Exponential Lifetime Improvement in Topological Quantum Memories

We propose a simple yet efficient mechanism for passive error correction in topological quantum memories. Our scheme relies on driven-dissipative ancilla systems which couple to local excitations (anyons) and make them "sink" in energy, with no required interaction among ancillae or anyons. Through this process, anyons created by some thermal environment end up trapped in potential "trenches" that they themselves generate, which can be interpreted as a "memory foam" for anyons. This self-trapping mechanism provides an energy barrier for anyon propagation, and removes entropy from the memory by favoring anyon recombination over anyon separation (responsible for memory errors). We demonstrate that our scheme leads to an exponential increase of the memory-coherence time with system size $L$, up to an upper bound $L_\mathrm{max}$ which can increase exponentially with $\Delta/T$, where $T$ is the temperature and $\Delta$ is some energy scale defined by potential trenches. This results in a double exponential increase of the memory time with $\Delta/T$, which greatly improves over the Arrhenius (single-exponential) scaling found in typical quantum memories.Comment: 18 pages including appendices; 8 figure

Topological polaritons from photonic Dirac cones coupled to excitons in a magnetic field

We introduce an alternative scheme for creating topological polaritons (topolaritons) by exploiting the presence of photonic Dirac cones in photonic crystals with triangular lattice symmetry. As recently proposed, topolariton states can emerge from a coupling between photons and excitons combined with a periodic exciton potential and a magnetic field to open up a topological gap. We show that in photonic crystals the opening of the gap can be substantially simplified close to photonic Dirac points. Coupling to Zeeman-split excitons breaks time reversal symmetry and allows to gap out the Dirac cones in a nontrival way, leading to a topological gap similar to the strength of the periodic exciton potential. Compared to the original topolariton proposal [T. Karzig et al., Phys. Rev. X 5, 031001 (2015)], this scheme significantly increases the size of the topological gap over a wide range of parameters. Moreover, the gap opening mechanism highlights an interesting connection between topolaritons and the scheme of [F. D. M. Haldane and S. Raghu, Phys. Rev. Lett. 100, 013904 (2008)] to create topological photons in magneto-optically active materials

Shortcuts to nonabelian braiding

Topological quantum information processing relies on adiabatic braiding of nonabelian quasiparticles. Performing the braiding operations in finite time introduces transitions out of the ground-state manifold and deviations from the nonabelian Berry phase. We show that these errors can be eliminated by suitably designed counterdiabatic correction terms in the Hamiltonian. We implement the resulting shortcuts to adiabaticity for simple protocols of nonabelian braiding and show that the error suppression can be substantial even for approximate realizations of the counterdiabatic terms.Comment: 5 pages, 3 figures plus supplementary materia

Topological Polaritons

The interaction between light and matter can give rise to novel topological states. This principle was recently exemplified in Floquet topological insulators, where \emph{classical} light was used to induce a topological electronic band structure. Here, in contrast, we show that mixing \emph{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 non-trivial 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 spin-orbit coupling 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.Comment: For Supplementary Information and Video see source files; v3: updated to published versio

Interaction effects in superconductor/quantum spin Hall devices: universal transport signatures and fractional Coulomb blockade

Interfacing s-wave superconductors and quantum spin Hall edges produces time-reversal-invariant topological superconductivity of a type that can not arise in strictly 1D systems. With the aim of establishing sharp fingerprints of this novel phase, we use renormalization group methods to extract universal transport characteristics of superconductor/quantum spin Hall heterostructures where the native edge states serve as leads. We determine scaling forms for the conductance through a grounded superconductor and show that the results depend sensitively on the interaction strength in the leads, the size of the superconducting region, and the presence or absence of time-reversal-breaking perturbations. We also study transport across a floating superconducting island isolated by magnetic barriers. Here we predict e-periodic Coulomb-blockade peaks, as recently observed in nanowire devices [Albrecht et al., Nature 531, 206 (2016)], with the added feature that the island can support fractional charge tunable via the relative orientation of the barrier magnetizations. As an interesting corollary, when the magnetic barriers arise from strong interactions at the edge that spontaneously break time-reversal symmetry, the Coulomb-blockade periodicity changes from e to e/2. These findings suggest several future experiments that probe unique characteristics of topological superconductivity at the quantum spin Hall edge.Comment: 18 pages, 7 figure

A geometric protocol for a robust Majorana magic gate

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 manuscript we present a protocol that achieves the missing, so called, $\pi/8$ 'magic' phase gate. The protocol is based on the manipulation of geometric phases in a universal manner, and does not require fine tuning for distinct physical realizations. The protocol converges exponentially with the number of steps in the geometric path. Furthermore, the magic gate protocol relies on the most basic hardware previously suggested for topologically protected gates, and can be extended to any-phase-gate, where $\pi/8$ is substituted by any $\alpha$.Comment: 14 pages, 8 figures (including appendices), v3: simplified derivation, more explicit connection between topological protection and exponential convergenc

Chiral Bogoliubons in Nonlinear Bosonic Systems

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 (2D) nonlinear Schr\"odinger 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.Comment: 6 pages, 3 figures; with Supplemental Material (5 pages; in source

Boosting Majorana zero modes

One-dimensional topological superconductors are known to host Majorana zero modes at domain walls terminating the topological phase. Their non-Abelian nature allows for processing quantum information by braiding operations that are insensitive to local perturbations, making Majorana zero modes a promising platform for topological quantum computation. Motivated by the ultimate goal of executing quantum-information processing on a finite time scale, we study domain walls moving at a constant velocity. We exploit an effective Lorentz invariance of the Hamiltonian to obtain an exact solution of the associated quasiparticle spectrum and wave functions for arbitrary velocities. Essential features of the solution have a natural interpretation in terms of the familiar relativistic effects of Lorentz contraction and time dilation. We find that the Majorana zero modes remain stable as long as the domain wall moves at subluminal velocities with respect to the effective speed of light of the system. However, the Majorana bound state dissolves into a continuous quasiparticle spectrum after the domain wall propagates at luminal or even superluminal velocities. This relativistic catastrophe implies that there is an upper limit for possible braiding frequencies even in a perfectly clean system with an arbitrarily large topological gap. We also exploit our exact solution to consider domain walls moving past static impurities present in the system

Topological Polaritons and Excitons in Garden Variety Systems

Topological polaritons (aka topolaritons) present a new frontier for topological behavior in solid-state 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.Comment: 6 pages, 4 figures; v2: improved figures and text, with added details regarding achievable topological gap