Probing high-frequency noise with macroscopic resonant tunneling

Lanting, T.; Amin, M. H. S.; Johnson, Mark W.; Altomare, Fabio; Berkley, A. J.; Gildert, S.; Harris, Richard E.; Johansson, Jan; Bunyk, P.; Ladizinsky, E.; Tolkacheva, E.; Averin, D. V.

doi:10.1103/physrevb.83.180502

Cited by 24 publications

(47 citation statements)

References 23 publications

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“…In the case of pure 1/f noise, where S L 1 w~w ( ) , the integrals in (7) diverge. To avoid this problem we prefer to use parameters W and ε L , which are directly extracted from experiments such as performed in [27,34]. We also note that in the real systems (see, e.g.…”

Section: W = D +mentioning

confidence: 99%

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Theory of open quantum dynamics with hybrid noise

Smirnov

Amin

2018

New J. Phys.

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We develop a theory to describe dynamics of a non-stationary open quantum system interacting with a hybrid environment, which includes high-frequency and low-frequency noise components. One part of the system-bath interaction is treated in a perturbative manner, whereas the other part is considered exactly. This approach allows us to derive a set of master equations where the relaxation rates are expressed as convolutions of the Bloch-Redfield and Marcus formulas. Our theory enables analysis of systems that have extremely small energy gaps in the presence of a realistic environment. As an illustration, we apply the theory to the 16 qubit quantum annealing problem with dangling qubits (Dickson et al 2013 Nat. Commun. 4 1903) and show qualitative agreement with experimental results.[28, 29] is not applicable. We provide an intuitively appealing and computationally convenient form for the transition rates in terms of a convolution between Redfield and Marcus formulas. As an example, we investigate a dissipative evolution of a 16 qubit system strongly interacting with LF noise and weakly coupled to a HF environment [33]. The problem is characterized by an extremely small gap in the energy spectrum of qubits in the middle of annealing. Solving the problem requires the right combination of Bloch-Redfield and Marcus approaches as well as a proper consideration of the calculation basis, which takes into account the nonstationary effects. The results of the present paper can also be applied to any other open quantum system within the validity range of the approximations.The paper is organized in the following way. Section 2 describes a single-qubit system to provide the necessary intuition before moving to more complicated multiqubit problems. Section 3 formulates the Hamiltonian and introduces important definitions and notations for the system and the bath. Master equations for the probability distribution of the quantum system are derived in section 4. Section 5 presents the relaxation rates as convolution integrals of the Bloch-Redfield and Marcus envelopes. In the section 6 we show that in equilibrium the master equations obey the detailed balance conditions. We also demonstrate that the convolution expression for the relaxation rates turns into the Marcus or to Bloch-Redfield formulas in the corresponding limits. Dissipative dynamics of a 16 qubit system with an extremely small energy gap is considered in section 7. A brief compilation of the commonly encountered notations is presented in appendix A. In other appendixes we provide a detailed derivation of many important formulas.

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Section: W = D +mentioning

confidence: 99%

“…A complete (hybrid) open quantum model should account for both LF and HF environments. Such a model for a single qubit has been developed and agreement with experiment has been demonstrated [25][26][27]. A generalization of this theory to multiqubit systems has also been developed and compared with experimental observation [28,29].…”

Section: Introductionmentioning

confidence: 98%

Theory of open quantum dynamics with hybrid noise

Smirnov

Amin

2018

New J. Phys.

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“…Some of these qubits have been used in previously published experiments. For example, qubit 48 was used in a single-qubit experiment 40 , qubits 48-55 were used in two-qubit experiments 41 , as well as the 8-qubit experiments discussed in Harris et al 22 and Johnson et al 23 The annealing procedure we use here is the same as that described in Harris et al 22 The rf-SQUID flux qubit. The qubits used in this experiment are superconducting compound Josephson junction rf-SQUID flux qubits described in detail in Harris et al 33 A simplified version of the qubit is illustrated in Supplementary Fig.…”

Section: Methodsmentioning

confidence: 99%

Thermally assisted quantum annealing of a 16-qubit problem

et al. 2013

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Efforts to develop useful quantum computers have been blocked primarily by environmental noise. Quantum annealing is a scheme of quantum computation that is predicted to be more robust against noise, because despite the thermal environment mixing the system's state in the energy basis, the system partially retains coherence in the computational basis, and hence is able to establish well-defined eigenstates. Here we examine the environment's effect on quantum annealing using 16 qubits of a superconducting quantum processor. For a problem instance with an isolated small-gap anticrossing between the lowest two energy levels, we experimentally demonstrate that, even with annealing times eight orders of magnitude longer than the predicted single-qubit decoherence time, the probabilities of performing a successful computation are similar to those expected for a fully coherent system. Moreover, for the problem studied, we show that quantum annealing can take advantage of a thermal environment to achieve a speedup factor of up to 1,000 over a closed system.

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“…At the lowest frequencies, the noise is of 1/f form [47]. There is a large window between the high-frequency [46] and the low-frequency measurements [47] in which the noise has not been directly measured. The measured current noise characteristics do not, therefore, preclude the possibility of γ > 1 and initial overdamped dynamics.…”

Section: -6mentioning

confidence: 99%

“…Measurements of high-frequency flux noise via macroscopic resonant tunneling [46] indicate that above a cutoff ω HF = 0.5 GHz noise is Ohmic with γ HF = 2 0 S (0)/8 k B T L 2 ≈ 0.5, where the values for inductance L = 265.4 pH and shunt resistance R = 2kT L 2 /S (0) = 20 k measured in Ref. [46], and 0 is the magnetic flux quantum. However, our analysis shows that the qubit is also sensitive to noise with frequency lower than the system frequency.…”

Section: -6mentioning

confidence: 99%

Anisotropic Landau-Lifshitz-Gilbert models of dissipation in qubits

Crowley

Green

2016

Phys. Rev. A

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We derive a microscopic model for dissipative dynamics in a system of mutually interacting qubits coupled to a thermal bath that generalizes the dissipative model of Landau-Lifshitz-Gilbert to the case of anisotropic bath couplings. We show that the dissipation acts to bias the quantum trajectories towards a reduced phase space. This model applies to a system of superconducting flux qubits whose coupling to the environment is necessarily anisotropic. We study the model in the context of the D-Wave computing device and show that the form of environmental coupling in this case produces dynamics that are closely related to several models proposed on phenomenological grounds.

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Probing high-frequency noise with macroscopic resonant tunneling

Cited by 24 publications

References 23 publications

Theory of open quantum dynamics with hybrid noise

Theory of open quantum dynamics with hybrid noise

Thermally assisted quantum annealing of a 16-qubit problem

Anisotropic Landau-Lifshitz-Gilbert models of dissipation in qubits

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