Related papers: A symmetry principle for Topological Quantum Order
This Letter discusses topological quantum computation with gapped boundaries of two-dimensional topological phases. Systematic methods are presented to encode quantum information topologically using gapped boundaries, and to perform…
The concept of entangled quantum states is considered in the context of systems of identical particles, based on the requirement that in order to represent physical states both for the overall system and the sub-systems which may be…
We propose the convex-roof extension of quantum conditional mutual information ("co(QCMI)") as a diagnostic of topological order in a mixed state. We focus primarily on topological states subjected to local decoherence, and employ the…
Higher-order networks encode the many-body interactions of complex systems ranging from the brain to biological transportation networks. Simplicial and cell complexes are ideal higher-order network representations for investigating…
We discuss the existence of stable topological quantum memory at finite temperature. At stake here is the fundamental question of whether it is, in principle, possible to store quantum information for macroscopic times without the…
Quantum entanglement exists in nature but is absent in classical physics, hence it fundamentally distinguishes quantum from classical theories. While entanglement is routinely observed for few-body systems, it is significantly more…
Topological states of matter are promising resources for composing fault-tolerant quantum computers, advancing beyond the limitations of current noisy intermediate-scale quantum devices. To enable this progress, a deep understanding of…
We examine two proposals for marginally self-correcting quantum memory, the cubic code by Haah and the welded code by Michnicki. In particular, we prove explicitly that they are absent of topological order above zero temperature, as their…
For a long time, we thought that only symmetry breaking can give rise to different phases of matter. If there was no symmetry breaking, there would be no pattern and it would be featureless. But now we realize that, for quantum matter at…
Topological gauge theories describe the low-energy properties of certain strongly correlated quantum systems through effective weakly interacting models. A prime example is the Chern-Simons theory of fractional quantum Hall states, where…
We study out-of-time-order correlators (OTOCs) of local operators in spatial-temporal invariant or random quantum circuits using light-like generators (LLG) -- many-body operators that exist in and act along the light-like directions. We…
We analyze surface codes, the topological quantum error-correcting codes introduced by Kitaev. In these codes, qubits are arranged in a two-dimensional array on a surface of nontrivial topology, and encoded quantum operations are associated…
Discoveries of topological states and topological materials reshape our understanding of physics and materials over the last 15 years. First-principles calculations have been playing a significant role in bridging the theory of topology and…
Describing dynamics in a gravitational universe with positive cosmological constant, such as de Sitter space, is a conceptually challenging problem. We propose a principle for constructing a quantum system that can potentially be used to…
Distributed quantum computing offers a promising approach to scaling quantum devices by networking multiple quantum processors. We present a quantum state tomography protocol tailored for distributed quantum computers that avoids assuming…
In this paper, the degenerate ground states of Z2 topological order on a plane with holes (the so-called surface codes) are used as the protected code subspace to build a topological quantum computer by tuning their quantum tunneling…
We demonstrate that two toric code layers on the square lattice coupled by an Ising interaction display two distinct phases with intrinsic topological order. The second-order quantum phase transition between the weakly-coupled…
Systems as diverse as mechanical structures assembled from elastic components, and photonic metamaterials enjoy a common geometrical feature: a sublattice symmetry. This property realizes a chiral symmetry first introduced to characterize a…
We study quantum field theories which have quantum groups as global internal symmetries. We show that in such theories operators are generically non-local, and should be thought as living at the ends of topological lines. We describe the…
We provide a quantitative analysis of the splittings in low-lying numerical entanglement spectra (ES), at given momentum, of a number of quantum states that can be identified, based on "Li-Haldane state-counting", as ground states of…