The 2019 demonstration of high-coherence fluxonium qubits (Nguyen et al., Phys. Rev. X 9, 041041) reproducibly achieved T2>100 μsT_2>100~\mu\mathrm{s} and identified the physics that its own loss budget left unexplained: the microscopic origin and weak power-law frequency dependence of the effective capacitive loss tangent, the thermalization of the approximately 20 GHz Josephson-chain plasma modes, the anomalously low quasiparticle density and its conjectured vortex-trapping mechanism, and whether a disordered-superconductor superinductor with inductive loss tangent of order 10−810^{-8} can be realized. The quantum-computing-integration part of the 2019 paper's open questions has since been substantially achieved (two-qubit gates above 99.9% fidelity, improved readout, scalable coupler architectures), and millisecond coherence has been reached in a single junction-chain device; however, the microscopic accounting of what limits fluxonium energy relaxation remains open: the defects responsible for dielectric loss and their temperature and magnetic-field dependence lack a microscopic theory, the primary loss location is still unidentified, background quasiparticle densities and the vortex-trapping conjecture are untested, chain-mode thermalization is uncharacterized, and disordered-film superinductors remain one to two orders of magnitude too lossy. This problem asks for a validated quantitative microscopic decoherence budget of the fluxonium and a resolution of the materials question for ultra-low-loss superinductance.

Background

A fluxonium is a superconducting qubit circuit in which a single small Josephson tunnel junction (the weak junction) is shunted by a very large inductance and closed into a loop threaded by magnetic flux. The large shunt inductance is itself made from a superinductor — an element whose impedance exceeds the superconducting resistance quantum RQ≈6.5 kΩR_Q\approx 6.5~\mathrm{k\Omega}, realized in practice as a chain of roughly one hundred larger Josephson junctions in series. Introduced by Manucharyan, Koch, Glazman, and Devoret in 2009, the circuit is usually operated at half a flux quantum, a sweet spot where the qubit transition frequency is strongly suppressed (to a few hundred MHz) and becomes first-order insensitive to flux noise, while the spectrum remains far more anharmonic than that of the transmon, the industry-standard capacitively shunted superconducting qubit.

Coherence in such circuits is quantified by the energy relaxation time T1T_1 and the Ramsey dephasing time T2T_2. Dissipation is conventionally parameterized by loss tangents: for a capacitor or inductor, tan⁡δ\tan\delta is the ratio of the lossy (imaginary) part of the element's impedance to the reactive (real) part, and it limits T1T_1 to roughly (ωtan⁡δ)−1(\omega\tan\delta)^{-1} at qubit frequency ω\omega. In superconducting devices the dominant known microscopic loss channels are: (i) dielectric loss from tunneling two-level systems (TLS) — atom-like defects in amorphous oxides and interfaces that absorb energy resonantly and are described phenomenologically by the standard tunneling model; (ii) relaxation induced by quasiparticles, meaning unpaired electron excitations above the superconducting gap that tunnel across junctions, a mechanism whose general theory (Catelani, Schoelkopf, Devoret, and Glazman, 2011) predicts a strong dependence on flux bias in fluxonium-like circuits, including coherent suppression at the half-flux point; and (iii) occupation of parasitic electromagnetic circuit modes by nonequilibrium photons — for fluxonium specifically the N−1N-1 collective plasma modes of the junction chain, bunched near the junction plasma frequency of about 20 GHz, where a single photon in any one mode would shift the qubit frequency far beyond its natural linewidth and dephase it.

Nguyen et al. (2019) demonstrated fluxoniums with over one hundred junctions reproducibly satisfying T2>100 μsT_2>100~\mu\mathrm{s} (above 300 μs300~\mu\mathrm{s} in one device), overturning the assumption that large junction counts necessarily degrade coherence. Its loss budget attributed relaxation mainly to surface dielectric loss with an effective capacitive loss tangent tan⁡δC≈(2.0−3.6)×10−6\tan\delta_C\approx(2.0-3.6)\times10^{-6} at 6 GHz and a weak phenomenological frequency dependence tan⁡δC∝ωϵ\tan\delta_C\propto\omega^{\epsilon} with ϵ≈0.15−0.5\epsilon\approx0.15-0.5 depending on the assumed device temperature; it inferred that the quasiparticle density in the chains must satisfy xQP<10−8x_{\mathrm{QP}}<10^{-8} (fewer than one quasiparticle in the entire chain), speculating that vortices (quantized threads of magnetic flux in the superconducting film) might be trapping quasiparticles; it noted that the chain plasma modes appeared effectively empty of nonequilibrium photons without any characterized thermalization mechanism; it observed that replacing the junction chain by a patterned disordered-superconductor film — a kinetic inductor, whose inductance arises from the inertia of the Cooper-pair condensate rather than from the circuit geometry — would require an inductive loss tangent of order 10−810^{-8} to preserve the measured coherence; and it projected that coherence beyond 1 ms should be reachable given state-of-the-art surface loss and flux noise. A later device from the same group reached T2∗=1.48 msT_2^{*}=1.48~\mathrm{ms} (Somoroff et al., 2023), so the headline timescale has been achieved once; what remains at issue is the microscopic accounting of the loss, and its reproducibility across devices and fabrication processes.

