Related papers: Knots, links, and long-range magic
Topological quantum field theories can be used as a powerful tool to probe geometry and topology in low dimensions. Chern-Simons theories, which are examples of such field theories, provide a field theoretic framework for the study of knots…
Magic, or nonstabilizerness, characterizes how far away a state is from the stabilizer states, making it an important resource in quantum computing, under the formalism of the Gotteman-Knill theorem. In this paper, we study the magic of the…
We introduce a monotone to quantify the amount of non-stabilizerness (or magic for short), in an arbitrary quantum state. The monotone gives a necessary and sufficient criterion for detecting the presence of magic for both pure and mixed…
Consumption of magic states promotes the stabilizer model of computation to universal quantum computation. Here, we propose three different classical algorithms for simulating such universal quantum circuits, and characterize them by…
Finding ways to quantify magic is an important problem in quantum information theory. Recently Leone, Oliviero and Hamma introduced a class of magic measures for qubits, the stabilizer entropies of order $\alpha$, to aid in studying…
The level-rank duality of SU(2)k Chern-Simons theory is discussed, and applied to graph, hypergraph, and magic states.
Quantum computing's promise lies in its intrinsic complexity, with entanglement initially heralded as its hallmark. However, the quest for quantum advantage extends beyond entanglement, encompassing the realm of nonstabilizer (magic)…
Magic describes the distance of a quantum state to its closest stabilizer state. It is -- like entanglement -- a necessary resource for a potential quantum advantage over classical computing. We study magic, quantified by stabilizer…
We present a family of consistent quantum field theories of monodromy quintessence in strong coupling, which can serve as benchmarks in modeling dark energy different from cosmological constant. These theories have discrete gauge symmetries…
To achieve universal quantum computation via general fault-tolerant schemes, stabilizer operations must be supplemented with other non-stabilizer quantum resources. Motivated by this necessity, we develop a resource theory for magic quantum…
Ground states of quantum many-body systems are both entangled and possess a kind of quantum complexity as their preparation requires universal resources that go beyond the Clifford group and stabilizer states. These resources - sometimes…
We prove that magic states from the Clifford hierarchy give optimal solutions for tasks involving nonlocality and entropic uncertainty with respect to Pauli measurements. For both the nonlocality and uncertainty tasks, stabilizer states are…
Correlations in multiparticle systems are constrained by restrictions from quantum mechanics. A prominent example for these restrictions are monogamy relations, limiting the amount of entanglement between pairs of particles in a…
The state of a knot is defined in the realm of Chern-Simons topological quantum field theory as a holomorphic section on the SU(2) character manifold of the peripheral torus. We compute the asymptotics of the torus knot states in terms of…
In quantum computing, non-stabilizerness -- the magic -- refers to the computational advantage of certain quantum states over classical computers and is an essential ingredient for universal quantum computation. Employing the second order…
Chern-Simons field theory based on a compact non-abelian gauge group is studied as a theory of knots and links in three dimensions. A method to obtain the invariants for links made from braids of upto four strands is developed. This…
We study the set of Crowell states for alternating knot projections and show that for prime alternating knots the space of states for a reduced projection is connected, a result similar to that for Kauffman states. As an application we give…
$\rm SL(2,\mathbb{C})$ Chern-Simons theory on a closed 3-manifold is one of the most interesting, yet tractable examples of a QFT. On one hand, its non-perturbative structure is not yet fully understood; on the other, the mathematical…
Quantum many-body systems have been extensively studied from the perspective of quantum technology, and conversely, critical phenomena in such systems have been characterized by operationally relevant resources like entanglement. In this…
The way in which geometry encodes entanglement is a topic of much recent interest in quantum many-body physics and the AdS/CFT duality. This relation is particularly pronounced in the case of topological quantum field theories, where…