A one-dimensional spin-orbit coupled nanowire with proximity-induced pairing from a nearby $s$-wave superconductor may be in topological nontrivial state, which it has zero-energy Majorana bound state at each end. We find that the trivial phase have fermionic end states an exponentially small energy, if confinement potential wire's ends is smooth. The possible existence of such near-zero-energy levels implies mere observation zero-bias peak tunneling conductance not exclusive signature...

We study a free fermion model where two sets of non-commuting non-projective measurements stabilize area-law entanglement scaling phases distinct topological order. show the presence phase transition that is different universality class than observed in stroboscopic projective circuits. In unitary dynamics, topologically are separated by region with sub-volume entropy. find this well identified combination bipartite entropy and further diagram qualitatively captured an analytically tractable...

A recent experiment Mourik et al. [Science 336, 1003 (2012)] on InSb quantum wires provides possible evidence for the realization of a topological superconducting phase and formation Majorana bound states. Motivated by this experiment, we consider signature states in differential tunneling conductance multisubband wires. We show that weight Majorana-induced zero-bias peak is strongly enhanced mixing subbands, when disorder added to end wire. also how transition reflected gap structure...

It is by now well recognized that the naive application of projection postulate on composite quantum systems can induce signalling between their constituent components, indicative a breakdown causality in relativistic spacetime context. Here we introduce necessary and sufficient condition for an ideal measurement observable to be nonsignalling. As as being particularly simple, it generalizes previous no-signalling conditions allows degeneracies applied all bounded self-adjoint operators. The...

One-dimensional $p$-wave superconductors are known to harbor Majorana bound states at their ends. Superconducting wires with a finite width $W$ may have fermionic subgap in addition possible end states. While they do not necessarily inhibit the use of for topological computation, these can obscure identification phase through density-of-states measurement. We present two simple models describe low-energy If wire's is much smaller than superconductor coherence length $\ensuremath{\xi}$,...

We study the nonequilibrium dynamics of quenching through a quantum critical point in topological systems, focusing on one their defining features: ground-state degeneracies and associated sectors. present notion ``topological blocking,'' experienced by due to mismatch between two phases, we argue that dynamic evolution quench depends strongly sector being probed. demonstrate this interplay topology models stemming from extensively studied transverse Ising chain Kitaev honeycomb model....

We present a solution of Kitaev's spin model on the honeycomb lattice and related topologically ordered models. employ Jordan-Wigner type fermionization find that Hamiltonian takes BCS form, allowing system to be solved by Bogoliubov transformation. Our does not non-physical auxiliary degrees freedom eigenstates we obtain are completely explicit in terms variables. The ground-state is obtained as condensate fermion pairs over vacuum state which corresponds toric code with same vorticity....

The one-dimensional p-wave topological superconductor model with open-boundary conditions is examined in its phase. Using the eigenbasis of non-interacting system I show that, provided interactions are local and do not result a closing gap, then even odd parity sectors unitarily equivalent. Following on from this, it possible to define two many-body operators that connect each state one sector degenerate counterpart opposite parity. This applies all states therefore establishes, for long...

Resonance effects lead to surprising and beautiful phenomena in many areas of physics. Here, the authors identify resonance points as key understanding breakdown revival strong zero modes parafermionic clock models. Through analytic numerical methods, they have been able determine behavior at away from points, proving statements about asymptotic these systems. In particular, show that there exists special parameter space where can exist and, such, topological degeneracy is preserved all energies.

Quantum control, which refers to the active manipulation of physical systems described by laws quantum mechanics, constitutes an essential ingredient for development technology. Here we apply Differentiable Programming (DP) and Natural Evolution Strategies (NES) optimal transport Majorana zero modes in superconducting nanowires, a key element success Majorana-based topological computation. We formulate motion control as optimization problem propose new categorization four different regimes...

In the topological phase of $p$-wave superconductors, zero-energy Majorana quasiparticle excitations can be well defined in presence local density-density interactions. Here, we examine this phenomenon from perspective matrix representations commutator $\mathcal{H}=[H,\ifmmode\bullet\else\textbullet\fi{}]$, with aim characterizing multiparticle content many-body mode. To do show that, for quadratic fermionic systems, $\mathcal{H}$ always decomposed into subblocks that act as generalizations...

The classification of loop symmetries in Kitaev's honeycomb lattice model provides a natural framework to study the Abelian topological degeneracy. We derive perturbative low-energy effective Hamiltonian that is valid all orders expansion and for possible toroidal configurations. Using this form we demonstrate at what order system's degeneracy lifted by finite size effects note thermodynamic limit it robust orders. Further, themselves correspond creation, propagation, annihilation fermions....

