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The Flux Qubit Revisited

Fei Yan, Simon Gustavsson, Archana Kamal, Jeffrey Birenbaum, Adam Sears, David J. Hover, Gabriel Samach, Theodore Gudmundsen, Jonilyn Yoder, Terry P. Orlando, John L. Clarke, Andrew J. Kerman, William D. Oliver

Published Aug 25, 2015• 6 citations
OpenAlex

Abstract

The scalable application of quantum information science will stand on reproducible and controllable high-coherence quantum bits (qubits). Here, we revisit the design and fabrication of the superconducting flux qubit, achieving a planar device with broad frequency tunability, strong anharmonicity, high reproducibility, and relaxation times in excess of $40\,\mu$s at its flux-insensitive point. Qubit relaxation times $T_1$ across 22 qubits are consistently matched with a single model involving resonator loss, ohmic charge noise, and 1/f flux noise, a noise source previously considered primarily in the context of dephasing. We furthermore demonstrate that qubit dephasing at the flux-insensitive point is dominated by residual thermal photons in the readout resonator. The resulting photon shot noise is mitigated using a dynamical decoupling protocol, resulting in $T_2\approx 85\,\mu$s, approximately the $2T_1$ limit. In addition to realizing an improved flux qubit, our results uniquely identify photon shot noise as limiting $T_2$ in contemporary qubits based on transverse qubit-resonator interaction.

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The flux qubit revisited to enhance coherence and reproducibility

Fei Yan, Simon Gustavsson, Archana Kamal +12 more

Abstract The scalable application of quantum information science will stand on reproducible and controllable high-coherence quantum bits (qubits). Here, we revisit the design and fabrication of the superconducting flux qubit, achieving a planar device with broad-frequency tunability, strong anharmonicity, high reproducibility and relaxation times in excess of 40 μs at its flux-insensitive point. Qubit relaxation times T 1 across 22 qubits are consistently matched with a single model involving resonator loss, ohmic charge noise and 1/f -flux noise, a noise source previously considered primarily in the context of dephasing. We furthermore demonstrate that qubit dephasing at the flux-insensitive point is dominated by residual thermal-photons in the readout resonator. The resulting photon shot noise is mitigated using a dynamical decoupling protocol, resulting in T 2 ≈85 μs, approximately the 2 T 1 limit. In addition to realizing an improved flux qubit, our results uniquely identify photon shot noise as limiting T 2 in contemporary qubits based on transverse qubit–resonator interaction.

arXiv:1508.06299•Nature Communications•Nov 3, 2016•582 citations

Reproducibility and control of superconducting flux qubits

T. Chang, Itamar Holzman, T. Cohen +3 more

Superconducting flux qubits are promising candidates for the physical realization of a scalable quantum processor. Indeed, these circuits may have both a small decoherence rate and a large anharmonicity. These properties enable the application of fast quantum gates with high fidelity and reduce scaling limitations due to frequency crowding. The major difficulty of flux qubits' design consists of controlling precisely their transition energy - the so-called qubit gap - while keeping long and reproducible relaxation times. Solving this problem is challenging and requires extremely good control of e-beam lithography, oxidation parameters of the junctions and sample surface. Here we present measurements of a large batch of flux qubits and demonstrate a high level of reproducibility and control of qubit gaps, relaxation times and pure echo dephasing times. These results open the way for potential applications in the fields of quantum hybrid circuits and quantum computation.

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Reproducibility and Gap Control of Superconducting Flux Qubits

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Superconducting flux qubits are promising candidates for the physical realization of a scalable quantum processor. Indeed, these circuits may have both a small decoherence rate and a large anharmonicity. These properties enable the application of fast quantum gates with high fidelity and reduce scaling limitations due to frequency crowding. The major difficulty of flux qubits' design consists of controlling precisely their transition energy---the so-called qubit gap---while keeping long and reproducible relaxation times. Solving this problem is challenging and requires extremely good control of e-beam lithography, oxidation parameters of the junctions, and sample surface. Here we present measurements of a large batch of flux qubits and demonstrate a high level of reproducibility and control of qubit gaps ($\ifmmode\pm\else\textpm\fi{}0.6\phantom{\rule{0.2em}{0ex}}\mathrm{GHz}$), relaxation times ($15$--$20\phantom{\rule{0.2em}{0ex}}\text{\ensuremath{\mu}}\mathrm{s}$), and pure echo dephasing times ($15$--$30\phantom{\rule{0.2em}{0ex}}\text{\ensuremath{\mu}}\mathrm{s}$). These results open the way for potential applications in the fields of quantum hybrid circuits and quantum computation.

