Observation of Classical-Quantum Crossover of 1/f Flux Noise and Its Paramagnetic Temperature Dependence

The effects of disorder in superconducting materials on qubit coherence

Introducing disorder in the superconducting materials has been considered promising to enhance the electromagnetic impedance and realize noise-resilient superconducting qubits. Despite a number of pioneering implementations, the understanding of the correlation between the material disorder and the qubit coherence is still developing. Here, we demonstrate a systematic characterization of fluxonium qubits with the superinductors made by spinodal titanium-aluminum-nitride with varied disorder. From qubit noise spectroscopy, the flux noise and the dielectric loss are extracted as a measure of the coherence properties. Our results reveal that the 1/f α flux noise dominates the qubit decoherence around the flux-frustration point, strongly correlated with the material disorder; while the dielectric loss are largely similar under a wide range of material properties. From the flux-noise amplitudes, the areal density (σ) of the phenomenological spin defects and material disorder are found to be approximately correlated by σ ∝ ρ x x 3 , or effectively( k F l ) - 3 . This work has provided new insights on the origin of decoherence channels beyond surface defects and within the superconductors, and could serve as a useful guideline for material design and optimization.

Dissipative Landau-Zener tunneling in the crossover regime from weak to strong environment coupling

Landau-Zener tunneling, which describes the transition in a two-level system during a sweep through an anti-crossing, is a model applicable to a wide range of physical phenomena. Realistic quantum systems are affected by dissipation due to coupling to their environments. An important aspect of understanding such open quantum systems is the relative energy scales of the system itself and the system-environment coupling, which distinguishes the weak- and strong-coupling regimes. Using a tunable superconducting flux qubit, we observe the crossover from weak to strong coupling to the environment in Landau-Zener tunneling. Our results confirm previous theoretical studies of dissipative Landau-Zener tunneling in the weak and strong coupling limits. We devise a spin bath model that effectively captures the crossover regime. This work is relevant for understanding the role of dissipation in quantum annealing, where the system is expected to go through a cascade of Landau-Zener transitions before reaching the target state.

Simulating the Landau-Zener sweep in deeply sub-Ohmic environments

With the goal to study dissipative Landau-Zener (LZ) sweeps in realistic solid-state qubits, we utilize novel methods from non-Markovian open quantum system dynamics that enable reliable long-time simulations for sub-Ohmic environments. In particular, we combine a novel representation of the dynamical propagator, the uniform time evolving matrix product operator method, with a stochastic realization of finite temperature fluctuations. The latter greatly reduces the computational cost for the matrix product operator approach, enabling convergence in the experimentally relevant deeply sub-Ohmic regime. Our method allows the exact simulation of dynamical protocols with long operation times, such as the LZ sweep, in challenging parameter regimes that are realized in current experimental platforms.

Spatially correlated classical and quantum noise in driven qubits

Correlated noise across multiple qubits poses a significant challenge for achieving scalable and fault-tolerant quantum processors. Despite recent experimental efforts to quantify this noise in various qubit architectures, a comprehensive understanding of its role in qubit dynamics remains elusive. Here, we present an analytical study of the dynamics of driven qubits under spatially correlated noise, including both Markovian and non-Markovian noise. Surprisingly, we find that by operating the qubit system at low temperatures, where correlated quantum noise plays an important role, significant long-lived entanglement between qubits can be generated. Importantly, this generation process can be controlled on-demand by turning the qubit driving on and off. On the other hand, we demonstrate that by operating the system at a higher temperature, the crosstalk between qubits induced by the correlated noise is unexpectedly suppressed. We finally reveal the impact of spatio-temporally correlated 1/f noise on the decoherence rate, and how its temporal correlations restore lost entanglement. Our findings provide critical insights into not only suppressing crosstalk between qubits caused by correlated noise but also in effectively leveraging such noise as a beneficial resource for controlled entanglement generation.

Nonergodic Measurements of Qubit Frequency Noise

Slow fluctuations of a qubit frequency are one of the major problems faced by quantum computers. To understand their origin it is necessary to go beyond the analysis of their spectra. We show that characteristic features of the fluctuations can be revealed using comparatively short sequences of periodically repeated Ramsey measurements, with the sequence duration smaller than needed for the noise to approach the ergodic limit. The outcomes distribution and its dependence on the sequence duration are sensitive to the nature of the noise. The time needed for quantum measurements to display quasiergodic behavior can strongly depend on the measurement parameters.

