Quantum Natural Language Processing (QNLP) with lambeq (Quantinuum, Inc.)

This repository is the submission entry for the "Quantum Natural Language Processing (QNLP) with lambeq" challenge provided by Quantinuum, Inc. during the first Womanium Quantum Hackathon 2022 by the team:

• Name: neiljdo
• Members: Neil John D. Ortega (neiljdo#9361, @neiljdo, [email protected])
• Presenter: Neil John D. Ortega
• Challenge: Quantum Natural Language Processing with lambeq (Quantinuum)

Available files

1. ntbks/QNLP Experiments.ipynb - this notebook contains the experiment runner function that combines the learnings from the exploratory notebook (ntbks/QNLP.ipynb) into a single function that can be parametrized to run different experiments. For asynchronous inspection of the results, the experiment runner writes its (partial) results into a JSON file that can be analyzed on its own. This is to maximize efficiency as the experiment trials can take same time, even using the jax-optimized NumpyModel class.
2. ntbks/QNLP Experiment Results.ipynb - this notebook contains the logic for processing the results from the experiment runs so that they can be rendered as plots. The main results we display are the learning curve, i.e. train/validation loss vs epochs, and the metrics curve, i.e. train/validation accuracy vs epochs.
3. ntbks/QNLP.ipynb - this notebook contains exploratory work done by the team to explore the challenge problem and, more importantly, to explore the lambeq library to be able to perform the challenge task(s).

Problem Statement

For the input, we have 2 sentences, where each sentence can be classified as exclusively either about "IT" or "Food". For the output, we are asked to determine if the two sentences are about the same topic, i.e. both about "IT" or both about "Food". More specifically, the label "1" means that both sentences are about the same topic while the label "0" means otherwise.

Can we use QNLP for this task?

Solution & Approach

We implemented the following extensions to the existing lambeq functionality to be able to perform the task.

Implement a different word ansatz

In addition to the IQP Ansatz by Havlíček et al. (2019), we use the ansatz introduced by Samuel Yen-Chi Chen et al. (2019) for deep reinforcement learning. Because only the former in included in the default lambeq package, we implemented a Customansatz class extending discopy.quantum.circuit.Circuit. We visualize a sample 3-qubit, 2-layer word ansatz below.

In addition to the custom class above, we implemented a CustomAnsatz class extending lambeq.CircuitAnsatz. This class is responsible for converting diagrams into quantum circuits. We depict a sample quantum circuit that uses the custom ansatz in the image below. It corresponds to the sentence "John cooks delicious food."

Experiment setup

Ansatz parametrization

We parametrized the ansatze with the 4-tuple (qsn, qss, pn, d), similar to the scheme by Lorenz et al. (2021). The meaning of each parameter and allowed values are as follows.

• qsn is the number of qubits for the noun atomic type, either 1 or 2.
• qss is the number of qubits for the sentence atomic type, either 1 or 2.
• pn is the number of parameters in the Euler decomposition, either 1 or 3.
• d is the depth of the word ansatz, either 1 or 2.

The values are restricted to keep the number of qubits as low as possible. For both the IQP and the custom ansatz, we try all the possible 4-tuple of parameters, resulting in 32 different model/ansatz parametrizations.

Dataset preparation

The entire dataset consists of 100 sentence pairs, each with a binary label. We created a held-out test dataset of 10 sentences to be used for final verification. The remaining 90 sentences were used in 4-repeated 5-fold cross validation scheme to control the variance of any of the results that we collected from the experiment.

Model pipeline

We trained each parametrization of the quantum circuit model on all the 20 folds for 500 epochs each. Our pipeline closely followed the pipeline of Lorenz et al. (2021) which we show below.

(Lorenz et al., 2021)

We implemented the following changes and/or restrictions to the pipeline to accomodate the problem at hand:

1. Preprocess two sentences at a time instead of a single sentence.
2. Used a custom NumpyModel class combined with jit for reasonable training times. This class implements a different forward pass to make sure that we get a probability vector for each sentence pair input. We used cosine similarity between the circuit outputs to generate these probability vectors.
3. Fixed the parser to BobcatParser.
4. Fixed the optimizer type and hyperparameters.
5. Logged training and validation costs, and training and validation accuracies for the entire experiment incrementally into a JSON file.

We summarized the entire model pipeline into a fully parametrized and customizable run_experiment function - please refer to ntbks/QNLP Experiments.ipynb for the full implementation and usage.

Results & Discussion

We processed the experiment log data in the notebook ntbks/QNLP Experiment Results.ipynb. We took the mean values across fold to generate a single plot for each ansatz parametrization. We compared the learning curves and metric curves for all ansatz parametrization per ansatz class in a single plot.

IQPAnsatz training results

CustomAnsatz training results

The best models are the ones that used the custom ansatz, with the best parametrization of (1, 1, 3, 2). This parametrization, we think, offers the right balance of number of qubits and number of trainable parameters to provide a good capacity for the model to learn. Surprisingly, too many qubits and too many trainable parameters adversely affects the training of the model. In addition, the custom ansatz also converged to near perfect validation accuracy 5x faster compared to the IQP ansatz.

After knowing the best ansatz class and parametrization, we retrained a new model that used the CustomTketModel with the Qiskit Aer backend instead. This time, the training time is way slower than the CustomNumpyModel that we limited the experiment to a single split. We chose the split where the custom ansatz with (1, 1, 3, 2) parametrization performed well. We created a similar set of plots for the final results of this single-split experiment.

Best split for CustomAnsatz(1, 1, 3, 2) based on validation accuracy is #18

Retraining results for CustomAnsatz(1, 1, 3, 2)

Future Work

We list several ideas for future extensions of this hackathon below.

1. Use a bigger dataset as the 100 rows provided could lead to overfitting easily.
2. Use a different dataset in terms of grammatical structure of the sentences.
3. Implement a different reader (as suggested in the original challenge).
4. Implement a rewrite rule (as suggested in the original challenge).
5. Extend lambeq and discopy to make creation of custom ansatze easier. After this, we can try the ansatzes listed in Yeung (2020) and see if there's a difference in the model performance.
6. Try a different task other than classification-based tasks. Some that come into mind are translation (is there a grammar algebra for translation?) or generation (not entirely sure if this is possible).
7. Try running the circuit optimization with real quantum hardware.

References

1. discopy: Qnlp tutorial. https://discopy.readthedocs.io/en/main/notebooks/qnlp-tutorial.html. Accessed: 2022-08-24.
2. lambeq: Online documentation. https://cqcl.github.io/lambeq/. Accessed: 2022-08-24.
3. Vojtech Havlıcek, Antonio D Corcoles, Kristan Temme, Aram W Harrow, Abhinav Kandala, Jerry M Chow, and Jay M Gambetta. 2019. Supervised Learning with Quantum-Enhanced Feature Spaces. Nature, 567(7747):209–212.
4. Thomas Hoffmann. Quantum models for word-sense disambiguation. https://hdl.handle.net/20.500.12380/302687. Accessed: 2022-08-24.
5. Robin Lorenz, Anna Pearson, Konstantinos Meichanetzidis, Dimitri Kartsaklis, and Bob Coecke. QNLP in practice: Running compositional models of meaning on a quantum computer. CoRR, abs/2102.12846, 2021.
6. Richie Yeung. Diagrammatic design and study of ansatze for quantum machine learning. arXiv preprint arXiv:2011.11073, 2020.