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The C-shunt Flux Qubit: A New Generation of Superconducting Flux Qubit

Jeffrey Birenbaum

While quantum computation has the potential to revolutionize the scientific community, to date no architecture has been developed which offers the necessary combination of high coherence times and massive scalability. Superconducting flux qubits satisfy the second requirement well but to date useful devices are limited to coherence times of typically only a few &mus. In this dissertation we examine the possibilities of improving the coherence performance of the flux qubit to the levels required for fault-tolerant quantum computation. We find that coherence times for many devices are limited by photon-induced quasiparticles and mitigation of these quasiparticles increases coherence times by more than a factor of two. Beyond this, however, we find little improvement in flux qubit performance compared to prior results. Despite improved fabrication techniques and varied device designs we find flux qubit coherence times are still typically below 5 &mus. Furthermore, wide device-to-device variations are observed which prevent effective scaling of the flux qubit to quantum information circuits.Based on the proposal by You, et al. we develop of a capacitively-shunted version of the flux qubit called the C-shunt flux qubit. With the addition of a capacitive shunt across the small junction of the flux qubit we are able to reduce the amplitude sensitivity to both charge and flux noise by more than a factor of three. The result is a predicted ten-fold enhancement in the coherence times compared to the unshunted flux qubit. At the same time we preserve much of the anharmonicity of the flux qubit resulting in a device with coherence times comparable to modern transmons but with a factor of four better anharmonicity and more flexible coupling configurations.By using a high-quality MBE aluminum shunt process on an annealed sapphire substrate coupled with a more conventional electron-beam-evaporated aluminum Josephson junction process we fabricate hybrid C-shunt flux qubits. We also incorporate a new bridgeless junction technique which offers more robust and repeatable fabrication processing. This technique enables improved accuracy of the junction sizing, a trait which will become essential as we move to multi-qubit experiments. T1 and T2 times for these C-shunt devices reach in excess of 40 &mus at degeneracy, achieving the predicted ten-fold improvement based on the reduced noise sensitivity. At the same time we see decreased device-to-device variation with typical T1 times exceeding 20&ndash25 &mus at all bias points. Combined with the high anharmonicity and standard planar fabrication techniques these coherence times make the C-shunt flux qubit a competitive candidate for fault-tolerant quantum computation.

•Jan 1, 2014•3 citations

Characterization and Comparison of Energy Relaxation in Fluxonium Qubits

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Fluxonium superconducting qubits have demonstrated long coherence times and high single- and two-qubit gate fidelities, making them a favorable building block for superconducting quantum processors. We investigate the dominant limitations to fluxonium qubit energy relaxation time $T_1$ using a set of eight planar, aluminum-on-silicon qubits. We find that a circuit-based model for capacitive dielectric loss best captures the frequency dependence of $T_1$, which we analyze within both a two-level and a six-level energy relaxation model. We convert the measured $T_1$ into an effective capacitive quality factor $Q_\mathrm{C}^{\mathrm{eff}}$ to compare qubits on equal footing, accounting for independently estimated contributions from $1/f$ flux noise and radiative loss to the control and readout circuitry. We apply this methodology to compare qubits from two fabrication processes: a baseline process and one that applies a fluorine-based wet treatment prior to Josephson junction deposition. We resolve a small improvement of (13.8 $\pm$ 8.4$)\%$ in the process mean $Q_\mathrm{C}^{\mathrm{eff}}$, indicating that the fluorine treatment may have reduced loss from the metal-substrate interface, but did not address the primary source of loss in these fluxonium qubits.

quant-pharXiv:2603.23636•Physical Review Research•Mar 26, 2026•0 citations

Characterization of Loss Mechanisms in a Fluxonium Qubit

Hantao Sun, Feng Wu, Hsiang‐Sheng Ku +9 more

Using a fluxonium qubit with in situ tunability of its Josephson energy, we characterize its energy relaxation at different flux biases as well as different Josephson energy values. The relaxation rate at qubit energy values, ranging more than 1 order of magnitude around the thermal energy ${k}_{B}T$, can be quantitatively explained by a combination of dielectric loss and $1/f$ flux noise with a crossover point. The amplitude of the $1/f$ flux noise is consistent with that extracted from the qubit dephasing measurements at the flux sensitive points. In the dielectric loss dominant regime, the loss is consistent with that arising from the electric dipole interaction with two-level-system (TLS) defects. In particular, by increasing the Josephson energy, thus decreasing the qubit frequency at the flux insensitive spot, we find that the qubit exhibits increasingly weaker coupling to TLS defects, which is desirable for high-fidelity quantum operations. Our work establishes a generic noise model for the design of high coherence fluxonium and future generations of noise resilient superconducting qubits.

