Operating in a deep underground facility improves the locking of gradiometric fluxonium qubits at the sweet spots
Daria Gusenkova, Francesco Valenti, Martin Spiecker, Simon Günzler, Patrick Paluch, Dennis Rieger, Larisa-Milena Pioraş-Ţimbolmaş, Liviu P. Zârbo, N. Casali, I. Colantoni, Angelo Cruciani, Stefano Pirro, L. Cardani, Alexandru Petrescu, Wolfgang Wernsdorfer, Patrick Winkel, Ioan M. Pop
We demonstrate flux-bias locking and operation of a gradiometric fluxonium artificial atom using two symmetric granular aluminum (grAl) loops to implement the superinductor. The gradiometric fluxonium shows two orders of magnitude suppression of sensitivity to homogeneous magnetic fields, which can be an asset for hybrid quantum systems requiring strong magnetic field biasing. By cooling down the device in an external magnetic field while crossing the metal-to-superconductor transition, the gradiometric fluxonium can be locked either at 0 or Φ0/2 effective flux bias, corresponding to an even or odd number of trapped fluxons, respectively. At mK temperatures, the fluxon parity prepared during initialization survives to magnetic field bias exceeding 100 Φ0. However, even for states biased in the vicinity of 1 Φ0, we observe unexpectedly short fluxon lifetimes of a few hours, which cannot be explained by thermal or quantum phase slips. When operating in a deep-underground cryostat of the Gran Sasso laboratory, the fluxon lifetimes increase to days, indicating that ionizing events activate phase slips in the grAl superinductor.
We demonstrate flux-bias locking and operation of a gradiometric fluxonium artificial atom using two symmetric granular aluminum (grAl) loops to implement the superinductor. The gradiometric fluxonium shows two orders of magnitude suppression of sensitivity to homogeneous magnetic fields, which can be an asset for hybrid quantum systems requiring strong magnetic field biasing. By cooling down the device in an external magnetic field while crossing the metal-to-superconductor transition, the gradiometric fluxonium can be locked either at 0 or Φ0/2 effective flux bias, corresponding to an even or odd number of trapped fluxons, respectively. At mK temperatures, the fluxon parity prepared during initialization survives to magnetic field bias exceeding 100 Φ0. However, even for states biased in the vicinity of 1 Φ0, we observe unexpectedly short fluxon lifetimes of a few hours, which cannot be explained by thermal or quantum phase slips. When operating in a deep-underground cryostat of the Gran Sasso laboratory, the fluxon lifetimes increase to days, indicating that ionizing events activate phase slips in the grAl superinductor.
Efforts to scale up superconducting processors that employ flux qubits face numerous challenges, among which is the crosstalk created by neighboring flux lines, which are necessary to bias the qubits at the zero-field and Φ0/2 sweet spots. A solution to this problem is to use symmetric gradiometric loops, which incorporate a flux-locking mechanism that, once a fluxon is trapped during cooldown, holds the device at the sweet spot and limits the need for active biasing. We demonstrate this technique by simultaneously locking multiple gradiometric fluxonium qubits in which an aluminum loop retains the trapped fluxon indefinitely. By compensating the inductive asymmetry between the two loops of the design, we are able to lock the effective flux bias within Φeff =−3 ×10−4 Φ0 from the target, corresponding to only 15% degradation in 𝑇2,E when operated in zero external field. The design strategy demonstrated here reduces integration complexity for flux qubits by minimizing crosstalk and potentially eliminating the need for local flux bias.
Efforts to scale up superconducting processors that employ flux qubits face numerous challenges, among which is the crosstalk created by neighboring flux lines, which are necessary to bias the qubits at the zero-field and Φ 0 / 2 sweet spots. A solution to this problem is to use symmetric gradiometric loops, which incorporate a flux-locking mechanism that, once a fluxon is trapped during cooldown, holds the device at the sweet spot and limits the need for active biasing. We demonstrate this technique by simultaneously locking multiple gradiometric fluxonium qubits in which an aluminum loop retains the trapped fluxon indefinitely. By compensating the inductive asymmetry between the two loops of the design, we are able to lock the effective flux bias within Φ eff = − 3 × 10 − 4 Φ 0 from the target, corresponding to only 15 % degradation in T 2 , E when operated in zero external field. The design strategy demonstrated here reduces integration complexity for flux qubits by minimizing crosstalk and potentially eliminating the need for local flux bias.
In pursuit of superconducting quantum computing, fluxonium qubits have recently garnered attention for their large anharmonicity and high coherence at the sweet spot. Towards the large-scale integration of fluxonium qubits, a major obstacle is the need for precise external magnetic flux bias: To achieve high performance at its sweet spot, each qubit requires a DC bias line. However, such lines inductively coupled to the qubits bring in additional wiring overhead, crosstalk, heating, and decoherence, necessitating measures for mitigating the problems. In this work, we propose a flux-trapping fluxonium qubit, which, by leveraging fluxoid quantization, enables the optimal phase biasing without using external magnetic flux control at the operating temperature. We introduce the design and working principle, and demonstrate the phase biasing achieved through fluxoid quantization.
