Models

Quantum Boltzmann Machine

class zyglrox.models.qbm.QuantumBoltzmannMachine(nqubits: int, qc: zyglrox.core.circuit.QuantumCircuit, pdf: numpy.ndarray, hamiltonian, optimizer=None, **kwargs)

Bases: object

Quantum Boltzmann Machine according to Kappen (2019)

Initialize

Args:

nqubits (int):

The number of qubits in the system.

qc (QuantumCircuit):

Parametrized quantum circuit for \(N\) spins.

pdf (np.ndarray):

array containing the target distribution \(q(x)\).

optimizer (tf.optimizer.Optimizer):

Tensorflow optimizer.

Returns (inplace):

None

train(eta_qbm=0.001, tol_qbm=0.0001, tol_qve=1e-08, epochs_qbm=100, epochs_qve=1500)

Train the quantum Boltzmann machine. We minimize the value of the gradient \(\frac{1}{M}\sum_i^M |\nabla_{\theta_i} \mathcal{L}(\theta)|\) as defined above

Args:

eta_qbm (float):

Learning rate for the QuantumBoltzmannMachine.

tol_qbm (float):

Tolerance \(\epsilon_{qbm}\) on the mean squared error of the statistics. If the absolute difference between iterations is smaller than this value, training stops. QuantumBoltzmannMachine.

tol_qve (float):

Tolerance \(\epsilon_{qve}\) on the energy. If the absolute difference between iterations is smaller than this value, training stops.

epochs_qbm (int):

Number of max iterations for the training algorithm of the QuantumBoltzmannMachine.

epochs_qve (int):

Number of max iterations for the training algorithm QuantumVariationalEigensolver.

Returns (inplace):

None

plot()

Plot the convergence of the QuantumBoltzmannMachine learning step. Convergence is obtained when \(\frac{1}{M}\sum_i^M |\nabla_{\theta_i} \mathcal{L}(\theta)|<\epsilon_{qbm}\), where \(\epsilon_{qbm}\) is the tolerance defined when calling the train method.

Returns (inplace):

None

get_statistics(plot=True)

Compare the statistics of learned QuantumBoltzmannMachine with the target ground state statistics.

\[\begin{split}\text{MSE}_{h} = \frac{1}{M} \sum_i^M (\langle \sigma_i \rangle - \langle \hat{\sigma}_i \rangle)^2 \\ \text{MSE}_{w} = \frac{1}{M} \sum_{i,j}^M (\langle \sigma_i \sigma_j \rangle - \langle \hat{\sigma}_i \hat{\sigma}_j\rangle)^2\end{split}\]

Warning

We do not for sure know if the QuantumVariatonalEigensolver was succesful in obtaining the ground state of the model QBM hamiltonian unless we compare it with the exact ground state first.

Args:

plot (bool):

Whether to plot the training schedule.

Returns (dict):

Dict with entries ‘field’ and ‘coupling’ with the respective MSE between the circuit and true statistics.

Quantum Variational Eigensolver

We have both a Gradient-based and Derivative-free Quantum Variational Eigensolver.

qve.QuantumVariationalEigensolver(…[, …])	Quantum Variational Eigensolver according to Peruzzo et al.(2014) with gradient based optimization..
qve.QuantumVariationalEigensolverGradFree(…)	Quantum Variational Eigensolver according to Peruzzo et al.(2014) using only gradient free optimizers..