相关论文: Resource complexity of Symmetry Protected Topologi…

Here we investigate the connection between topological order and the geometric entanglement, as measured by the logarithm of the overlap between a given state and its closest product state of blocks. We do this for a variety of…

Under unitary evolution, chaotic quantum systems initialized in simple states rapidly develop high complexity, precluding any efficient classical description. Quantum chaos is traditionally characterized by spectral properties of the…

Recent results on the non-universality of fault-tolerant gate sets underline the critical role of resource states, such as magic states, to power scalable, universal quantum computation. Here we develop a resource theory, analogous to the…

Magic and entanglement are two measures that are widely used to characterize quantum resources. We study the interplay between magic and entanglement in two-qubit systems, focusing on the two extremes: maximal magic and minimal magic for a…

A self-correcting quantum memory can store and protect quantum information for a time that increases without bound with the system size and without the need for active error correction. We demonstrate that symmetry can lead to…

We show that the low-energy states of non-Abelian topological orders possess extensive magic which is long-ranged, and cannot be eliminated by a constant-depth local unitary circuit. This refines conventional notions of complexity beyond…

Topological phases have been extensively studied over the past two decades, primarily in quantum pure states, where they are protected by exact symmetries. Recently, numerous studies have theoretically demonstrated the existence of average…

Magic, or nonstabilizerness, characterizes the deviation of a quantum state from the set of stabilizer states and plays a fundamental role from quantum state complexity to universal fault-tolerant quantum computing. However, analytical or…

Symmetry-protected topological (SPT) phases exhibit nontrivial order if symmetry is respected but are adiabatically connected to the trivial product phase if symmetry is not respected. However, unlike the symmetry-breaking phase, there is…

We discuss the interplay between thermodynamics and magic resources in closed quantum dynamics by introducing Clifford ergotropy, the amount of extractable energy under the restriction to Clifford operations. We provide universal upper…

Symmetry protected topological (SPT) phases with gapless edge excitations have been shown to exist in principle in strongly interacting bosonic/fermionic systems and it is highly desirable to find practical systems to realize such phases…

We study symmetry-protected topological (SPT) phases of matter in 2D protected by symmetries acting on fractal subsystems of a certain type. Despite the total symmetry group of such systems being subextensively large, we show that only a…

We reveal the connection between two-dimensional subsystem symmetry-protected topological (SSPT) states and two-dimensional topological orders via a self-dual frustrated toric code model. This model, an enrichment of the toric code (TC)…

Topological entanglement entropy has been extensively used as an indicator of topologically ordered phases. We study the conditions needed for two-dimensional topologically trivial states to exhibit spurious contributions that contaminates…

Motivated by their necessity for most fault-tolerant quantum computation schemes, we formulate a resource theory for magic states. We first show that robustness of magic is a well-behaved magic monotone that operationally quantifies the…

We discuss the symmetry-protected topological (SPT) orders for bosonic systems from an information-theoretic viewpoint. We show that with a proper choice of the onsite basis, the degenerate ground-state space of SPT orders (on a manifold…

Symmetry protected topological phases exhibit nontrivial short-ranged entanglement protected by symmetry and cannot be adiabatically connected to trivial product states while preserving the symmetry. In contrast, intrinsic topological…

We consider the possibility for phases of matter in which a continuous symmetry is spontaneously broken in a \emph{topologically non-trivial} way, which, roughly, means that the action for the Goldstone modes contains a quantized…

Topological phases are unique states of matter which support non-local excitations which behave as particles with fractional statistics. A universal characterization of gapped topological phases is provided by the topological entanglement…

Non-stabilizerness, or magic, is a resource for universal quantum computation in most fault-tolerant architectures; access to states with non-stabilizerness allows for non-classically simulable quantum computation to be performed.…