Related papers: Topological line in frustrated Toric code models

Topological phase transitions beyond anyon condensation remain poorly understood. A notable example is the transition between the toric code (TC) and double semion (DS) phases, which has two distinct $\mathbb{Z}_2$ topological orders in (2…

We consider a one-dimensional, time-reversal-invariant system with attractive interactions and spin-orbit coupling. Such a system is gapless due to the strong quantum fluctuations of the superconducting order parameter. However, we show…

A general strategy of alternated slide construction to craft topological metals is proposed, where there is a relative slide between the odd and even chains in the trivial spinless quantum wire array. Firstly, taking the three-leg ladder as…

The Topological Hypothesis states that phase transitions should be related to changes in the topology of configuration space. The necessity of such changes has already been demonstrated. We characterize exactly the topology of the…

Topologically ordered phases in $2+1$ dimensions are generally characterized by three mutually-related features: fractionalized (anyonic) excitations, topological entanglement entropy, and robust ground state degeneracy that does not…

Topologically protected edge states exactly at topological phase boundaries challenge the conventional belief that topological states must be associated with a bulk energy gap. Because periodically driven (Floquet) systems host unusually…

Landau theory's implicit assumption that microscopic details cannot affect the system's phases has been challenged only recently in systems such as antiferromagnetic quantum spin chains with periodic boundary conditions, where topological…

A quantum error correcting code protects encoded logical information against errors. Transversal gates are a naturally fault-tolerant way to manipulate logical qubits but cannot be universal themselves. Protocols such as magic state…

Topological defects (such as monopoles, vortex lines, or domain walls) mark locations where disparate choices of a broken symmetry vacuum elsewhere in the system lead to irreconcilable differences. They are energetically costly (the energy…

The exploration of topologically-ordered states of matter is a long-standing goal at the interface of several subfields of the physical sciences. Such states feature intriguing physical properties such as long-range entanglement, emergent…

Motivated by the recent success of realizing the topologically ordered ground state of the exactly solvable toric code model by a quantum circuit on the real quantum device [K. J. Satzinger {\it et al}., Science \textbf{374}, 1237 (2021)],…

It is known that noisy topological quantum codes are related to random bond Ising models where the order-disorder phase transition in the classical model is mapped to the error threshold of the corresponding topological code. On the other…

Topological superconductors harbor, at their boundaries and vortex cores, zero-energy Majorana bound states, which can be the building blocks in fault-tolerant topological quantum computing. Planar Josephson junctions host such topological…

Quantum computers, with parallel computing and entanglement effects, excel in cryptography analysis and big data processing. However, they are not fully developed yet, and their performance needs further evaluation. Traditional computer…

Topological magnetic textures are particle-like spin configurations stabilized by competing interactions. Their formation is commonly attributed to fluctuation-driven, first-order nucleation processes requiring activation over a topological…

In practice, since many communication networks are huge in scale, or complicated in structure, or even dynamic, the predesigned linear network codes based on the network topology is impossible even if the topological structure is known.…

In topology, a torus remains invariant under certain non-trivial transformations known as modular transformations. In the context of topologically ordered quantum states of matter, these transformations encode the braiding statistics and…

Topological quantum computing is a way of allowing precise quantum computations to run on noisy and imperfect hardware. One implementation uses surface codes created by forming defects in a highly-entangled cluster state. Such a method of…

Despite the evident necessity of topological protection for realizing scalable quantum computers, the conceptual underpinnings of topological quantum logic gates had arguably remained shaky, both regarding their physical realization as well…

Predictive coding has emerged as an influential normative model of neural computation, with numerous extensions and applications. As such, much effort has been put into mapping PC faithfully onto the cortex, but there are issues that remain…