Correlated flux noise and decoherence in two inductively coupled flux qubits

Abstract

We have studied decoherence in a system where two Josephson-junction flux qubits share a part of their superconducting loops and are inductively coupled. By tuning the flux bias condition, we control the sensitivities of the energy levels to flux noises in each qubit. The dephasing rate of the first excited state is enhanced or suppressed depending on the amplitudes and the signs of the sensitivities. We have quantified the 1/f flux noises and their correlations and found that the dominant contribution is by local fluctuations.PACS numbers: 03.67. Lx,85.25.Cp,74.50.+r The presence of low-frequency flux noise in superconducting devices has been known for decades. It was discovered as an excess noise in SQUIDs 1,2 and has recently been intensively studied as a source of dephasing in various types of superconducting qubits, such as charge,4-8 and phase qubits. 9-11The noise spectrum typically follows 1/f frequency dependence with a spectral density of about 1-40 µΦ 0 /Hz 1/2 at 1 Hz, where Φ 0 is the superconducting flux quantum. The noise spectrum depends only weakly on geometry-samples with a loop area of 1 µm 2 up to a few mm 2 are within the above range-and does not show a clear dependence on the material used. However, the microscopic origin of the noise has been elusive so far. It is crucial to identify and eliminate the source of such noise in order to improve the performance of these devices; i.e., the sensitivity of SQUIDs and coherence of qubits.A few recent experimental observations have suggested as the source of the flux noise a high density of electron spins existing on the surface of superconducting electrodes. Rogachev et al. attributed the magnetic-fieldinduced enhancement of the critical current in superconducting nanowires to suppression of spin-flip scattering at the surface, 12 while Sendelbach et al. directly measured the magnetization of SQUIDs at low temperatures as well as correlated inductance fluctuations.13,14 Electron spin resonance studies on Si/SiO 2 interfaces 15 as well as scanning-SQUID measurements on Au surfaces 16 have also indicated the presence of electron spins. As the microscopic origins of these surface spins, theoretical studies have proposed localized electrons at disordered interfaces between surface oxides and metals/semiconductors [17][18][19] or at defects in the surface oxides. 20In the present study, we approached this issue by means of dephasing measurements in coupled flux qubits. Decoherence in coupled qubits depends on the correlations between noises in each qubit.21-25 It can therefore be used to characterize the noise correlations without the need for measuring the correlations directly. In the echo decay signal of the qubits, we observed the contributions of pure dephasing due to 1/f flux noises and evaluated the correlations. The results indicated local rather than global flux fluctuations in accordance with the surface spin model.The experiments were carried out using a sample fabricated by electron-beam lithography and shadow evaporation of Al films, wi...

Spectroscopy of low-frequency noise and its temperature dependence in a superconducting qubit

“…The result (12) is equivalent to the explicit subtraction of the incoherent noise S n from S k (Eqs. 6,8), with the advantage, however, of drastically reduced uncertainty, in particular at high frequencies where the (1/f -noise) signal is much smaller than the white noise. This method is appropriate for the analysis of, e.g., 1/f -type noise.…”

“…We just have to replace the mean-square b 2 by the variance σ 2 b and set δ(f k ) = δ k,0 ∆t to obtain Eq. (8).…”

“…Their noise is known to be due to local fluctuators [6][7][8][9] and the spectrum exhibits a 1/f α powerlaw dependence from hertz to tens of megahertz [10][11][12][13][14] . Its dependence on the device geometry 15,16 merits further study.…”

Flux qubit noise spectroscopy using Rabi oscillations under strong driving conditions

“…The spectra typically follow 1/f frequency dependence with a spectral density of 1-10 μ 0 / √ Hz at 1 Hz, where 0 = h/2e is the superconducting flux quantum. The accessible frequency range of the PSD was limited to approximately 10 MHz in spin-echo measurements [4,5,9,15] and was extended to a few tens of megahertz using Carr-Purcell-Meiboom-Gill pulse sequences [9]. Recently, spin-locking measurements provided the PSD up to approximately 100 MHz [16], and a study of qubit relaxation due to dressed dephasing in a driven resonator revealed the PSD at approximately 1 GHz [17].…”

Flux-vector model of spin noise in superconducting circuits: Electron versus nuclear spins and role of phase transition

“…This value has not changed in order of magnitude since the first measurements of flux noise in the 1980's; 3,4 only minor improvements are observed in modern devices. [5][6][7][8][9][10] While flux noise is sufficiently low for several applications, it is still considered a barrier for the use of the SQUID as a quantum bit (the flux qubit) in a superconductor-based quantum computer architecture.…”