Bachelor defense by Ulrik S. Andersen

Connectivity-Aware Error Mitigation Approaches - Using IBM Quantum and qiskit in investigating simple Hamiltonians

In this project, three different problem instances are used as the basis for investigating connectivity-aware mappings of qubits as to mitigate errors inherent in the current state of hardware at IBM Quantum. Analysing the Greenberger-Horne-Zeilinger-state (GHZ-state) is a first step into understanding the impact of including noise in simulated hardware and transpiling circuits onto different layouts of qubits. Quantum Phase Estimation (QPE) is used for finding the eigenphase of a unitary operator; in this case, a time evolution of a Hamiltonian. It is concluded that the current state of quantum hardware, combined with the available error mitigation schemes, are not ready for the Hamiltonians used in QPE for this project. Finally, the groundstate energy of Lithium hydride is estimated using the classical-quantum hybrid algorithm variational quantum eigensolver (VQE). The VQE is the premise for analysing different initial states, optimisers, ans¨ atze, interaction graphs and layouts on noisy simulators and real hardware. The project concludes that IBM Quantum’s processors and their implementation of VQE are not yet ready for simple molecules, as implemeted in this project, and are not resilient enough for the current limitations in running time.