We calculate the fermion Green function and particle-hole susceptibilities for a degenerate twodimensional fermion system with a singular gauge interaction. We show that this is a strong coupling problem, with no small parameter other than the fermion spin degeneracy, N. We consider two interactions, one arising in the context of the t − J model and the other in the theory of half-filled Landau level. For the fermion self energy we show in contrast to previous claims that the qualitative behavior found in the leading order of perturbation theory is preserved to all orders in the interaction. The susceptibility χQ at a general wavevector Q = 2pF retains the fermi-liquid form. However the 2pF susceptibility χ2p F either diverges as T → 0 or remains finite but with nonanalytic wavevector, frequency and temperature dependence. We express our results in the language of recently discussed scaling theories, give the fixed-point action, and show that at this fixed point the fermion-gauge-field interaction is marginal in d = 2, but irrelevant at low energies in d ≥ 2.

The simulation of fermionic systems is among the most anticipated applications of quantum computing. We performed several quantum simulations of chemistry with up to one dozen qubits, including modeling the isomerization mechanism of diazene. We also demonstrated error-mitigation strategies based on N-representability that dramatically improve the effective fidelity of our experiments. Our parameterized ansatz circuits realized the Givens rotation approach to noninteracting fermion evolution, which we variationally optimized to prepare the Hartree-Fock wave function. This ubiquitous algorithmic primitive is classically tractable to simulate yet still generates highly entangled states over the computational basis, which allowed us to assess the performance of our hardware and establish a foundation for scaling up correlated quantum chemistry simulations.

We develop a semi-quantitative theory of electron pairing and resulting superconductivity in bulk "poor conductors" in which Fermi energy E F is located in the region of localized states not so far from the Anderson mobility edge E c . We assume attractive interaction between electrons near the Fermi surface. We review the existing theories and experimental data and argue that a large class of disordered films is described by this model.Our theoretical analysis is based on analytical treatment of pairing correlations, described in the basis of the exact single-particle eigenstates of the 3D Anderson model, which we combine with numerical data on eigenfunction correlations. Fractal nature of critical wavefunction's correlations is shown to be crucial for the physics of these systems.We identify three distinct phases: 'critical' superconductive state formed at E F = E c , superconducting state with a strong pseudogap, realized due to pairing of weakly localized electrons and insulating state realized at E F still deeper inside localized band. The 'critical' superconducting phase is characterized by the enhancement of the transition temperature with respect to BCS result, by the inhomogeneous spatial distribution of superconductive order parameter and local density of states. The major new feature of the pseudo-gaped state is the presence of two independent energy scales: superconducting gap ∆, that is due to many-body correlations and a new "pseudogap" energy scale ∆ P which characterizes typical binding energy of localized electron pairs and leads to the insulating behavior of the resistivity as a function of temperature above superconductive T c . Two gap nature of the pseudogapped superconductor is shown to lead to specific features seen in scanning tunneling spectroscopy and point-contact Andreev spectroscopy. We predict that pseudogaped superconducting state demonstrates anomalous behavior of the optical spectral weight. The insulating state is realized due to presence of local pairing gap but without superconducting correlations; it is characterized by a hard insulating gap in the density of single electrons and by purely activated low-temperature resistivity ln R(T ) ∼ 1/T .Based on these results we propose a new "pseudospin" scenario of superconductorinsulator transition and argue that it is realized in a particular class of disordered superconducting films. We conclude by the discussion of the experimental predictions of the theory and the theoretical issues that remain unsolved.

Unconventional superconductors exhibit an order parameter symmetry lower than the symmetry of the underlying crystal lattice. Recent phase sensitive experiments on YBa2Cu3O7 single crystals have established the d-wave nature of the cuprate materials, thus identifying unambiguously the first unconventional superconductor [1,2]. The sign change in the order parameter can be exploited to construct a new type of s-wave-d-wave-s-wave Josephson junction exhibiting a degenerate ground state and a double-periodic current-phase characteristic. Here we discuss how to make use of these special junction characteristics in the construction of a quantum computer. Combining such junctions together with a usual s-wave link into a SQUID loop we obtain what we call a 'quiet' qubit -a solid state implementation of a quantum bit which remains optimally isolated from its environment.PACS numbers: 85.25. Cp, 85.25.Hv, 89.80.+h Quantum computers take advantage of the inherent parallelism of the quantum state propagation, allowing them to outperform classical computers in a qualitative manner. Although the concept of quantum computation has been introduced quite a while ago [3], wide spread interest has developed only recently when specific algorithms exploiting the character of coherent state propagation have been proposed [4]. Here we deal with the device aspect of quantum computers, which is florishing in the wake of the recent successes achieved on the algorithmic side. Two conflicting difficulties have to be faced by all hardware implementations of quantum computation: while the computer must be scalable and controllable, the device should be almost completely detached from the environment during operation in order to minimize phase decoherence. The most advanced propositions are based on trapped ions [5,6], photons in cavities [7], NMR spectroscopy of molecules [8], and various solid state implementations based on electrons trapped in quantum dots [9], the Coulomb blockade in superconducting junction arrays [10,11], or the flux dynamics in Superconducting Quantum Interference Devices (SQUIDs) [12]. Nanostructured solid state quantum gates offer the attractive feature of large scale integrability, once the limitations due to decoherence can be overcome [13].Here we propose a new device concept for a (quantum) logic gate exploiting the unusual symmetry properties of unconventional superconductors. The basic idea is sketched in Fig. 1: connecting the positive (100) and negative (010) lobes of a d-wave superconductor with a s-wave material produces the famous π-loop with a current carrying ground state characteristic of d-wave symmetry [1]. Here we make use of an alternative geometry and match the s-wave superconductors (S) to the (110) boundaries of the d-wave (D) material. As a consequence, the usual Josephson coupling ∝ (1 − cos φ) vanishes due to symmetry reasons and we arrive at a bistable device, where the leading term in the coupling takes the form E d cos 2φ with minima at φ = ±π/2 (here, φ denotes the gauge invariant phas...

International audienceThe 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

We extend the Keldysh technique to enable the computation of out-of-time order correlators such as O(t)Õ(0)O(t)Õ(0) . We show that the behavior of these correlators is described by equations that display initially an exponential instability which is followed by a linear propagation of the decoherence between two initially identically copies of the quantum many body systems with interactions. At large times the decoherence propagation (quantum butterfly effect) is described by a diffusion equation with non-linear dissipation known in the theory of combustion waves. The solution of this equation is a propagating non-linear wave moving with constant velocity despite the diffusive character of the underlying dynamics.Our general conclusions are illustrated by the detailed computations for the specific models describing the electrons interacting with bosonic degrees of freedom (phonons, two-level-systems etc.) or with each other.

A hundred years after discovery of superconductivity, one fundamental prediction of the theory, the coherent quantum phase slip (CQPS), has not been observed. CQPS is a phenomenon exactly dual1 to the Josephson effect: whilst the latter is a coherent transfer of charges between superconducting contacts 2,3 , the former is a

We develop a theory of a pseudogap state appearing near the superconductor-insulator (SI) transition in strongly disordered metals with an attractive interaction. We show that such an interaction combined with the fractal nature of the single-particle wave functions near the mobility edge leads to an anomalously large single-particle gap in the superconducting state near SI transition that persists and even increases in the insulating state long after the superconductivity is destroyed. We give analytic expressions for the value of the pseudogap in terms of the inverse participation ratio of the corresponding localization problem.