arXiv:2302.08110•Physical Review Applied•Sep 8, 2023•23 citations
The scalable application of quantum information science will stand on reproducible and controllable high-coherence quantum bits (qubits). Here, we revisit the design and fabrication of the superconducting flux qubit, achieving a planar device with broad frequency tunability, strong anharmonicity, high reproducibility, and relaxation times in excess of 40 μ40\,\mu40μs at its flux-insensitive point. Qubit relaxation times T1T_1T1​ across 22 qubits are consistently matched with a single model involving resonator loss, ohmic charge noise, and 1/f flux noise, a noise source previously considered primarily in the context of dephasing. We furthermore demonstrate that qubit dephasing at the flux-insensitive point is dominated by residual thermal photons in the readout resonator. The resulting photon shot noise is mitigated using a dynamical decoupling protocol, resulting in T2≈85 μT_2\approx 85\,\muT2​≈85μs, approximately the 2T12T_12T1​ limit. In addition to realizing an improved flux qubit, our results uniquely identify photon shot noise as limiting T2T_2T2​ in contemporary qubits based on transverse qubit-resonator interaction.
Abstract The scalable application of quantum information science will stand on reproducible and controllable high-coherence quantum bits (qubits). Here, we revisit the design and fabrication of the superconducting flux qubit, achieving a planar device with broad-frequency tunability, strong anharmonicity, high reproducibility and relaxation times in excess of 40 μs at its flux-insensitive point. Qubit relaxation times T 1 across 22 qubits are consistently matched with a single model involving resonator loss, ohmic charge noise and 1/f -flux noise, a noise source previously considered primarily in the context of dephasing. We furthermore demonstrate that qubit dephasing at the flux-insensitive point is dominated by residual thermal-photons in the readout resonator. The resulting photon shot noise is mitigated using a dynamical decoupling protocol, resulting in T 2 ≈85 μs, approximately the 2 T 1 limit. In addition to realizing an improved flux qubit, our results uniquely identify photon shot noise as limiting T 2 in contemporary qubits based on transverse qubit–resonator interaction.
Superconducting flux qubits are promising candidates for the physical realization of a scalable quantum processor. Indeed, these circuits may have both a small decoherence rate and a large anharmonicity. These properties enable the application of fast quantum gates with high fidelity and reduce scaling limitations due to frequency crowding. The major difficulty of flux qubits' design consists of controlling precisely their transition energy - the so-called qubit gap - while keeping long and reproducible relaxation times. Solving this problem is challenging and requires extremely good control of e-beam lithography, oxidation parameters of the junctions and sample surface. Here we present measurements of a large batch of flux qubits and demonstrate a high level of reproducibility and control of qubit gaps, relaxation times and pure echo dephasing times. These results open the way for potential applications in the fields of quantum hybrid circuits and quantum computation.
Superconducting flux qubits are promising candidates for the physical realization of a scalable quantum processor. Indeed, these circuits may have both a small decoherence rate and a large anharmonicity. These properties enable the application of fast quantum gates with high fidelity and reduce scaling limitations due to frequency crowding. The major difficulty of flux qubits' design consists of controlling precisely their transition energy---the so-called qubit gap---while keeping long and reproducible relaxation times. Solving this problem is challenging and requires extremely good control of e-beam lithography, oxidation parameters of the junctions, and sample surface. Here we present measurements of a large batch of flux qubits and demonstrate a high level of reproducibility and control of qubit gaps ($\ifmmode\pm\else\textpm\fi{}0.6\phantom{\rule{0.2em}{0ex}}\mathrm{GHz}$), relaxation times (151515--$20\phantom{\rule{0.2em}{0ex}}\text{\ensuremath{\mu}}\mathrm{s}$), and pure echo dephasing times (151515--$30\phantom{\rule{0.2em}{0ex}}\text{\ensuremath{\mu}}\mathrm{s}$). These results open the way for potential applications in the fields of quantum hybrid circuits and quantum computation.