Problem Statement

The problem is to construct and experimentally validate a quantitative microscopic decoherence budget for high-coherence fluxonium qubits, resolving the channels that the 2019 source paper left unidentified. Concretely: (1) Dielectric loss — determine the microscopic origin, physical location, and full dependence of the effective capacitive loss tangent tan⁡δC(ω,T,B)\tan\delta_C(\omega,T,B) on frequency, temperature, and magnetic field; in particular, establish whether the weak power law tan⁡δC∝ωϵ\tan\delta_C\propto\omega^{\epsilon} with ϵ≈0.15−0.5\epsilon\approx0.15-0.5 reflects thermally activated two-level systems, an elevated effective device temperature, or another mechanism; identify the origin of the reported T3T^3-like temperature scaling of the dielectric loss and its unexpected growth in weak in-plane magnetic field, including establishing whether these trends are intrinsic to the dielectric loss or reflect other effects such as an elevated effective device temperature; and establish where the responsible defects reside (metal-air and metal-substrate interfaces, or the oxide barriers of the chain junctions). (2) Chain plasma modes — characterize the occupation and thermalization dynamics of the approximately 20 GHz collective modes of the Josephson chain: what empties them of nonequilibrium photons, on what timescale they thermalize to the cryogenic environment, and what residual photon occupation the circuit can tolerate before photon-shot-noise dephasing appears — in the source's estimate, a single nonequilibrium photon in any one of the N−1N-1 modes shifts the qubit frequency by about 0.1% of its value, far beyond the qubit's natural linewidth, so that sustaining a coherence time T2T_2 requires each mode to remain photon-free on average for longer than N×T2N\times T_2 (for the 2019 devices, with N≈100N\approx100 junctions and T2T_2 of a few hundred microseconds, this is tens of milliseconds). (3) Quasiparticles — determine the background (non-injected) quasiparticle densities in the small junction and in the junction array; test whether the inferred bound xQP<10−8x_{\mathrm{QP}}<10^{-8} and the conjectured vortex-trapping mechanism are correct for background quasiparticles; and establish how asymmetry of the superconducting energy gap between the two electrodes of a junction (gap asymmetry) and deliberate gap engineering can suppress quasiparticle-induced relaxation and correlated errors. (4) Superinductor materials — determine whether a superinductor with inductive loss tangent of order 10−810^{-8} — the requirement for millisecond coherence if the junction chain is replaced by a patterned disordered superconducting film with comparable kinetic inductance (L∼102L\sim10^{2} nH) — can be realized, given that current high-kinetic-inductance films show loss dominated by quasiparticles localized in superconducting-gap fluctuations and increasing with disorder. These four questions are entries of one loss budget and are coupled through the same measured datasets — the T1T_1 and T2T_2 versus frequency, flux bias, temperature, and magnetic field reported for the high-coherence fluxonium devices in references 1, 7, 8, 9, and 14, together with the superinductor loss measurements of references 13 and 14 — across devices and fabrication runs. A resolution of a channel should be microscopic and quantitative: identified physical mechanisms, with independently constrained parameters, that quantitatively reproduce the measured coherence across these axes (for channel (4), which concerns a superinductor that has not yet been realized, the corresponding test is a quantitative demonstration that the required inductive loss tangent is achievable), together with a quantification of any remaining unexplained budget. A channel counts as resolved only when its identified mechanisms reproduce the measured coherence across these axes to within the experimental uncertainty; otherwise the unexplained residual must be quantified and the channel counts as unresolved. Completion requires all four: the task is resolved only when each of these channels meets this standard and the four resolutions are combined into a single budget that quantitatively reproduces the measured coherence. The quantum-computing-integration portion of the 2019 paper's open questions (fast single-shot readout, flux tuning, and high-fidelity two-qubit gates in the same device) is not part of this problem, as later work has substantially achieved it.

References

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