Performance and Noise Levels of Grover’s Algorithm on Quantum Computers with Different Qubit Connectivities

Sammanfattning

In this thesis, we study the impact of qubit connectivity on the performance and error rate of Grover’s algorithm. The methods of our investigation consist of utilising IBM Qiskit to construct, transpile and run a 3-qubit single-iteration Grover’s algorithm circuit that requires 2 ancilla qubits. This 5-qubit construction was run on all possible 5-qubit connectivities with varying noise models, Qiskit optimisation levels and marked elements. Several versions of the circuit were run on 6 of IBM Qiskit’s fake providers to further reinforce our results. Our findings were that qubit connectivity significantly affects the depth of the circuit, but there seem to be other factors that are more impactful on the error rate of the execution. These factors include basis gate sets and different error types. We conclude that our findings align with that of previous research and may further help the design of efficient and high-performing quantum computer architectures. Finally, we propose that future studies should focus on what factors are mostly affecting the error rates of circuits to develop a complete picture of what affects measurement results.