Abstract

Superconducting qubits are one of the most promising platforms for the construc-tion of quantum computers. The state-of-the-art qubits and associated control gates are unfortunately still too prone to errors for general purpose quantum computing to be feasible. However, the circuits used to build the qubits can already be utilised in analogue quantum simulation. That is, they can be used as a building block of relatively simple and easy to control quantum mechanical device, used to emulate some aspects of more complicated systems. Here we focus specifically on the transmon, which is currently the most common qubit design. The few lowest energy levels of transmons can be described as an anharmonic oscillator. While the anharmonicity allows the two lowest levels to be used as a qubit, that does not mean that the higher levels should necessarily be neglected. Beyond the two-level approximation, the behaviour of transmon arrays can be well approximated with the Bose–Hubbard model with attractive interactions. Here we discuss analytical and numerical studies of the model, focusing on the higher excited levels of transmons.

We begin by constructing ground state phase diagrams of the attractive model for constant numbers of bosons, including the effect of disorder, an unavoidable feature of manufactured devices. In the phase diagrams we find three distinct phases: the localised phase at strong disorder, the superfluid phase at high hopping frequencies, and the W phase when both disorder and hopping are dominated by the attractive interactions. Next, we study the dynamics of the model, utilising the wide-gapped band structure of the Bose–Hubbard spectrum. We describe the dynamics within each band with a compact and unified framework based on high-order degenerate perturbation theory. The unitary dynamics effectively occur within a single band, resulting in various forms of collective behaviour, such as bosons on a single site moving as a single quasiparticle and effective longer-range interactions between multiple quasiparticles. Finally, to account for the imperfect isolation of the transmons from their environment, we include dissipation and dephasing into our model of the dynamics. We provide analytical descriptions on how the environment affects the dynamics within the bands, and causes transitions between them.

Osajulkaisut / Original papers

Osajulkaisut eivät sisälly väitöskirjan elektroniseen versioon. / Original papers are not included in the electronic version of the dissertation.

1. Mansikkamäki, O., Laine, S., & Silveri, M. (2021). Phases of the disordered Bose-Hubbard model with attractive interactions. Physical Review B, 103(22), L220202. https://doi.org/10.1103/PhysRevB.103.L220202

   Rinnakkaistallennettu versio / Self-archived version

2. Mansikkamäki, O., Laine, S., Piltonen, A., & Silveri, M. (2022). Beyond hard-core bosons in transmon arrays. PRX Quantum, 3(4), 040314. https://doi.org/10.1103/PRXQuantum.3.040314

   Rinnakkaistallennettu versio / Self-archived version

3. Busel, O., Laine, S., Mansikkamäki, O., & Silveri, M. (2023). Dissipation and dephasing of interacting photons in transmon arrays. Manuscript submitted for publication.