx_u[n, gate.targets[0]] = np.sign(gate.arg_value) * g
T = abs(gate.arg_value) / (2 * g)
self.T_list.append(T)
n += 1
elif gate.name == "GLOBALPHASE":
self.global_phase += gate.arg_value
else:
raise ValueError("Unsupported gate %s" % gate.name)