Multimode spinless $p$-wave superconducting wires with a width $W$ much smaller than the coherence length $\ensuremath{\xi}$ are known to have multiple low-energy subgap states localized near wire's ends. Here we compare typical energies of such endstates for various terminations wire: A wire coupled normal-metal stub, weakly disordered superconductor and smooth confinement. Depending on termination, find that can be higher or lower case rectangular hard-wall boundaries.

Interest in quantum memory devices based on topological superconductors and their non-Abelian zero modes is motivated by the observation that at temperature information stored these exponentially protected. In noninteracting systems, due to fact system can be described using normal modes, much of this protection also exists higher temperatures. The authors examine here how picture gradually breaks down temperatures when interactions are present, explore conjecture may recovered...

We show that networks of superconducting topological nanowires can realize the physics exactly solvable Kitaev spin models on trivalent lattices. This connection arises from low-energy theory both systems being described by a tight-binding model Majorana modes. In description provides convenient representation to solve model, whereas in an array Josephson junctions it localized physical modes tunneling between wire ends. explicitly three wires---a setup relevant quantum computing with...

We investigate dynamical evolution of a topological memory that consists two $p$-wave superconducting wires separated by nontopological junction, focusing on the primary errors (i.e., qubit loss) and secondary (bit phase flip) arise due to nonadiabaticity. On question loss we examine system's response both periodic boundary driving deliberate shuttling Majorana bound states. In former scenario, show how frequency-dependent rate is strongly correlated with local density states at edge wire,...

Exactly solvable lattice models for spins and non-interacting fermions provide fascinating examples of topological phases, some them exhibiting the localized Majorana that feature in proposals quantum computing. The Chern invariant ν is an important characterization such phases. Here we look at square–octagon variant Kitaev's honeycomb model. It maps to spinful paired enjoys a rich phase diagram featuring distinct Abelian non-Abelian phases with = 0,±1,±2,±3 ±4. ±1 ±3 all support modes are...

We examine the star lattice Kitaev model whose ground state is a chiral spin liquid. fermionize such that fermionic vacua are toric-code states on an effective Kagome lattice. This implies Abelian phase of system inherited from and time-reversal symmetry spontaneously broken at level vacuum. In terms these fermions we derive Bloch-matrix Hamiltonians for vortex-free sector its time-reversed counterpart illuminate relationships between sectors. The diagram shown to be sphere in space coupling...

In this work we discuss the formation of zero energy vortex and chiral edge modes in a fermionic representation Kitaev honeycomb model. We introduce show how associated Jordan-Wigner procedure naturally defines so called branch cuts that connect topological excitations. Using notion to, non-Abelian phase model, describe Majorana mode structure with Furthermore how, by intersecting edges between Abelian domains, dictate character modes. particular will see what situations exact exist. On...

Quantum many-body scarring is believed to be the mechanism behind long-lived coherent oscillations in interacting Rydberg atom chains. These persistent are due large overlap of scars with certain initial states. We show that "effective dimension" a useful measure for identifying non-thermalising states scarred systems. By minimising effective dimension we find physically reasonable chain lead more pronounced and longer lived oscillations, accentuating effect on dynamics.

We analyze low energy spectral properties of small toroidal configurations the Kitaev honeycomb spin model in Abelian topological phase. begin with a brief classification lattices on torus. Then, using Brillouin–Wigner perturbation theory, we explain order finite size effects that can occur these systems and show how they affect their ground state degeneracy. Finally, demonstrate accuracy perturbative method by means exact diagonalization, use insights into to reconstruct degeneracy example system.

We study a free fermion model where two sets of non-commuting non-projective measurements stabilize area-law entanglement scaling phases distinct topological order. show the presence phase transition that is different universality class than observed in stroboscopic projective circuits. In unitary dynamics, topologically are separated by region with sub-volume entropy. find this well identified combination bipartite entropy and further diagram qualitatively captured an analytically tractable...

It has recently been established that quantum many-body scarring can prevent the thermalisation of some isolated systems, starting from certain initial states. One first models to show this was so-called PXP Hamiltonian, which used theoretically model an experiment on a chain strongly interacting Rydberg atoms. A defining feature Hamiltonian is set dynamical constraints make states inaccessible dynamics. In paper we construct class spin are parameterised by discrete variable $\ell$ controls...

We propose an efficient procedure for numerically evolving the quantum dynamics of delta-kicked harmonic oscillator. The method allows longer and more accurate simulations system as well a simple calculating system's Floquet eigenstates quasienergies. is used to examine dynamical behavior in cases where ratio kicking frequency natural both rational irrational.