Absolutely Stable Time Crystals at Finite Temperature

We show that locally interacting, periodically driven (Floquet) Hamiltonian dynamics coupled to a Langevin bath support finite-temperature discrete time crystals (DTCs) with an infinite autocorrelation time. By contrast to both prethermal and many-body localized DTCs, the time crystalline order we uncover is stable to arbitrary perturbations, including those that break the time translation symmetry of the underlying drive. Our approach utilizes a general mapping from probabilistic cellular automata to open classical Floquet systems undergoing continuous-time Langevin dynamics. Applying this mapping to a variant of the Toom cellular automaton, which we dub the "π-Toom time crystal," leads to a 2D Floquet Hamiltonian with a finite-temperature DTC phase transition. We provide numerical evidence for the existence of this transition, and analyze the statistics of the finite temperature fluctuations. Finally, we discuss how general results from the field of probabilistic cellular automata imply the existence of discrete time crystals (with an infinite autocorrelation time) in all dimensions, d≥1.

Quantum bath suppression in a superconducting circuit by immersion cooling

Quantum circuits interact with the environment via several temperature-dependent degrees of freedom. Multiple experiments to-date have shown that most properties of superconducting devices appear to plateau out at T ≈ 50 mK - far above the refrigerator base temperature. This is for example reflected in the thermal state population of qubits, in excess numbers of quasiparticles, and polarisation of surface spins - factors contributing to reduced coherence. We demonstrate how to remove this thermal constraint by operating a circuit immersed in liquid ³He. This allows to efficiently cool the decohering environment of a superconducting resonator, and we see a continuous change in measured physical quantities down to previously unexplored sub-mK temperatures. The ³He acts as a heat sink which increases the energy relaxation rate of the quantum bath coupled to the circuit a thousand times, yet the suppressed bath does not introduce additional circuit losses or noise. Such quantum bath suppression can reduce decoherence in quantum circuits and opens a route for both thermal and coherence management in quantum processors.

Evolution of 1/f Flux Noise in Superconducting Qubits with Weak Magnetic Fields

The microscopic description of 1/f magnetic flux noise in superconducting circuits has remained an open question for several decades despite extensive experimental and theoretical investigation. Recent progress in superconducting devices for quantum information has highlighted the need to mitigate sources of qubit decoherence, driving a renewed interest in understanding the underlying noise mechanism(s). Though a consensus has emerged attributing flux noise to surface spins, their identity and interaction mechanisms remain unclear, prompting further study. Here, we apply weak in-plane magnetic fields to a capacitively shunted flux qubit (where the Zeeman splitting of surface spins lies below the device temperature) and study the flux-noise-limited qubit dephasing, revealing previously unexplored trends that may shed light on the dynamics behind the emergent 1/f noise. Notably, we observe an enhancement (suppression) of the spin-echo (Ramsey) pure-dephasing time in fields up to B=100  G. With direct noise spectroscopy, we further observe a transition from a 1/f to approximately Lorentzian frequency dependence below 10 Hz and a reduction of the noise above 1 MHz with increasing magnetic field. We suggest that these trends are qualitatively consistent with an increase of spin cluster sizes with magnetic field. These results should help to inform a complete microscopic theory of 1/f flux noise in superconducting circuits.

Possible Origin of Low-Frequency Magnetic Flux Noise in Superconducting Devices

The magnetic flux noise caused by surface spin fluctuations in superconducting quantum interference devices (SQUIDs) limits their development. In this work, we report that different adsorbents such as H, O₂, NO, and NO₂ that adsorb on the surfaces of Mg-based and Pb-based SQUIDs, respectively, producing large local magnetic moments ranging from 0.7-1.6 μ_B, with energy barriers for thermal spin fluctuation as low as 10-30 mK. Moreover, we observe that the presence of H atoms on the surface of MgO can cause the coadsorption of other molecules, which generates additional spin sources. Monte Carlo simulations of the weakly coupled spin on a two-dimensional square lattice produce a low-frequency flux noise spectrum. We suggest eliminating the surface magnetism by coating the surface with monolayer indium phosphide or protecting the surface from other molecules by nonmagnetic preoccupants with a larger adsorption energy. The work provides important physical insights and feasible strategies for reducing magnetic noise sources in superconducting circuits.

