We present designs for scalable quantum computers composed of qubits encoded in aggregates of four or more Majorana zero modes, realized at the ends of topological superconducting wire segments that are assembled into superconducting islands with significant charging energy. Quantum information can be manipulated according to a measurement-only protocol, which is facilitated by tunable couplings between Majorana zero modes and nearby semiconductor quantum dots. Our proposed architecture designs have the following principal virtues:(1) the magnetic field can be aligned in the direction of all of the topological superconducting wires since they are all parallel; (2) topological T junctions are not used, obviating possible difficulties in their fabrication and utilization; (3) quasiparticle poisoning is abated by the charging energy; (4) Clifford operations are executed by a relatively standard measurement: detection of corrections to quantum dot energy, charge, or differential capacitance induced by quantum fluctuations; (5) it is compatible with strategies for producing good approximate magic states.

The interaction between light and matter can give rise to novel topological states. This principle was recently exemplified in Floquet topological insulators, where classical light was used to induce a topological electronic band structure. Here, in contrast, we show that mixing single photons with excitons can result in new topological polaritonic states-or "topolaritons." Taken separately, the underlying photons and excitons are topologically trivial. Combined appropriately, however, they give rise to nontrivial polaritonic bands with chiral edge modes allowing for unidirectional polariton propagation. The main ingredient in our construction is an exciton-photon coupling with a phase that winds in momentum space. We demonstrate how this winding emerges from the finite-momentum mixing between s-type and p-type bands in the electronic system and an applied Zeeman field. We discuss the requirements for obtaining a sizable topological gap in the polariton spectrum and propose practical ways to realize topolaritons in semiconductor quantum wells and monolayer transition metal dichalcogenides.

We present a novel route to realizing topological superconductivity using magnetic flux applied to a full superconducting shell surrounding a semiconducting nanowire core. In the destructive Little-Parks regime, reentrant regions of superconductivity are associated with integer number of phase windings in the shell. Tunneling into the core reveals a hard induced gap near zero applied flux, corresponding to zero phase winding, and a gapped region with a discrete zero-energy state around one applied flux quantum, Φ0 = h/2e, corresponding to 2π phase winding. Theoretical analysis indicates that in the presence of radial spin-orbit coupling in the semiconductor, the winding of the superconducting phase can induce a transition to a topological phase supporting Majorana zero modes. Realistic modeling shows a topological phase persisting over a wide range of parameters, and reproduces experimental tunneling conductance data. Further measurements of Coulomb blockade peak spacing around one flux quantum in full-shell nanowire islands shows exponentially decreasing deviation from 1e periodicity with device length, consistent with Majorana modes at the ends of the nanowire. arXiv:2003.13177v1 [cond-mat.mes-hall]

Topological polaritons (aka topolaritons) present a new frontier for topological behavior in solidstate systems. They combine light and matter, which allows to probe and manipulate them in a variety of ways. They can also be made strongly interacting, due to their excitonic component. So far, however, their realization was deemed rather challenging. Here we present a scheme which allows to realize topolaritons in garden variety zinc-blende quantum wells. Our proposal requires a moderate magnetic field and a potential landscape which can be implemented, e.g., via surface acoustic waves or patterning. We identify indirect excitons in double quantum wells as a particularly appealing alternative for topological states in exciton-based systems. Indirect excitons are robust and long lived (with lifetimes up to milliseconds), and, therefore, provide a flexible platform for the realization, probing, and utilization of topological coupled light-matter states.

