Automated qubit design for superconducting circuit topologies via autodifferentiation

In this thesis, we explore the possibility of optimizing general superconducting circuits via autodifferentiation. Following a summary of the essential components of superconducting circuits leading to a generalized expression for their Hamiltonian, we use an analytical solution for the gradient of the eigenvalues and eigenvectors to fill in a missing gradient step and form a general computational graph for arbitrary smooth loss functions that depend on circuit parameter values and its eigenvalues or eigenvectors.

After verifying numerically that the resultant gradients predicted match a first-order approximation to high precision, we leverage knowledge of the gradient to perform optimization over key metrics including the fundamental resonant frequency of the circuit, its anharmonicity, charge and flux sensitivities, and both its longitudinal and dephasing coherence times. We demonstrate by comparison of these key metrics before and after that the minimization of our objective loss functions corresponds to the intended improvement in circuit characteristics. We demonstrate concurrent optimization of each of these objectives in the flux-tunable transmon and fluxonium circuit topologies, then show that randomly sampling parameter values within some fixed range can lead to optimization on-par with SOTA experimental devices.

Finally, we assess how to address the problem of allocating truncation numbers for fixed computational resources, to maximize the convergence of the circuit eigenspectrum. Using this means of truncation number allocation, we undertake a preliminary investigation of a circuit with N = 3 inductive (Josephson junction) elements, showing that its overall performance for a small set of random samples can outperform that of both kinds of circuits with only N = 2 single-loop inductive elements. We conclude with an outlook on further applications of the tools and methodologies developed here, particularly with regards to designing better qubits for design and experimentation in-lab.