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learning the mixed state by qWGAN

This file outlines the procedure to learn mixed states using the qWGAN framwork. Example settings are provided in the configuration file config_mixed.py

Preparation

  1. Create a random mixed quantum state which is an ensemble of two pure states as our target state
input_state = list()
angle = np.random.randint(1,10,size=[cf.num_to_mix,cf.system_size,3])
for i in range(cf.num_to_mix):
    matrix = Identity(cf.system_size)
    for j in range(cf.system_size):
        row_i_mat = np.matmul(Z_Rotation(cf.system_size, j, np.pi * angle[i][j][2], False),
                              np.matmul(Y_Rotation(cf.system_size, j, np.pi * angle[i][j][1], False),
                                        X_Rotation(cf.system_size, j, np.pi * angle[i][j][0], False)))
        matrix = np.matmul(row_i_mat, matrix)
    state = np.matmul(matrix, zero_state)
    input_state.append(np.asmatrix(state))
prob_real = [0.2, 0.8]
real_state = getreal_denmat(cf,prob_real,input_state)
  1. Define the Generator and Discriminator
  • Create an instance of the generator
gen = Generator(cf.system_size, cf.num_to_mix)
  • Construct and assign a quantum circuit as the generator
gen.set_qcircuit(construct_qcircuit(qc_list_gen, cf.system_size))
  • Create an instance of the Discriminator

Define the set of Hermitian matrices whose linear combination is used in the discriminator.

herm = [I, X, Y, Z]
    dis = Discriminator(herm, cf.system_size)

Training

Alternately update the parameters of Generator and Discriminator until the fidelity between the generated quantum state and target state converges to 1.

gen.update_gen(dis,real_state)
dis.update_dis(gen,real_state)

Save the model and plot the figure

After training, the generator and discriminator weights can be saved
``` python
save_model(gen, cf.model_gen_path)
save_model(dis, cf.model_gen_path)

and the training loss and fidelity curves can be plotted

plt_fidelity_vs_iter(fidelities, losses, cf)

Output

the fidelity curve and loss curve of 2 qubits mixed state learning task Alt text