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Strictly speaking, the laws of the conventional statistical physics, based on the equipartition postulate [Gibbs J W (1902) Elementary Principles in Statistical Mechanics, developed with especial reference to the rational foundation of thermodynamics] and ergodicity hypothesis [Boltzmann L (1964) Lectures on Gas Theory], apply only in the presence of a heat bath. Until recently this restriction was believed to be not important for real physical systems because a weak coupling to the bath was assumed to be sufficient. However, this belief was not examined seriously until recently when the progress in both quantum gases and solid-state coherent quantum devices allowed one to study the systems with dramatically reduced coupling to the bath. To describe such systems properly one should revisit the very foundations of statistical mechanics. We examine this general problem for the case of the Josephson junction chain that can be implemented in the laboratory and show that it displays a novel high-temperature nonergodic phase with finite resistance. With further increase of the temperature the system undergoes a transition to the fully localized state characterized by infinite resistance and exponentially long relaxation.

The most profound effect of disorder on electronic systems is the localization of the electrons transforming an otherwise metallic system into an insulator. If the metal is also a superconductor then, at low temperatures, disorder can induce a pronounced transition from a superconducting into an insulating state. An outstanding question is whether the route to insulating behaviour proceeds through the direct localization of Cooper pairs or, alternatively, by a two-step process in which the Cooper pairing is first destroyed followed by the standard localization of single electrons. Here we address this question by studying the local superconducting gap of a highly disordered amorphous superconductor by means of scanning tunnelling spectroscopy. Our measurements reveal that, in the vicinity of the superconductor–insulator transition, the coherence peaks in the one-particle density of states disappear whereas the superconducting gap remains intact, indicating the presence of localized Cooper pairs. Our results provide the first direct evidence that the superconductor–insulator transition in some homogeneously disordered materials is driven by Cooper-pair localization. Disorder leads to localization of electrons at low temperatures, changing metals to insulators. In a superconductor the electrons are paired up, and scanning tunnelling microscopy shows that the pairs localize together rather than breaking up and forming localized single electrons in the insulating state.

Scalable quantum computing can become a reality with error correction, provided that coherent qubits can be constructed in large arrays 1 , 2 . The key premise is that physical errors can remain both small and sufficiently uncorrelated as devices scale, so that logical error rates can be exponentially suppressed. However, impacts from cosmic rays and latent radioactivity violate these assumptions. An impinging particle can ionize the substrate and induce a burst of quasiparticles that destroys qubit coherence throughout the device. High-energy radiation has been identified as a source of error in pilot superconducting quantum devices 3 – 5 , but the effect on large-scale algorithms and error correction remains an open question. Elucidating the physics involved requires operating large numbers of qubits at the same rapid timescales necessary for error correction. Here, we use space- and time-resolved measurements of a large-scale quantum processor to identify bursts of quasiparticles produced by high-energy rays. We track the events from their initial localized impact as they spread, simultaneously and severely limiting the energy coherence of all qubits and causing chip-wide failure. Our results provide direct insights into the impact of these damaging error bursts and highlight the necessity of mitigation to enable quantum computing to scale. Cosmic rays flying through superconducting quantum devices create bursts of excitations that destroy qubit coherence. Rapid, spatially resolved measurements of qubit error rates make it possible to observe the evolution of the bursts across a chip.

For successful realization of a quantum computer, its building blocks—the individual qubits—should be simultaneously scalable and sufficiently protected from environmental noise. Recently, a novel approach to the protection of superconducting qubits has been proposed. The idea is to prevent errors at the hardware level, by building a fault-free logical qubit from ‘faulty’ physical qubits with properly engineered interactions between them. The decoupling of such a topologically protected logical qubit from local noises is expected to grow exponentially with the number of physical qubits. Here, we report on proof-of-concept experiments with a prototype device that consists of twelve physical qubits made of nanoscale Josephson junctions. We observed that owing to properly tuned quantum fluctuations, this qubit is protected against magnetic flux variations well beyond linear order, in agreement with theoretical predictions. These results suggest that topologically protected superconducting qubits are feasible. An array of superconducting nanocircuits has been designed that provides built-in protection from environmental noises. Such ‘topologically protected’ qubits could lead the way to a scalable architecture for practical quantum computation.

