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From the perspective of many-body physics, the transmon qubit architectures currently developed for quantum computing are systems of coupled nonlinear quantum resonators. A certain amount of intentional frequency detuning (‘disorder’) is crucially required to protect individual qubit states against the destabilizing effects of nonlinear resonator coupling. Here we investigate the stability of this variant of a many-body localized phase for system parameters relevant to current quantum processors developed by the IBM, Delft, and Google consortia, considering the cases of natural or engineered disorder. Applying three independent diagnostics of localization theory — a Kullback–Leibler analysis of spectral statistics, statistics of many-body wave functions (inverse participation ratios), and a Walsh transform of the many-body spectrum — we find that some of these computing platforms are dangerously close to a phase of uncontrollable chaotic fluctuations.

Motivated by the proposal of a Weyl-semimetal phase in pyrochlore iridates, we consider a Hubbardtype model on the pyrochlore lattice. To shed light on the question as to why such a state has not been observed experimentally, its robustness is analyzed. On the one hand, we study the possible phases when the system is doped. Magnetic frustration favors several phases with magnetic and charge order that do not occur at half filling, including additional Weyl-semimetal states close to quarter filling. On the other hand, we search for density waves that break translational symmetry and destroy the Weylsemimetal phase close to half filling. The uniform Weyl semimetal is found to be stable, which we attribute to the low density of states close to the Fermi energy. different basis sites that nevertheless do not break translational symmetry. Since they do break other lattice symmetries, we still call them charge density waves (CDWs).Second, we consider the stability of the undoped and weakly doped material with respect to density waves (DWs) that do break translational symmetry. A TWS can be unstable towards the formation of a DW due to the following mechanism [3, 25-28]: a (commensurate) DW enlarges the unit cell and thus leads to backfolding of bands. This can place Weyl points of opposite chirality that are far apart in the original Brillouin zone close together. It is then possible to move them to the same k point by a small change of the mean-field order parameters, where they can annihilate and gap out. Thereby, density of states is shifted away from the chemical potential, pushing the energy of occupied states down and lowering the free energy. This reduction could overcompensate the increase incurred by changing the order parameters away from their optimum values for uniform states. Laubach et al [28] have studied a model with tetragonal symmetry within the variational cluster approach and indeed find a fully gapped CDW for strong attractive interactions. Yang et al [29] have proposed that an applied magnetic field can induce a CDW in a TWS with ordering vector Q connecting two Weyl points. We show that while this mechanism can, in principle, work for the cubic pyrochlore lattice, the Weyl points in the pyrochlore system are very robust against this type of instability. This is ultimately due to the low density of states close to the Fermi energy. Our results are obtained within a Hartree-Fock approximation [30] that is unrestricted beyond fixing a commensurate DW ordering vector Q, which can be zero.The rest of this paper is organized as follows: in section 2, we introduce the model Hamiltonian and review its mean-field decoupling. In section 3, we present results, first for the doping dependence and then for the search for DWs. The paper concludes with a summary and outlook in section 4.New J. Phys. 20 (2018) 043057 C Berke et al

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