from hamiltonians import tfi_chain
num_qubits = 8
# The simulator.
dev = qml.device('default.qubit', wires=num_qubits, analytic=True)
# The TFI model at the critical point.
h = 1.0
periodic = False
H = tfi_chain(num_qubits, h, periodic=periodic)
print(H)
# The TTN circuit.
fix_layers = False
ansatz = ttn_circuit(num_qubits, two_qubit_gate, fix_layers=fix_layers)
# The circuit for computing the expectation value of H.
cost_fn = qml.ExpvalCost(ansatz, H, dev, optimize=True)
num_params_per_gate = 15 # The number of parameters in each two-qubit gate.
depth = int(np.floor(np.log2(num_qubits))) # The depth of the TTN.
num_gates = num_qubits - 1 # The number of two-qubit gates in the TTN.
if fix_layers:
num_params = num_params_per_gate * depth
else:
num_params = num_params_per_gate * num_gates # The total number of parameters in the TTN.
# Initialize the parameters.
np.random.seed(1)
params = np.pi*(np.random.rand(num_params) - 1.0)
num_qubits = 16
# The simulator.
dev = qml.device('default.qubit', wires=num_qubits)
# The TFI model at the critical point.
h = 1.0
H = tfi_chain(num_qubits, h)
print(H)
# According to this website: https://dmrg101-tutorial.readthedocs.io/en/latest/tfim.html
# (though their Hamiltonian has a typo: it should be Pauli matrices not spin operators.)
exact_E0 = 1.0 - 1.0/np.sin(np.pi/(2.0 * (2.0 * num_qubits + 1.0)))
# The TTN circuit.
ansatz = ttn_circuit(num_qubits, simple_two_qubit_gate2)
# The circuit for computing the expectation value of H.
cost_fn = qml.ExpvalCost(ansatz, H, dev, optimize=True)
num_params_per_gate = 2 # The number of parameters in each two-qubit gate.
depth = int(np.floor(np.log2(num_qubits))) # The depth of the TTN.
num_gates = num_qubits - 1 # The number of two-qubit gates in the TTN.
num_params = num_params_per_gate * num_gates # The total number of parameters in the TTN.
# Initialize the parameters.
np.random.seed(1)
params0 = np.pi*(np.random.rand(num_params) - 1.0)
# Optimizer parameters.
rtol = 1e-5
elif args.two_qubit == "simple2":
unitary_parameterization = simple_two_qubit_gate2
num_params_per_gate = 2
elif args.two_qubit == "arbitrary":
unitary_parameterization = arb_qubit_gate
num_params_per_gate = 15
else:
raise NotImplementedError("Two Qubit Parameterization not found!")
# Choose which ansatz
if args.ansatz == "ttn":
depth = int(np.floor(np.log2(num_qubits))) # The depth of the TTN.
num_gates = num_qubits - 1 # The number of two-qubit gates in the TTN.
num_params = num_params_per_gate * num_gates # The total number of parameters in the TTN.
base_ansatz = ttn_circuit(num_qubits, unitary_parameterization)
elif args.ansatz == "mera":
periodic = args.periodic == 1
fix_layers = args.fix_layers == 1
depth = int(np.floor(np.log2(num_qubits))) # The depth of the TTN.
num_gates = get_num_mera_gates(num_qubits, periodic, fix_layers)
num_params = num_params_per_gate * num_gates
base_ansatz = mera_circuit(num_qubits,
unitary_parameterization,
periodic=periodic,
fix_layers=fix_layers)
elif args.ansatz == "hea":
hea_depth = 3
num_params = (num_qubits * hea_depth - 1) * 3
g = 0.5 # Longitudinal field
initializations = [
"Random |0...0>", "Random |+...+>", "Zero |0...0>", "Zero |+...+>"
]
data_dicts = []
for num_qubits in qubits:
print(f"=== Number of qubits = {num_qubits} ===")
dev = qml.device("default.qubit.autograd", wires=num_qubits)
constant_hea_depth = 3
ansatze = [
ttn_circuit(num_qubits),
mera_circuit(num_qubits),
hea_circuit(num_qubits),
hea_circuit(num_qubits),
hea_circuit(num_qubits)
]
num_params_ansatz = [
num_params_per_gate * get_num_ttn_gates(num_qubits),
num_params_per_gate * get_num_mera_gates(num_qubits),
3 * (num_qubits * constant_hea_depth),
3 * (num_qubits * int(np.floor(np.log2(num_qubits)))),
3 * (num_qubits * num_qubits)
]
ansatz_names = [
"TTN", "MERA", "HEA (constant)", "HEA (log)", "HEA (linear)"
]