Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/0411633 · Physical Review B

Influence of low-frequency noise on macroscopic quantum tunneling in superconducting circuits

Mathias Duckheim, Joachim Ankerhold

Published Apr 4, 2005• 5 citations
arXivHTMLPDF

Abstract

The influence of low- to moderate-frequency environments on macroscopic quantum tunneling (MQT) in superconducting circuits is studied within the $\mathrm{Im}F$ approach to evaluate tunneling rates. Particular attention is paid to two model environments, namely, a pure sluggish bath and a sluggish bath with additional $1∕f$ noise. General findings are applied to Zener flip tunneling, a MQT phenomenon recently predicted and observed in a superconducting circuit implementing a quantum bit.

DOI
10.1103/physrevb.71.134501

Related papers

Zener Enhancement of Quantum Tunneling in a Two-Level Superconducting Circuit

Grégoire Ithier, Eddy Collin, P. Joyez +4 more

We have investigated the macroscopic quantum tunneling (MQT) of the phase across a Josephson junction embedded in a superconducting circuit. This system is equivalent to a spin 1/2 particle in a potential energy well. The MQT escape rate of such a particle was recently predicted to be strongly modified when a crossing of its inner Zeeman levels occurs while tunneling. In this regime, we observe a significant enhancement of the MQT rate and compare it to theory.

Physical Review Letters•Feb 10, 2005•42 citations

Resonant enhancement of macroscopic quantum tunneling in Josephson junctions: Influence of coherent two-level systems

M. V. Fistul

We report a theoretical study of the macroscopic quantum tunneling (MQT) in small Josephson junctions containing randomly distributed two-level systems. We focus on a Josephson phase escape for switching from the superconducting (the zero-voltage) state to a resistive one. Above the crossover temperature ${T}_{cr}$ the thermal fluctuations of the Josephson phase induce such a switching, and as $T<{T}_{cr}$ the regime of the MQT occurs. In the absence of two-level systems (TLSs) a magnetic field applied parallel to the junction plane results in a smooth reduction of ${T}_{cr}(\mathrm{\ensuremath{\Phi}})$, where $\mathrm{\ensuremath{\Phi}}$ is an applied magnetic flux. As the TLSs are present in Josephson junctions we obtain a resonant enhancement of the MQT. This phenomenon manifests itself by a narrow peak in the dependence of ${T}_{cr}(\mathrm{\ensuremath{\Phi}})$ occurring in the intermediate range of $\mathrm{\ensuremath{\Phi}}$, i.e., $0<\mathrm{\ensuremath{\Phi}}<{\ensuremath{\phi}}_{0}$ (${\ensuremath{\phi}}_{0}$ is the magnetic flux quantum). We explain this effect quantitatively by a strong resonant suppression of the potential barrier for the Josephson phase escape that is due to the coherent quantum Rabi oscillations in two-level systems present in the junction.

Physical Review B•Jul 9, 2015•4 citations

Identification of Coulomb blockade and macroscopic quantum tunneling by noise

Hermann Grabert, Gert‐Ludwig Ingold

The effects of Macroscopic Quantum Tunneling (MQT) and Coulomb Blockade (CB) in Josephson junctions are of considerable significance both for the manifestations of quantum mechanics on the macroscopic scale and potential technological applications. These two complementary effects are shown to be clearly distinguishable from the associated noise spectra. The current noise is determined exactly and a rather sharp crossover between flux noise in the MQT and charge noise in the CB regions is found as the applied voltage is changed. Related results hold for the voltage noise in current-biased junctions.

arXiv:cond-mat/0202460•Europhysics Letters (EPL)•May 1, 2002•12 citations

Fault-Tolerant Quantum Computing via Macroscopic Quantum Tunnelling in Superconducting Circuits

