超導量子位元與共平面波導共振腔耦合系統之研究

Abstract

本論文探討超導Xmon 量子位元的設計、製造與量測。每個量子位元耦合至具有相應頻率的共平面波導（CPW），其中量子位元頻率為ωq = √8EJEC − EC，EJ 為約瑟夫森能，EC 為充電能。我們將庫柏對盒（CPB）設計成具有205.3 MHz的充電能，與24.1 GHz 的約瑟夫森能，使量子位元的頻率約略落在6 GHz。用以讀取量子位元訊號的共振腔頻率分別設計為5.6、6.1、6.6 GHz，而量子位元與共振腔之間的耦合強度則設計為28.8 MHz。 藉由此設計製造出多個量子位元並進行低溫量測後，發現共振腔頻率的量測值與設計值相當吻合。量子位元頻率在零磁通下的量測值為5.9 GHz，量子位元與共振腔耦合強度的量測值為29.3 MHz，皆與設計值接近。根據本設計所製造的量子位元的T1 超過1 μs。

In this thesis work, we designed, fabricated and measured several superconducting Xmon qubits. Each qubit is coupled to a coplanar waveguide (CPW) of specified resonant frequency. The qubit frequency ωq is related to the Josephson coupling energy EJ and charging energy EC as ωq = √8EJEC − EC. The Cooper Pair Box (CPB) geometry is designed to give a charging energy of 205.3 MHz, and the coupling strength between the two superconducting leads of the qubit tunneling junctions is about 24.1 GHz, yielding a qubit frequency of around 6GHz. The resonant frequencies of the three readout cavities are designed to be 5.6, 6.1, 6.6 GHz, and the coupling strength between the qubit and cavity is determined by the coupling capacitance and is designed to be 28.8 MHz. Using this design, several qubit devices were fabricated and measured at mK temperatures. The cavity frequencies were found to be very close to the designed values, and the qubit frequency measured by two tone technique was determined to be 5.9 GHz at zero magnetic flux. The qubit-cavity coupling strength extracted from the dispersive shift is 29.3 MHz, which consists well with the designed value. The relaxation time T1 of the qubit coupling system exceeds 1 μs.