On the nature of decoherence in quantum circuits: Revealing the structural motif of the surface radicals in α-Al2O3

Quantum information technology puts stringent demands on the quality of materials and interfaces in the pursuit of increased device coherence. Yet, little is known about the chemical structure and origins of paramagnetic impurities that produce flux/charge noise that causes decoherence of fragile quantum states and impedes the progress toward large-scale quantum computing. Here, we perform high magnetic field electron paramagnetic resonance (HFEPR) and hyperfine multispin spectroscopy on α-Al₂O₃, a common substrate for quantum devices. In its amorphous form, α-Al₂O₃ is also unavoidably present in aluminum-based superconducting circuits and qubits. The detected paramagnetic centers are immanent to the surface and have a well-defined but highly complex structure that extends over multiple hydrogen, aluminum, and oxygen atoms. Modeling reveals that the radicals likely originate from well-known reactive oxygen chemistry common to many metal oxides. We discuss how EPR spectroscopy might benefit the search for surface passivation and decoherence mitigation strategies.

Materials challenges and opportunities for quantum computing hardware

Quantum computing hardware technologies have advanced during the past two decades, with the goal of building systems that can solve problems that are intractable on classical computers. The ability to realize large-scale systems depends on major advances in materials science, materials engineering, and new fabrication techniques. We identify key materials challenges that currently limit progress in five quantum computing hardware platforms, propose how to tackle these problems, and discuss some new areas for exploration. Addressing these materials challenges will require scientists and engineers to work together to create new, interdisciplinary approaches beyond the current boundaries of the quantum computing field.

Multi-level quantum noise spectroscopy

System noise identification is crucial to the engineering of robust quantum systems. Although existing quantum noise spectroscopy (QNS) protocols measure an aggregate amount of noise affecting a quantum system, they generally cannot distinguish between the underlying processes that contribute to it. Here, we propose and experimentally validate a spin-locking-based QNS protocol that exploits the multi-level energy structure of a superconducting qubit to achieve two notable advances. First, our protocol extends the spectral range of weakly anharmonic qubit spectrometers beyond the present limitations set by their lack of strong anharmonicity. Second, the additional information gained from probing the higher-excited levels enables us to identify and distinguish contributions from different underlying noise mechanisms.

Two-level systems in superconducting quantum devices due to trapped quasiparticles

A major issue for the implementation of large-scale superconducting quantum circuits is the interaction with interfacial two-level system (TLS) defects that lead to qubit parameter fluctuations and relaxation. Another major challenge comes from nonequilibrium quasiparticles (QPs) that result in qubit relaxation and dephasing. Here, we reveal a previously unexplored decoherence mechanism in the form of a new type of TLS originating from trapped QPs, which can induce qubit relaxation. Using spectral, temporal, thermal, and magnetic field mapping of TLS-induced fluctuations in frequency tunable resonators, we identify a highly coherent subset of the general TLS population with a low reconfiguration temperature ∼300 mK and a nonuniform density of states. These properties can be understood if the TLS are formed by QPs trapped in shallow subgap states formed by spatial fluctutations of the superconducting order parameter. This implies that even very rare QP bursts will affect coherence over exponentially long time scales.

Towards understanding two-level-systems in amorphous solids: insights from quantum circuits

Amorphous solids show surprisingly universal behaviour at low temperatures. The prevailing wisdom is that this can be explained by the existence of two-state defects within the material. The so-called standard tunneling model has become the established framework to explain these results, yet it still leaves the central question essentially unanswered-what are these two-level defects (TLS)? This question has recently taken on a new urgency with the rise of superconducting circuits in quantum computing, circuit quantum electrodynamics, magnetometry, electrometry and metrology. Superconducting circuits made from aluminium or niobium are fundamentally limited by losses due to TLS within the amorphous oxide layers encasing them. On the other hand, these circuits also provide a novel and effective method for studying the very defects which limit their operation. We can now go beyond ensemble measurements and probe individual defects-observing the quantum nature of their dynamics and studying their formation, their behaviour as a function of applied field, strain, temperature and other properties. This article reviews the plethora of recent experimental results in this area and discusses the various theoretical models which have been used to describe the observations. In doing so, it summarises the current approaches to solving this fundamentally important problem in solid-state physics.

Non-Gaussian noise spectroscopy with a superconducting qubit sensor

Accurate characterization of the noise influencing a quantum system of interest has far-reaching implications across quantum science, ranging from microscopic modeling of decoherence dynamics to noise-optimized quantum control. While the assumption that noise obeys Gaussian statistics is commonly employed, noise is generically non-Gaussian in nature. In particular, the Gaussian approximation breaks down whenever a qubit is strongly coupled to discrete noise sources or has a non-linear response to the environmental degrees of freedom. Thus, in order to both scrutinize the applicability of the Gaussian assumption and capture distinctive non-Gaussian signatures, a tool for characterizing non-Gaussian noise is essential. Here, we experimentally validate a quantum control protocol which, in addition to the spectrum, reconstructs the leading higher-order spectrum of engineered non-Gaussian dephasing noise using a superconducting qubit as a sensor. This first experimental demonstration of non-Gaussian noise spectroscopy represents a major step toward demonstrating a complete spectral estimation toolbox for quantum devices.