The dream of universal quantum computing promises to revolutionize many fields due to its potential to drastically speed up certain calculations compared to classical computers. This has naturally attracted attention and investment. For example, in 2024, Google unveiled their Willow superconducting quantum processor, achieving a significant milestone by demonstrating quantum error correction below the surface code threshold. Despite these advances, the road to a fully fledged quantum computer is still uncharted, and current technology is not sufficient to get there. Therefore, unconventional materials hold great potential for addressing challenges faced by traditional approaches. This work focuses on fluxonium qubits made from the disordered superconductor granular aluminum (grAl), aiming to gain deeper insights into underlying loss mechanisms and noise sources. One of the main results of this work is the identification of inductive loss as the dominant decoherence mechanism in grAl fluxonium qubits with frequencies lower than 300 MHz at the half flux bias. The observed inductive loss tangent aligns with previously measured single-photon internal quality factors of grAl resonators, and the energy relaxation profiles are well described by a combination of inductive, dielectric, and Purcell loss. The study endeavors to deepen the understanding of decoherence by refining loss models via the quantum fluctuation-dissipation theorem and proposing an improved framework for Purcell loss. A comparison with other qubit materials underscores the universal nature of inductive loss in grAl fluxoniums, in contrast to well established Josephson junction array (JJA) based fluxoniums which show no such limitation at even lower qubit frequencies. The second outcome of this thesis is the validation of flexible striplines (`flexlines') for the use in future cryogenic microwave setups. This enables at least an order of magnitude increase in the density of microwave input circuitry without thermally overloading the cryostat, paving the way for increasingly complex superconducting detectors and quantum devices. The study found no significant differences in qubit performance between setups using flexlines and conventional coaxial cables. Passive heat load measurements indicated comparable photon shot noise-induced dephasing for both setups. The introduced heating pulse method demonstrated a faster thermalization time for flexlines compared to coaxial cables, and it can serve as a simple health check for other groups as well. An extended thermal model was developed to better understand the contributions of various attenuators in the input chains to the measured heat loads and to propose improved input chains. To further exploit the versatility of grAl for fluxonium qubits, the investigation of the microscopic origin of the limiting inductive loss is of interest to develop potential suppression methods. JJA-based fluxoniums could play a crucial role in this context, as particularly long arrays with increased plasma frequencies can emulate the properties of grAl while leveraging their better-understood behavior.
Hybrid superconducting circuits have been used to investigate mesoscopic superconductivity, but mostly just at low magnetic fields, as typical Al-based circuits are incompatible with magnetic fields, and superconducting circuits are sensitive to external magnetic flux noise. To overcome these challenges, the authors build a hybrid fluxonium system composed of (Nb,Ti)N, with a gradiometric design. They observe the spectrum of the hybrid fluxonium in fields of up to 1T, and probe the ${\ensuremath{\phi}}_{0}$ Josephson effect. These results enable future exploration of topological superconductivity, as well as readout of long-lifetime spin-polarized qubits using superconducting circuitry.
Over the past two decades the performance of superconducting quantum bits (qubits) has been improved tremendously: the coherence time of individual qubits has been increased by five orders of magnitude, from a few nanoseconds to >100 μs. The much-improved coherence, lithographic scalability, and compatibility with microwave control place superconducting qubits in the leading position in the race amongst several quantum systems being considered for quantum information processing. Despite this very impressive progress, experimental realization of quantum error corrections and demonstration of logical qubits remains a considerable challenge.One of possible solutions to this problem is the development of so-called protected qubits whose errors would be suppressed by special symmetries of the underlying Hamiltonian. The realization of such qubits requires elements not found in the conventional superconducting circuit toolbox, such as Josephson elements with cos(ϕ/2) and cos(2ϕ) dependences of the Josephson energy E_J on the phase difference ϕ, circuits with a very large kinetic inductance, and junctions with unusually low E_J.This thesis focuses on design, fabrication and characterization of circuits based on low-E_J Josephson junctions (JJs) and superinductors (SIs). By analyzing limitations on the junction performance imposed by the thermally activated phase slips, we observed a dramatic reduction of the critical currents in the regime E_J≤T which was accompanied by an increase of the zero-bias resistance R_0. The first part of this work provides practical considerations for the use of such junctions in quantum circuits. With the aim of improving elements with a very high kinetic inductance, in the second part we developed superinductors based on the granular Aluminum (grAl) films, in which Josephson junctions are realized between nanoscale grains. The circuits based on such SIs demonstrate low microwave losses at ultra-low temperatures. Superinductors are an essential element of a novel qubit that we have developed – the so-called bifluxon. The qubit consists of a Cooper-pair box (CPB) with low-E_J Josephson junctions shunted by a superinductor, thus forming a superconducting loop. When the loop is threaded by the magnetic flux Φ=Φ_0⁄2 where Φ_0 is the flux quantum, the qubit offers exponential suppression of energy decay from charge and flux noises, and dephasing from flux noise. In the last part of this work, we observed an increase of the energy relaxation time by two orders of magnitude, up to 100μs, by turning on protection in the bifluxon qubit.