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We use conformal embeddings involving exceptional affine Kac-Moody algebras to derive new dualities of three-dimensional topological field theories. These generalize the familiar level-rank duality of Chern-Simons theories based on…
We show how to obtain the dual of any lattice model with inhomogeneous local interactions based on an arbitrary Abelian group in any dimension and on lattices with arbitrary topology. It is shown that in general the dual theory contains…
We study dualities of the general Galileon theory in d dimensions in terms of coordinate transformations on the coset space corresponding to the spontaneously broken Galileon group. The most general duality transformation is found to be…
Anyons exhibit a non-trivial interplay between local exclusion rules and non-local braiding and exchange phases, making a consistent commutation algebra and second-quantized formulation challenging. We develop an algebraic framework for…
Two gapped quantum ground states in the same phase are connected by an adiabatic evolution which gives rise to a local unitary transformation that maps between the states. On the other hand, gapped ground states remain within the same phase…
Quantum circuit transformation aims to produce equivalent circuits while optimizing for various aspects such as circuit depth, gate count, and compatibility with modern Noisy Intermediate Scale Quantum (NISQ) devices. There are two…
We introduce the first complete equational theory for quantum circuits. More precisely, we introduce a set of circuit equations that we prove to be sound and complete: two circuits represent the same unitary map if and only if they can be…
We present a complete characterization of diagonal unitary covariant (DU-covariant) superchannels, i.e. higher-order transformations transforming quantum channels into themselves. Necessary and sufficient conditions for complete positivity…
In the accompanying paper of arXiv:2408.13472, we have established the method of characterizing the maximal order of asymptotic unitary designs generated by symmetric local random circuits, and have explicitly specified the order in the…
The recent article [arXiv:2307.12552] gave local topological order (LTO) axioms for a quantum spin system, showed they held in Kitaev's Toric Code and in Levin-Wen string net models, and gave a bulk boundary correspondence to describe bulk…
Universal gate sets for quantum computing have been known for decades, yet no universal gate set has been proposed for particle-conserving unitaries, which are the operations of interest in quantum chemistry. In this work, we show that…
Dualities play a central role in the study of quantum spin chains, providing insight into the structure of quantum phase diagrams and phase transitions. In this work we study categorical dualities, which are defined as bounded-spread…
We characterise the quantum group gauge symmetries underlying q-deformations of two-dimensional Yang-Mills theory by studying their relationships with the matrix models that appear in Chern-Simons theory and six-dimensional N=2 gauge…
We show that in the perturbative regime defined by the coupling constant, the theta-exact Seiberg-Witten map applied to noncommutative U(N) Yang-Mills --with or without Supersymmetry-- gives an ordinary gauge theory which is, at the quantum…
The model systems for self-organized quantum dots formed from elemental and compound semiconductors, namely Ge grown on Si(001) and InAs on GaAs(001), are comparatively studied by scanning tunneling microscopy. It is shown that in both…
It is well-known that if we gauge a $\mathbb{Z}_n$ symmetry in two dimensions, a dual $\mathbb{Z}_n$ symmetry appears, such that re-gauging this dual $\mathbb{Z}_n$ symmetry leads back to the original theory. We describe how this can be…
(i) We point out that every local unitary circuit of depth smaller than the linear system size is easily distinguished from a global Haar random unitary if there is a conserved quantity that is a sum of local operators. This is always the…
We introduce an extended framework for the simultaneous gauging of modulated symmetries in $(d+1)$ dimensions, employing {\it multiple} gauge symmetry operators whose corresponding gauging procedures must be carried out simultaneously.…
We generalize the twisted quantum double model of topological orders in two dimensions to the case with boundaries by systematically constructing the boundary Hamiltonians. Given the bulk Hamiltonian defined by a gauge group $G$ and a…
A noncommutative algebra of the complex $q$-twistors and their differentials is considered on the basis of the quantum $GL_q (4)\times SL_q (2)$ group. Real and pseudoreal $q$-twistors are discussed too. We consider the quantum-group…