We present a versatile scheme for creating topological Bogoliubov excitations in weakly interacting bosonic systems. Our proposal relies on a background stationary field that consists of a kagome vortex lattice, which breaks time-reversal symmetry and induces a periodic potential for Bogoliubov excitations. In analogy to the Haldane model, no external magnetic field or net flux is required. We construct a generic model based on the two-dimensional nonlinear Schrödinger equation and demonstrate the emergence of topological gaps crossed by chiral Bogoliubov edge modes. Our scheme can be realized in a wide variety of physical systems ranging from nonlinear optical systems to exciton-polariton condensates. DOI: 10.1103/PhysRevB.93.020502 Introduction. The quantum Hall effect is one of the most celebrated results of modern condensed matter physics [1]. The robustness of the Hall conductance can be traced back to the nontrivial topology of the underlying electronic band structure [2], which ensures the existence of chiral edge states and thus eliminates backscattering. Recently there was a surge of interest in the possibility to exploit such topology to create chiral bosonic modes in driven-dissipative systemswith possible applications to one-way transport of photons [3][4][5][6][7][8][9][10][11][12][13], polaritons [14][15][16], excitons [16,17], magnons [18,19], and phonons [20,21]. A common thread through these seemingly diverse ideas has been to induce topology by external manipulations of a single-particle band structure, with interactions playing a negligible role. Exceptions from this noninteracting paradigm are proposals that combine strong interactions with externally induced artificial gauge fields to create nonequilibrium analogs of bosonic fractional quantum Hall states [22][23][24][25].Here, we take a new perspective and consider (bosonic) Bogoliubov excitations ("Bogoliubons") where weak interactions induce a nontrivial topology [26]. We demonstrate that topological Bogoliubons naturally occur on top of a condensate that exhibits a lattice of vortex-antivortex pairs, with no net flux required. Interactions are key to harness the time-reversal (TR) symmetry breaking induced by the condensate vortices. From the viewpoint of Bogoliubov excitations, they generate nontrivial "hopping" phases which lead to an analog of the Haldane lattice model [27]. The corresponding lattice can be defined by a periodic potential introduced either externally or via interactions with the condensate.Although our scheme can be applied to any system described by a two-dimensional (2D) nonlinear Schrödinger equation (Gross-Pitaevskii equation or analog thereof), our analysis focuses on systems of weakly interacting bosons that have a light component, where the required vortex lattice can readily be obtained from the interference of several coherent optical fields (see Fig. 1). In this setting, the phase-imprinting mechanism allowing for nontrivial topology is analogous to that proposed a few years ago in the context of optomech...

A universal quantum computer requires a full set of basic quantum gates. With Majorana bound states one can form all necessary quantum gates in a topologically protected way, bar one. In this paper, we present a scheme that achieves the missing, so-called, π=8 magic phase gate without the need of fine-tuning for distinct physical realizations. The scheme is based on the manipulation of geometric phases described by a universal protocol and converges exponentially with the number of steps in the geometric path. Furthermore, our magic gate proposal relies on the most basic hardware previously suggested for topologically protected gates, and can be extended to an any-phase gate, where π=8 is substituted by any α.

We develop a theory of energy relaxation and thermalization of hot carriers in real quantum wires. Our theory is based on a controlled perturbative approach for large excitation energies and emphasizes the important roles of the electron spin and finite temperature. Unlike in higher dimensions, relaxation in one-dimensional electron liquids requires three-body collisions and is much faster for particles than holes which relax at nonzero temperatures only. Moreover, co-moving carriers thermalize more rapidly than counterpropagating carriers. Our results are quantitatively consistent with a recent experiment.PACS numbers: 71.10.PmIntroduction.-The behavior of electrons confined to move in one spatial dimension is frequently described within the Tomonaga-Luttinger model which assumes a linear dispersion relation for the electrons. In this model, all excitations move at the same velocity so that electron-electron interactions become particularly significant. Consequently, the electron system can no longer be described as a Fermi liquid but instead, is expected to form a Luttinger liquid. In recent years, much effort has been expended on elucidating the consequences of Luttinger-liquid physics in quantum wires [1].A peculiar consequence of the Tomonaga-Luttinger model is the complete absence of inelastic processes for hot particles or holes. As emphasized by a recent experiment [2], the physics of energy relaxation is much richer in real quantum wires with a nonlinear dispersion. In this experiment, hot carriers of well-defined energy and momentum are injected into a quantum wire and their energy relaxation is probed in cleverly designed transport measurements. The experiment shows not only that hot carriers relax but also that energy relaxation is much more efficient for hot particles than for hot holes, in stark contrast to electron liquids in higher dimensions. Moreover, a simple model [2] reproducing the experimental observations assumed that thermalization occurs much faster among co-moving electrons than between rightand left-moving carriers.Foci of recent theoretical work on one-dimensional electron systems were nonequilibrium effects [3,4] and consequences of a nonlinear dispersion [5][6][7][8][9][10]. Nonequilibrium physics of systems with nonlinear dispersions has been accessible within a perturbative approach for weak interactions [11][12][13]. The latter is peculiar because pair collisions are ineffective for a quadratic dispersion. Indeed, by momentum and energy conservation, pair collisions result either in zero-momentum transfer or exchange of the momenta of the colliding particles. Both processes do not change the electronic distribution function. A kinetic theory of real one-dimensional electron systems therefore involves three-body collisions [11].

The Landauer-Büttiker theory of mesoscopic conductors was recently extended to nanoelectromechanical systems. In this extension, the adiabatic reaction forces exerted by the electronic degrees of freedom on the mechanical modes were expressed in terms of the electronic S matrix and its first nonadiabatic correction, the A matrix. Here, we provide a more natural and efficient derivation of these results within the setting and solely with the methods of scattering theory. Our derivation is based on a generic model of a slow classical degree of freedom coupled to a quantum-mechanical scattering system, extending previous work on adiabatic reaction forces for closed quantum systems.