Probing Noise in Flux Qubits via Macroscopic Resonant Tunneling

Harris, Richard E.; Johnson, Mark W.; Han, Susan S.; Berkley, A. J.; Johansson, J.; Bunyk, P.; Ladizinsky, E.; Govorkov, S. A.; Thom, M. C.; Uchaikin, S.; Bumble, B.; Fung, A.; Kaul, Anupama B.; Kleinsasser, A. W.; Amin, M. H. S.; Averin, D. V.

doi:10.1103/physrevlett.101.117003

Cited by 78 publications

(115 citation statements)

References 27 publications

(39 reference statements)

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“…15, theσ z -coupling is definitely the dominant noise mechanism when the qubit originates from a macroscopic twolevel system, as any off-diagonal coupling would be proportional to the "exponentially small" (overlap-related) tunnelling matrix element ∆. In the context of QA, thê σ z -noise is recognized to be the dominant noise mechanism for the D-Wave ® machine superconducting flux qubits 7,8 , albeit with important low-frequency noise contributions which tend to make the qubits dynamics typically dominated by incoherent tunnelling 20,21 . While a general AQC-QA HamiltonianĤ sys (t) would involve a complex dynamics of exponentially many states, a simple dissipative two-level system serves as a pedagogical example of the effect of the environment on the avoided-level crossing of the two lowest-lying adiabatic states ofĤ sys (t).…”

Section: Introductionmentioning

confidence: 99%

Dissipative Landau-Zener problem and thermally assisted Quantum Annealing

et al. 2017

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We revisit here the issue of thermally assisted Quantum Annealing by a detailed study of the dissipative Landau-Zener problem in presence of a Caldeira-Leggett bath of harmonic oscillators, using both a weak-coupling quantum master equation and a quasi-adiabatic path-integral approach. Building on the known zero-temperature exact results (Wubs et al., PRL 97, 200404 (2006)), we show that a finite temperature bath can have a beneficial effect on the ground-state probability only if it couples also to a spin-direction that is transverse with respect to the driving field, while no improvement is obtained for the more commonly studied purely longitudinal coupling. In particular, we also highlight that, for a transverse coupling, raising the bath temperature further improves the ground-state probability in the fast-driving regime. We discuss the relevance of these findings for the current quantum-annealing flux qubit chips.

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Section: Introductionmentioning

confidence: 99%

Dissipative Landau-Zener problem and thermally assisted Quantum Annealing

et al. 2017

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“…Flux noise has been investigated for decades to improve stability and sensitivity in superconducting flux-based devices. Its power spectral density (PSD) has been studied in superconducting quantum interference devices (SQUIDs) [1,2] and in various types of superconducting qubits, such as charge [3], flux [4][5][6][7][8][9][10], and phase qubits [11][12][13][14]. 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.…”

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Flux qubit noise spectroscopy using Rabi oscillations under strong driving conditions

et al. 2014

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We infer the high-frequency flux noise spectrum in a superconducting flux qubit by studying the decay of Rabi oscillations under strong driving conditions. The large anharmonicity of the qubit and its strong inductive coupling to a microwave line enabled high-amplitude driving without causing significant additional decoherence. Rabi frequencies up to 1.7 GHz were achieved, approaching the qubit's level splitting of 4.8 GHz, a regime where the rotating-wave approximation breaks down as a model for the driven dynamics. The spectral density of flux noise observed in the wide frequency range decreases with increasing frequency up to 300 MHz, where the spectral density is not very far from the extrapolation of the 1/f spectrum obtained from the free-induction-decay measurements. We discuss a possible origin of the flux noise due to surface electron spins. Flux noise has been investigated for decades to improve stability and sensitivity in superconducting flux-based devices. Its power spectral density (PSD) has been studied in superconducting quantum interference devices (SQUIDs) [1,2] and in various types of superconducting qubits, such as charge [3], flux [4][5][6][7][8][9][10], and phase qubits [11][12][13][14]. 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]. The spectrum in a higher-frequency range would give further information for better understanding of the microscopic origin of the flux fluctuations.Decay of Rabi oscillations has also been used as a tool to characterize the decoherence in superconducting qubits. PSDs of fluctuating parameters, such as charge, flux, or coupling strength to an external two-level system, at the Rabi frequency R can be detected [3,9,18,19]. The Rabi frequency is proportional to the amplitude of the driving field for weak to moderate driving at the qubit transition frequency, and Rabi frequencies in the gigahertz range have been achieved under a strong driving field [20][21][22]. However, the decay was not systematically studied because of the presence of extrinsic decoherence mechanisms under the strong driving conditions.To induce fast Rabi oscillations without significant extra decoherence, we choose a flux qubit having strong inductive coupling to a microwave line and large anharmonicity, * fumiki.yoshihara@riken.jp |(ω 12 − ω 01 )/ω 01 |, to avoid unwanted excitations to the higher energy levels, where ω ij is the transition frequency between the |i and |j states. We measured Rabi oscillations in a wide range of R /2π from 2.7 MHz to 1.7 GHz and evaluat...

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“…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, 3 flux, [4][5][6][7][8] and phase qubits. [9][10][11] The 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.…”

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Correlated flux noise and decoherence in two inductively coupled flux qubits

2010

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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...

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Probing Noise in Flux Qubits via Macroscopic Resonant Tunneling

Cited by 78 publications

References 27 publications

Dissipative Landau-Zener problem and thermally assisted Quantum Annealing

Dissipative Landau-Zener problem and thermally assisted Quantum Annealing

Flux qubit noise spectroscopy using Rabi oscillations under strong driving conditions

Correlated flux noise and decoherence in two inductively coupled flux qubits

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