Quantum computers have the potential to outperform their classical counterparts in a qualitative manner, as demonstrated by algorithms 1 which exploit the parallelism inherent in the time evolution of a quantum state. In quantum computers, the information is stored in arrays of quantum two-level systems (qubits), proposals for which include utilizing trapped atoms and photons 2 , 4 , magnetic moments in molecules 5 and various solid-state implementations 6 , 10 . But the physical realization of qubits is challenging because useful quantum computers must overcome two conflicting difficulties: the computer must be scalable and controllable, yet remain almost completely detached from the environment during operation, in order to maximize the phase coherence time 11 . Here we report a concept for a solid-state ‘quiet’ qubit that can be efficiently decoupled from the environment. It is based on macroscopic quantum coherent states in a superconducting quantum interference loop. Our two-level system is naturally bistable, requiring no external bias: the two basis states are characterized by different macroscopic phase drops across a Josephson junction, which may be switched with minimal external contact.

Experiments with superconductor-graphene hybrids, a novel platform to study quantum phase transitions, suggest that in the proximity of the critical point between superconducting and insulating phases, inhomogeneity emerges at large scales even in apparently uniform disordered systems.

The origin of continuous energy spectra in large disordered interacting quantum systems is one of the key unsolved problems in quantum physics. Although small quantum systems with discrete energy levels are noiseless and stay coherent forever in the absence of any coupling to external world, most large-scale quantum systems are able to produce a thermal bath and excitation decay. This intrinsic decoherence is manifested by a broadening of energy levels, which aquire a finite width. The important question is: what is the driving force and the mechanism of transition(s) between these two types of many-body systems - with and without intrinsic decoherence? Here we address this question via the numerical study of energy-level statistics of a system of interacting spin-1/2 with random transverse fields. We present the first evidence for a well-defined quantum phase transition between domains of discrete and continous many-body spectra in such spin models, implying the appearance of novel insulating phases in the vicinity of the superconductor–insulator transition in InO x and similar materials. Quantum phase transitions are most commonly found to occur at zero temperature. Cuevas et al. present numerical evidence confirming that a quantum phase transition can also occur at finite temperature, provided strong disorder is present.

Continuous quantum phase transitions are widely assumed and frequently observed in various systems of quantum particles or spins. Their characteristic trait involves scaling laws governing a second-order, gradual suppression of the order parameter as the quantum critical point is approached. The localization of Cooper pairs in disordered superconductors and the resulting breakdown of superconductivity have long stood as a prototypical example. Here, we show a departure from this paradigm, showcasing that amorphous superconducting films of indium oxide undergo a distinctive, discontinuous first-order quantum phase transition tuned by disorder. Through systematic measurements of the plasmon spectrum in superconducting microwave resonators, we provide evidence for a marked jump of both the zero-temperature superfluid stiffness and the transition temperature at the critical disorder. This discontinuous transition sheds light on the previously overlooked role of repulsive interactions between Cooper pairs and the subsequent competition between superconductivity and insulating Cooper-pair glass. Furthermore, our investigation shows that the critical temperature of the films no longer relates to the pairing amplitude but aligns with the superfluid stiffness, consistent with the pseudogap regime of preformed Cooper pairs. Our findings raise fundamental new questions into the role of disorder in quantum phase transitions and carry implications for superinductances in quantum circuits.

Continuous quantum phase transitions are widely assumed and frequently observed in various systems of quantum particles or spins. Their characteristic trait is a second-order, gradual suppression of the order parameter as the quantum critical point is approached. The localization of Cooper pairs in disordered superconductors and the resulting breakdown of superconductivity have long stood as a prototypical example. Here we show a departure from this paradigm, in which a discontinuous first-order quantum phase transition is tuned by disorder. We measure the plasmon spectrum in superconducting microwave resonators on amorphous superconducting films of indium oxide to provide evidence for a marked jump in both the zero-temperature superfluid stiffness and the transition temperature at the critical disorder. This discontinuous transition sheds light on the role of repulsive interactions between Cooper pairs and the subsequent competition between superconductivity and insulating Cooper-pair glass. Furthermore, we show that the critical temperature of the films no longer relates to the pairing amplitude but aligns with the superfluid stiffness, consistent with the pseudogap regime of preformed Cooper pairs. Our findings raise fundamental new questions about the role of disorder in quantum phase transitions and carry implications for superinductances in quantum circuits. A first-order, disorder-driven, superconductor–insulator phase transition is demonstrated. This is in contrast with the usually observed second-order transition and highlights the role of Coulomb interactions between preformed Cooper pairs.