I have implemented a quantum GAN that reproduces elements of the Bars and Stripes dataset. The Bars and Stripes dataset consists of rectangular images that contain only black or white pixels. Everything is fine image is "striped" (all pixels in the same row are of the same color) or "bar" (all pixels in the same column they are the same color). Completely black images are excluded or white. The code prints the loss of both the generator and the discriminator during learning. As the parameters are currently set, the dataset considered it is composed of 2x2 images (which are passed to the networks as vectors).
Code structure and workflow: The code consists of a MAIN which
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Load the parameters for the run from the "parameters.py" file
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Create the discriminator and generator objects, respectively imported from "Generators.py" and "Discriminator.py". In Generators.py there is both a classic generator and a quantum generator. The boolean variable "isquantum" in the parameters.py file decides which of the two is imported.
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Create the GAN object, calling the imported class from "GAN.py" (to which generator and discriminator are provided as input)
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Import the function that generates dataset elements from "utils.py"
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For each epoch iterate the training functions, printing the losses and printing an example of the vectors produced by the GAN every 20 eras.
Quantum Implementation Details:
I implemented on pennylane, with pytorch interface, a qGAN as described in the paper
https://www.nature.com/articles/s41534-019-0223-2
which represents the implementation on qiskit. In the paper, qGAN is used for loading random distributions while in our case it was applied to a generation of images. The qGAN therefore consists of a classical NN as a discriminator and by a quantum circuit as a generator. A bit string (z) is sampled from a uniform distribution e it is encoded in the state of the qubits. A dependent unit is then applied to the qubit register from trainable parameters. The output of the generator is a measure (x') of the qubit register versus to gate Z and then I get an array with values 1 and -1 matching to the black and white pixels of the image. NB: Further information on the quantum generator circuit is present in the Generators.py file.
Comments:
With a classic generator you can notice it, even after a few hundred eras, the phenomenon of mode collapse. There is no evidence to suggest that a quantum generator is capable to overcome this problem and in our tests we did not observe one convergence of the quantum generator since the training requires a lot longer than the classic counterpart. This is due to the gradient calculation method it requires for each parameter the simulation of two circuits. I spoke to an internal IBM researcher who confirmed that with 4 qubits the convergence is reached on the order of 1000 epochs even if in his case the task was the reproduction of a multimodal distribution. The choice of our task was made to have a more direct vision of work of the quantum generator given that each measurement of the qubits corresponds An image. In the case of the task of the article mentioned above or in the case of a multimodal distribution we have that the measurement of qubits is converted from binary string with decimal value creating a hierarchy between the multiple qubits significant and less significant ones making training more complicated (based on what we were told). We think that with more time available to do hyperparameter tuning it is possible to see a convergence even in the quantum case.