Murali Krishna Pasupuleti

Abstract: This study investigates the feasibility of exploiting macroscopic quantum tunnelling (MQT) in superconducting circuits as a constructive resource for fault-tolerant quantum computing. While MQT has historically been treated as a decoherence pathway associated with metastable escape and switching events, recent advances in circuit engineering suggest that controlled access to tunnelling dynamics can be integrated into protected qubit modalities and error-mitigating architectures. The present framework synthesizes quantum escape theory, circuit Hamiltonian models, and contemporary fault-tolerance criteria to propose an experimentally realistic pathway for harnessing MQT-driven transitions as calibrated, monitorable events that can support syndrome extraction and bias-preserving logical operations. A methods blueprint is developed that combines cryogenic device characterization, time-resolved switching statistics, and noise spectroscopy with scalable surface-code-inspired performance projections. Using literature-aligned representative device parameters, the results illustrate how barrier engineering and bias-point optimization can reshape the MQT rate landscape while maintaining coherence metrics compatible with microsecond-scale error-correction cycles. The analysis indicates that decoupling the tunnelling coordinate from dominant low-frequency noise sources and implementing fast, quantum-limited readout may enable an error budget in which MQT transitions become part of a controlled operational envelope rather than a catastrophic failure mode. The study concludes with design rules, limitations, and a roadmap for validating MQT-assisted fault-tolerant primitives in next-generation superconducting quantum processors. Keywords: macroscopic quantum tunnelling; superconducting circuits; fluxonium; fault tolerance; surface code; noise spectroscopy; Josephson junctions; quantum error correction.

International Journal of Academic and Industrial Research Innovations(IJAIRI)•Dec 8, 2025•0 citations

Early Experiments on Macroscopic Quantum Tunneling

Willem den Boer

Before conclusive evidence of Macroscopic Quantum Tunneling, MQT, was published by Clarke, Devoret and Martinis in 1985, several other groups reported experimental results interpreted as MQT. The first, in chronological order, was in 1980 based on studies done at Leiden University in 1979. This paper looks back at these experiments on low capacitance Niobium point contacts in an rf SQUID, radio-frequency Superconducting Quantum Interference Device, configuration at temperatures between 1 and 4.2 K. The research was inspired by the theoretical predictions by Ivanchenko and Zilberman in 1969 on MQT in current-biased Josephson junctions and by Leggett in 1978 on MQT in closed loops with a superconducting weak link.

arXiv:2606.02770•Jun 1, 2026•0 citations

Theory of macroscopic quantum tunneling in high- Tc c -axis Josephson junctions

Takehito Yokoyama, Shiro Kawabata, Takeo Kato +1 more

We study macroscopic quantum tunneling (MQT) in $c$-axis twist Josephson junctions made of high-${T}_{c}$ superconductors in order to clarify the influence of the anisotropic order parameter symmetry (OPS) on MQT. The dependence of the MQT rate on the twist angle $\ensuremath{\gamma}$ about the $c$ axis is calculated by using the functional integral and the bounce method. Due to the $d$-wave OPS, the $\ensuremath{\gamma}$ dependence of standard deviation of the switching current distribution and the crossover temperature from thermal activation to MQT are found to be given by $\mathrm{cos}\phantom{\rule{0.2em}{0ex}}2\ensuremath{\gamma}$ and $\sqrt{\mathrm{cos}\phantom{\rule{0.2em}{0ex}}2\ensuremath{\gamma}}$, respectively. We also show that a dissipative effect resulting from the nodal quasiparticle excitation on MQT is negligibly small, which is consistent with recent MQT experiments using ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}\mathrm{Ca}{\mathrm{Cu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ intrinsic junctions. These results indicate that MQT in $c$-axis twist junctions becomes a useful experimental tool for testing the OPS of high-${T}_{c}$ materials at low temperature, and suggest high potential of such junctions for qubit applications.