Electron-Phonon Coupling as the Source of 1/f Noise in Carbon Soot

Two 1/f noise peaks were found in a carbon soot resistor at voltages characteristic of Kohn anomalies in graphite. The ratio of the electron-phonon coupling matrix elements at the anomalies calculated from the noise peak intensities is the same as the one obtained from the Raman frequencies. This demonstrates that the electron-phonon coupling is the microscopic source of 1/f noise in carbon soot. A new, very general formula was deduced for the frequency exponent, wherein nonlinearity and dispersion are the only ingredients. The interplay between nonlinearity and dispersion in this formula describes the sublinear-supralinear transitions experimentally observed at both anomalies in the voltage dependence of the frequency exponent. A quadratic dependence of the 1/f noise parameter on the matrix element is proposed and applied to explain the M-shape of the 1/f noise in graphene. We found that the frequency exponent mimics the dependence of the noise intensity in the whole voltage range, while both are the image of the graphite phonon spectrum. This implies that the source of nonlinearity is in the electron-phonon coupling which modulates the slope of the spectrum. It requires the presence of 1/f noise in the thermal noise background of the resistor till phonon frequencies.

Distinguishing Coherent and Thermal Photon Noise in a Circuit Quantum Electrodynamical System

In the cavity-QED architecture, photon number fluctuations from residual cavity photons cause qubit dephasing due to the ac Stark effect. These unwanted photons originate from a variety of sources, such as thermal radiation, leftover measurement photons, and cross talk. Using a capacitively shunted flux qubit coupled to a transmission line cavity, we demonstrate a method that identifies and distinguishes coherent and thermal photons based on noise-spectral reconstruction from time-domain spin-locking relaxometry. Using these measurements, we attribute the limiting dephasing source in our system to thermal photons rather than coherent photons. By improving the cryogenic attenuation on lines leading to the cavity, we successfully suppress residual thermal photons and achieve T_{1}-limited spin-echo decay time. The spin-locking noise-spectroscopy technique allows broad frequency access and readily applies to other qubit modalities for identifying general asymmetric nonclassical noise spectra.

Suppression of low-frequency charge noise in superconducting resonators by surface spin desorption

Noise and decoherence due to spurious two-level systems located at material interfaces are long-standing issues for solid-state quantum devices. Efforts to mitigate the effects of two-level systems have been hampered by a lack of knowledge about their chemical and physical nature. Here, by combining dielectric loss, frequency noise and on-chip electron spin resonance measurements in superconducting resonators, we demonstrate that desorption of surface spins is accompanied by an almost tenfold reduction in the charge-induced frequency noise in the resonators. These measurements provide experimental evidence that simultaneously reveals the chemical signatures of adsorbed magnetic moments and highlights their role in generating charge noise in solid-state quantum devices.

Understanding Quality Factor Degradation in Superconducting Niobium Cavities at Low Microwave Field Amplitudes

In niobium superconducting radio frequency (SRF) cavities for particle acceleration, a decrease of the quality factor at lower fields-a so-called low field Q slope or LFQS-has been a long-standing unexplained effect. By extending the high Q measurement techniques to ultralow fields, we discover two previously unknown features of the effect: (i) saturation at rf fields lower than E_{acc}∼0.1  MV/m; (ii) strong degradation enhancement by growing thicker niobium pentoxide. Our findings suggest that the LFQS may be caused by the two level systems in the natural niobium oxide on the inner cavity surface, thereby identifying a new source of residual resistance and providing guidance for potential nonaccelerator low-field applications of SRF cavities.

Direct Identification of Dilute Surface Spins on Al_{2}O_{3}: Origin of Flux Noise in Quantum Circuits

An on-chip electron spin resonance technique is applied to reveal the nature and origin of surface spins on Al_{2}O_{3}. We measure a spin density of 2.2×10^{17}  spins/m^{2}, attributed to physisorbed atomic hydrogen and S=1/2 electron spin states on the surface. This is direct evidence for the nature of spins responsible for flux noise in quantum circuits, which has been an issue of interest for several decades. Our findings open up a new approach to the identification and controlled reduction of paramagnetic sources of noise and decoherence in superconducting quantum devices.