Related papers: Stabilizer operators and Barnes-Wall lattices
A general formula for the linearized Poincar\'e map of a billiard with a potential is derived. The stability of periodic orbits is given by the trace of a product of matrices describing the piecewise free motion between reflections and the…
In this paper we improve the layered implementation of arbitrary stabilizer circuits introduced by Aaronson and Gottesman in Phys. Rev. A 70(052328), 2004: to obtain a general stabilizer circuit, we reduce their $11$-stage computation…
The stabiliser formalism allows the efficient description of a sizeable class of pure as well as mixed quantum states of N-qubit systems. That same formalism has important applications in the field of quantum error correcting codes, where…
We introduce the notion of descriptor embedding for nonlinear systems and use it for the data-driven design of stabilizing controllers. Specifically, we provide sufficient data-dependent LMI conditions which, if feasible, return a…
A group-theoretical approach for studying localized periodic and quasiperiodic vibrations in 2D and 3D lattice dynamical models is developed. This approach is demonstrated for the scalar models on the plane square lattice. The…
Conditions for input-output stability of barrier-based model predictive control of linear systems with linear and convex nonlinear (hard or soft) constraints are established through the construction of integral quadratic constraints (IQCs).…
We present a novel classical algorithm designed to learn the stabilizer group -- namely the group of Pauli strings for which a state is a $\pm 1$ eigenvector -- of a given Matrix Product State (MPS). The algorithm is based on a clever and…
The stability problem of a class of nonlinear switched systems defined on compact sets with state-dependent switching is considered. Instead of the Caratheodory solutions, the general Filippov solutions are studied. This encapsulates…
We construct the type-preserving panel-regular lattices in buildings of type M, for M with entries two, three or infinity, which have cyclic stabilizers of spherical 2-residues. We obtain these lattices as fundamental groups of their…
To a set $\mathcal{B}$ of 4-subsets of a set $\Omega$ of size $n$ we introduce an invariant called the `hole stabilizer' which generalises a construction of Conway, Elkies and Martin of the Mathieu group $M_{12}$ based on Loyd's…
This paper aims to provide various applications for second-order variational analysis of extended-real-valued piecewise liner functions recently obtained in [1]. We mainly focus here on establishing relationships between full stability of…
A large family of deployable filamentary structures can be built by connecting two elastic rods along their length. The resulting structure has interesting shapes that can be stabilized by tuning the material properties of each rod. To…
The IIB matrix model is one of the candidates for nonperturbative formulation of string theory, and it is believed that the model contains gravitational degrees of freedom in some manner. In some preceding works, it was proposed that the…
The standard stabilizer formalism provides a setting to show that quantum computation restricted to operations within the Clifford group are classically efficiently simulable: this is the content of the well-known Gottesman-Knill theorem.…
We present a theoretical method to study driven-dissipative correlated systems on lattices with two spatial dimensions (2D). The steady-state density-matrix of the lattice is obtained by solving the master equation in a corner of the…
This paper is devoted to the stabilization of a linear control system $y' = A y + B u$ and its suitable non-linear variants where $(A, \cD(A))$ is an infinitesimal generator of a strongly continuous {\it group} in a Hilbert space $\mH$, and…
We derive bases of improved operators for all bilinear quark currents up to spin two (including the operators measuring the first moment of DIS Structure Functions), and compute their one-loop renormalization constants for arbitrary…
We discuss several aspects of D-brane moduli spaces and BPS spectra near orbifold points. We give a procedure to determine the decay products on a line of marginal stability, and we define the algebra of BPS states in terms of quivers.…
The quantum stabilizer formalism became foundational for understanding error correction soon after the realization of the first useful quantum error correction codes. Stabilizers provide a way to describe sets of quantum states which are…
We consider the problem of provably finding a stationary point of a smooth function to be minimized on the variety of bounded-rank matrices. This turns out to be unexpectedly delicate. We trace the difficulty back to a geometric obstacle:…