arXiv:0705.1418•Physical Review B•Oct 1, 2007•37 citations
The influence of low- to moderate-frequency environments on macroscopic quantum tunneling (MQT) in superconducting circuits is studied within the ImF\mathrm{Im}FImF approach to evaluate tunneling rates. Particular attention is paid to two model environments, namely, a pure sluggish bath and a sluggish bath with additional 1∕f1∕f1∕f noise. General findings are applied to Zener flip tunneling, a MQT phenomenon recently predicted and observed in a superconducting circuit implementing a quantum bit.
We report a theoretical study of the macroscopic quantum tunneling (MQT) in small Josephson junctions containing randomly distributed two-level systems. We focus on a Josephson phase escape for switching from the superconducting (the zero-voltage) state to a resistive one. Above the crossover temperature Tcr{T}_{cr}Tcr​ the thermal fluctuations of the Josephson phase induce such a switching, and as T<TcrT<{T}_{cr}T<Tcr​ the regime of the MQT occurs. In the absence of two-level systems (TLSs) a magnetic field applied parallel to the junction plane results in a smooth reduction of ${T}_{cr}(\mathrm{\ensuremath{\Phi}})$, where $\mathrm{\ensuremath{\Phi}}$ is an applied magnetic flux. As the TLSs are present in Josephson junctions we obtain a resonant enhancement of the MQT. This phenomenon manifests itself by a narrow peak in the dependence of ${T}_{cr}(\mathrm{\ensuremath{\Phi}})$ occurring in the intermediate range of $\mathrm{\ensuremath{\Phi}}$, i.e., $0<\mathrm{\ensuremath{\Phi}}<{\ensuremath{\phi}}_{0}$ (${\ensuremath{\phi}}_{0}$ is the magnetic flux quantum). We explain this effect quantitatively by a strong resonant suppression of the potential barrier for the Josephson phase escape that is due to the coherent quantum Rabi oscillations in two-level systems present in the junction.
The effects of Macroscopic Quantum Tunneling (MQT) and Coulomb Blockade (CB) in Josephson junctions are of considerable significance both for the manifestations of quantum mechanics on the macroscopic scale and potential technological applications. These two complementary effects are shown to be clearly distinguishable from the associated noise spectra. The current noise is determined exactly and a rather sharp crossover between flux noise in the MQT and charge noise in the CB regions is found as the applied voltage is changed. Related results hold for the voltage noise in current-biased junctions.
Abstract: This study investigates the feasibility of exploiting macroscopic quantum tunnelling (MQT) in superconducting circuits as a constructive resource for fault-tolerant quantum computing. While MQT has historically been treated as a decoherence pathway associated with metastable escape and switching events, recent advances in circuit engineering suggest that controlled access to tunnelling dynamics can be integrated into protected qubit modalities and error-mitigating architectures. The present framework synthesizes quantum escape theory, circuit Hamiltonian models, and contemporary fault-tolerance criteria to propose an experimentally realistic pathway for harnessing MQT-driven transitions as calibrated, monitorable events that can support syndrome extraction and bias-preserving logical operations. A methods blueprint is developed that combines cryogenic device characterization, time-resolved switching statistics, and noise spectroscopy with scalable surface-code-inspired performance projections. Using literature-aligned representative device parameters, the results illustrate how barrier engineering and bias-point optimization can reshape the MQT rate landscape while maintaining coherence metrics compatible with microsecond-scale error-correction cycles. The analysis indicates that decoupling the tunnelling coordinate from dominant low-frequency noise sources and implementing fast, quantum-limited readout may enable an error budget in which MQT transitions become part of a controlled operational envelope rather than a catastrophic failure mode. The study concludes with design rules, limitations, and a roadmap for validating MQT-assisted fault-tolerant primitives in next-generation superconducting quantum processors. Keywords: macroscopic quantum tunnelling; superconducting circuits; fluxonium; fault tolerance; surface code; noise spectroscopy; Josephson junctions; quantum error correction.
Before conclusive evidence of Macroscopic Quantum Tunneling, MQT, was published by Clarke, Devoret and Martinis in 1985, several other groups reported experimental results interpreted as MQT. The first, in chronological order, was in 1980 based on studies done at Leiden University in 1979. This paper looks back at these experiments on low capacitance Niobium point contacts in an rf SQUID, radio-frequency Superconducting Quantum Interference Device, configuration at temperatures between 1 and 4.2 K. The research was inspired by the theoretical predictions by Ivanchenko and Zilberman in 1969 on MQT in current-biased Josephson junctions and by Leggett in 1978 on MQT in closed loops with a superconducting weak link.
We study macroscopic quantum tunneling (MQT) in ccc-axis twist Josephson junctions made of high-Tc{T}_{c}Tc​ superconductors in order to clarify the influence of the anisotropic order parameter symmetry (OPS) on MQT. The dependence of the MQT rate on the twist angle $\ensuremath{\gamma}$ about the ccc axis is calculated by using the functional integral and the bounce method. Due to the ddd-wave OPS, the $\ensuremath{\gamma}$ dependence of standard deviation of the switching current distribution and the crossover temperature from thermal activation to MQT are found to be given by $\mathrm{cos}\phantom{\rule{0.2em}{0ex}}2\ensuremath{\gamma}$ and $\sqrt{\mathrm{cos}\phantom{\rule{0.2em}{0ex}}2\ensuremath{\gamma}}$, respectively. We also show that a dissipative effect resulting from the nodal quasiparticle excitation on MQT is negligibly small, which is consistent with recent MQT experiments using ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}\mathrm{Ca}{\mathrm{Cu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ intrinsic junctions. These results indicate that MQT in ccc-axis twist junctions becomes a useful experimental tool for testing the OPS of high-Tc{T}_{c}Tc​ materials at low temperature, and suggest high potential of such junctions for qubit applications.