Enhance Qiskit papers database & replication study (Youtube Link)

This project is a replication study of two papers Expressibility and entangling capability of parameterized quantum circuits for hybrid quantum-classical algorithms, arXiv:1905.10876 and Evaluation of Parameterized Quantum Circuits: on the relation between classification accuracy, expressibility and entangling capability, arXiv:2003.09887 using Qiskit environment.

We refer to the first and second paper as Th20 and Sim19, respectively. TH20 studies the relationship between the expressibility of a parameterized quantum circuit (PQC) and the accuracy attained by a simple quantum classifier based on that circuit. Sim19 defined expressibility and entangling capability of parameterized quantum circuits for hybrid quantum-classical algorithms.

The key ideas in TH20 are:

• Defining a minimal embedding for 2-dimensional data (Figure 3) using 4 qubits
• Utilizing the PQCs of Sim19 as templates for doing classification (See Figure 2 of Sim19.)
• Defining a particular aggregation function (mapping from bitstrings to classification labels)
• Utilizing L1 and L2 loss to measure error in the classifier
• Looking at both Gradient Descent and Adam optimizers for optimizing the loss function
• Utilizing 9 particular datasets on which to evaluate the classifier (Figure 2).
• TH20 utilizes the data already present in Sim19 regarding the expressibility and entangling capability of PQCs. We can do the same here.

The result of our study is:

• A replication of Figure 1 of Sim19 using the statevector simulator
• A replication of Figure 3 of Sim19 using the statevector simulator
• A replication of peice of machine learning accuracy of TH20 using pytorch connector
• Manually coded optimization algorithm

Repository Organization

The repository should contain a few different pieces:

• the data sets (dataset)
• Replication of Expressivility from Sim19 (Expressibility and entangling capability of parameterized quantum circuits)
• Replication of Machine Learning Accuracy from Th20 (Machine Learning PQC)
• Optimization code/circuits/and others (Pyfiles)

To run the code

• Please first install pytorch from https://pytorch.org/
• Install Qiskit https://qiskit.org/documentation/getting_started.html
• Install Qiskit Machin learning module