University of Oulu

Numerical simulation of a continuously measured transmon array

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Author: Tolppanen, Taneli1
Organizations: 1University of Oulu, Faculty of Science, Physics
Format: ebook
Version: published version
Access: open
Online Access: PDF Full Text (PDF, 10.2 MB)
Pages: 64
Persistent link:
Language: English
Published: Oulu : T. Tolppanen, 2022
Publish Date: 2022-06-22
Thesis type: Master's thesis
Tutor: Silveri, Matti
Reviewer: Martin Vazquez, Gonzalo
Silveri, Matti


In this thesis continuous measurement is first introduced in the context of optical physics, and the derivation for the stochastic differential equations for quantum jumps, homodyne and heterodyne measurement is shown in outline. To study continuous measurement in superconducting circuits, the transmon device is introduced. The Bose-Hubbard model is used to model interacting transmons in an array. The circuit functionality needed for the measurement and control of transmons in a superconducting circuit is discussed. The stochastic master equation and the stochastic Schrödinger equation for the heterodyne measurement of transmons is provided. A guide for using the programming language Julia with the differential equations package to solve the continuous measurement problems is given, and the suitability of Julia for numerically simulating continuous measurement is examined. Julia is found to be efficient and a great tool for solving stochastic differential equations when used together with the differential equations package. To further demonstrate the capabilities of the numerical program implemented, we model five transmons, where the transmon in the middle is being continuously measured. We plot the boson number at the middle and at the end of the array. Furthermore, we plot the entanglement entropy between the first two and the last three transmons.

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Copyright information: © Taneli Tolppanen, 2022. Except otherwise noted, the reuse of this document is authorised under a Creative Commons Attribution 4.0 International (CC-BY 4.0) licence ( This means that reuse is allowed provided appropriate credit is given and any changes are indicated. For any use or reproduction of elements that are not owned by the author(s), permission may need to be directly from the respective right holders.