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