While quantum computation has the potential to revolutionize the scientific community, to date no architecture has been developed which offers the necessary combination of high coherence times and massive scalability. Superconducting flux qubits satisfy the second requirement well but to date useful devices are limited to coherence times of typically only a few &mus. In this dissertation we examine the possibilities of improving the coherence performance of the flux qubit to the levels required for fault-tolerant quantum computation. We find that coherence times for many devices are limited by photon-induced quasiparticles and mitigation of these quasiparticles increases coherence times by more than a factor of two. Beyond this, however, we find little improvement in flux qubit performance compared to prior results. Despite improved fabrication techniques and varied device designs we find flux qubit coherence times are still typically below 5 &mus. Furthermore, wide device-to-device variations are observed which prevent effective scaling of the flux qubit to quantum information circuits.Based on the proposal by You, et al. we develop of a capacitively-shunted version of the flux qubit called the C-shunt flux qubit. With the addition of a capacitive shunt across the small junction of the flux qubit we are able to reduce the amplitude sensitivity to both charge and flux noise by more than a factor of three. The result is a predicted ten-fold enhancement in the coherence times compared to the unshunted flux qubit. At the same time we preserve much of the anharmonicity of the flux qubit resulting in a device with coherence times comparable to modern transmons but with a factor of four better anharmonicity and more flexible coupling configurations.By using a high-quality MBE aluminum shunt process on an annealed sapphire substrate coupled with a more conventional electron-beam-evaporated aluminum Josephson junction process we fabricate hybrid C-shunt flux qubits. We also incorporate a new bridgeless junction technique which offers more robust and repeatable fabrication processing. This technique enables improved accuracy of the junction sizing, a trait which will become essential as we move to multi-qubit experiments. T1 and T2 times for these C-shunt devices reach in excess of 40 &mus at degeneracy, achieving the predicted ten-fold improvement based on the reduced noise sensitivity. At the same time we see decreased device-to-device variation with typical T1 times exceeding 20&ndash25 &mus at all bias points. Combined with the high anharmonicity and standard planar fabrication techniques these coherence times make the C-shunt flux qubit a competitive candidate for fault-tolerant quantum computation.
Fluxonium superconducting qubits have demonstrated long coherence times and high single- and two-qubit gate fidelities, making them a favorable building block for superconducting quantum processors. We investigate the dominant limitations to fluxonium qubit energy relaxation time T1T_1T1​ using a set of eight planar, aluminum-on-silicon qubits. We find that a circuit-based model for capacitive dielectric loss best captures the frequency dependence of T1T_1T1​, which we analyze within both a two-level and a six-level energy relaxation model. We convert the measured T1T_1T1​ into an effective capacitive quality factor QCeffQ_\mathrm{C}^{\mathrm{eff}}QCeff​ to compare qubits on equal footing, accounting for independently estimated contributions from 1/f1/f1/f flux noise and radiative loss to the control and readout circuitry. We apply this methodology to compare qubits from two fabrication processes: a baseline process and one that applies a fluorine-based wet treatment prior to Josephson junction deposition. We resolve a small improvement of (13.8 ±\pm± 8.4)%)\%)% in the process mean QCeffQ_\mathrm{C}^{\mathrm{eff}}QCeff​, indicating that the fluorine treatment may have reduced loss from the metal-substrate interface, but did not address the primary source of loss in these fluxonium qubits.
Using a fluxonium qubit with in situ tunability of its Josephson energy, we characterize its energy relaxation at different flux biases as well as different Josephson energy values. The relaxation rate at qubit energy values, ranging more than 1 order of magnitude around the thermal energy kBT{k}_{B}TkB​T, can be quantitatively explained by a combination of dielectric loss and 1/f1/f1/f flux noise with a crossover point. The amplitude of the 1/f1/f1/f flux noise is consistent with that extracted from the qubit dephasing measurements at the flux sensitive points. In the dielectric loss dominant regime, the loss is consistent with that arising from the electric dipole interaction with two-level-system (TLS) defects. In particular, by increasing the Josephson energy, thus decreasing the qubit frequency at the flux insensitive spot, we find that the qubit exhibits increasingly weaker coupling to TLS defects, which is desirable for high-fidelity quantum operations. Our work establishes a generic noise model for the design of high coherence fluxonium and future generations of noise resilient superconducting qubits.