/Quantum_Machine_Learning_Express

This project is one of the Qiskit mentorship programs to replicate two papers arXiv:1905.10876 and arXiv:2003.09887 using the Qiskit environment. We evaluate the parameterized quantum circuit, reproduce the expressibility and entangling capability of the 19 circuits, and the classification accuracy.

Primary LanguageJupyter NotebookMIT LicenseMIT

Enhance Qiskit papers database & replication study

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