Numerical simulation of a continuously measured transmon array
Tolppanen, Taneli (2022-06-22)
Tolppanen, Taneli
T. Tolppanen
22.06.2022
© 2022 Taneli Tolppanen. Ellei toisin mainita, uudelleenkäyttö on sallittu Creative Commons Attribution 4.0 International (CC-BY 4.0) -lisenssillä (https://creativecommons.org/licenses/by/4.0/). Uudelleenkäyttö on sallittua edellyttäen, että lähde mainitaan asianmukaisesti ja mahdolliset muutokset merkitään. Sellaisten osien käyttö tai jäljentäminen, jotka eivät ole tekijän tai tekijöiden omaisuutta, saattaa edellyttää lupaa suoraan asianomaisilta oikeudenhaltijoilta.
Julkaisun pysyvä osoite on
https://urn.fi/URN:NBN:fi:oulu-202206223114
https://urn.fi/URN:NBN:fi:oulu-202206223114
Tiivistelmä
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.
Kokoelmat
- Avoin saatavuus [31657]