Related papers: Topological line in frustrated Toric code models
The discovery of topological order has revolutionized the understanding of quantum matter in modern physics and provided the theoretical foundation for many quantum error correcting codes. Realizing topologically ordered states has proven…
Circuits provide ideal platforms of topological phases and matter, yet the study of topological circuits in the strongly nonlinear regime, has been lacking. We propose and experimentally demonstrate strongly nonlinear topological phases and…
Topologically ordered phases have robust degenerate ground states against the local perturbations, providing a promising platform for fault-tolerant quantum computation. Despite of the non-local feature of the topological order, we find…
We present the first examples of topological phases of matter with uniform power for measurement-based quantum computation. This is possible thanks to a new framework for analyzing the computational properties of phases of matter that is…
Topological phases of matter are primarily studied in systems with short-range interactions. In nature, however, non-relativistic quantum systems often exhibit long-range interactions. Under what conditions topological phases survive such…
Recently topological states of matter have witnessed a new physical phenomenon where both edge modes and gapless bulk coexist at topological quantum criticality. The presence and absence of edge modes on a critical line can lead to an…
Topological color codes are widely acknowledged as promising candidates for fault-tolerant quantum computing. Neither a two-dimensional nor a three-dimensional topology, however, can provide a universal gate set $\{$H, T, CNOT$\}$, with the…
We study the phase diagram of a topological string-net type lattice model in the presence of geometrically frustrated interactions. These interactions drive several phase transitions that reduce the topological order, leading to a rich…
Topological frustration (or topological mechanics) is the existence of classical zero modes that are robust to many but not all distortions of the Hamiltonian. It arises naturally from locality in systems whose interactions form a set of…
Mixed-state phases of matter under local decoherence have recently garnered significant attention due to the ubiquitous presence of noise in current quantum processors. One of the key issues is understanding how topological quantum memory…
Quantum computers are predicted to utilize quantum states to perform memory and to process tasks far faster than those of conventional classical computers. In this paper we show a new road towards building fault tolerance quantum computer…
Three-dimensional (3D) topological codes offer the advantage of supporting fault-tolerant implementations of non-Clifford gates, yet their performance against realistic noise remains largely unexplored. In this work, we focus on the…
We theoretically propose a quantum simulation scheme for the toric-code Hamiltonian, the paradigmatic model of a quantum spin liquid, based on time-periodic driving. We develop a hybrid continuous-digital strategy that exploits the…
This work explores a deformation of the Kitaev toric code that induces a phase transition out of the topologically ordered phase. By placing the model on a cylinder, the bulk global 1-form symmetries separate into distinct boundary…
Topological phases of matter are considered the bedrock of novel quantum materials as well as ideal candidates for quantum computers that possess robustness at the physical level. The robustness of the topological phase at finite…
We investigate the quantum robustness of the topological order in the toric code on the honeycomb lattice in the presence of a uniform parallel field. For a field in $z$-direction, the low-energy physics is in the flux-free sector and can…
The inevitable presence of decoherence effects in systems suitable for quantum computation necessitates effective error-correction schemes to protect information from noise. We compute the stability of the toric code to depolarization by…
The robustness of the topological color code, which is a class of error correcting quantum codes, is investigated under the influence of an uniform magnetic field on the honeycomb lattice. Our study relies on two high-order series…
In this short review, I draw attention to new developments in the theory of fault tolerance in quantum computation that may give concrete direction to future work in the development of superconducting qubit systems. The basics of quantum…
Topological quantum codes are intrinsically fault-tolerant to local noise, and underlie the theory of topological phases of matter. We explore geometry to enhance the performance of topological quantum codes by rotating the four dimensional…