Related papers: The solution of the quantum $A_1$ T-system for arb…
Motivated by the challenge of seeking a rigorous foundation for the bulk-boundary correspondence for free fermions, we introduce an algorithm for determining exactly the spectrum and a generalized-eigenvector basis of a class of banded…
With the increasing popularity of quantum computing and in particular quantum annealing, there has been growing research to evaluate the meta-heuristic for various problems in linear algebra: from linear least squares to matrix and tensor…
For an infinite Toeplitz matrix $T$ with nonnegative real entries we find the conditions, under which the equation $\boldsymbol{x}=T\boldsymbol{x}$, where $\boldsymbol{x}$ is an infinite vector-column, has a nontrivial bounded positive…
It is well known that the unitary evolution of a closed $M-$level quantum system can be generated by a non-Hermitian Hamiltonian $H$ with real spectrum. Its Hermiticity can be restored via an amended inner-product metric $\Theta$. In…
The Liouville equation is well known to be linearizable by a point transformation. It has an infinite dimensional Lie point symmetry algebra isomorphic to a direct sum of two Virasoro algebras. We show that it is not possible to discretize…
We show that nonlinear problems including nonlinear partial differential equations can be efficiently solved by variational quantum computing. We achieve this by utilizing multiple copies of variational quantum states to treat…
A proposal of an algebraic model for the relation between a quantum environment and certain classical particle system is given. The quantum environment is described by a category of possible quantum states, the initial particle system is…
The general d-dimensional twisted group lattice is solved. The irreducible representations of the corresponding group are constructed by an explicit procedure. It is proven that they are complete. All matrix representation solutions to the…
We address the issue of the validity of linear response theory for a closed quantum system subject to a periodic external driving. Linear response theory (LRT) predicts energy absorption at frequencies of the external driving where the…
A new approximate solution to the quantum-classical Liouville equation is derived starting from the formal solution of this equation in forward-backward form. The time evolution of a mixed quantum-classical system described by this equation…
Universality of quantum mechanics -- its applicability to physical systems of quite different nature and scales -- indicates that quantum behavior can be a manifestation of general mathematical properties of systems containing…
In this work we present an intuitive construction of the quantum logical axiomatic system provided by George Mackey. The goal of this work is a detailed discussion of the results from the paper 'Physical justification for using the tensor…
Quantum networks offer a unifying set of opportunities and challenges across exciting intellectual and technical frontiers, including for quantum computation, communication, and metrology. The realization of quantum networks composed of…
There are two classes of quantum integrable systems on a manifold with quadratic integrals, the Liouville and the Lie integrable systems as it happens in the classical case. The quantum Liouville quadratic integrable systems are defined on…
The formalism of quantum theory over discrete systems is extended in two significant ways. First, quantum evolutions are generalized to act over entire network configurations, so that nodes may find themselves in a quantum superposition of…
Probabilistic quantum cloning and identifying machines can be constructed via unitary-reduction processes [Duan and Guo, Phys. Rev. Lett. 80, 4999 (1998)]. Given the cloning (identifying) probabilities, we derive an explicit representation…
The establishment of a scalable scheme for quantum computing with addressable and long-lived qubits would be a scientific watershed, harnessing the laws of quantum physics to solve classically intractable problems. The design of many…
We derive explicit expressions for the generating series of the fundamental solutions of the $A_r$ quantum $Q$-system of Ref. [P. Di Francesco and R. Kedem, arXiv:1006.4774 [math-ph]], expressed in terms of any admissible initial data.…
We define a random Liouville function (\lambda_Q) which depends on a random set (Q) of primes and prove that (A_Q = \{n \in \mathbb{N} | \lambda_Q(n) = -1 \}) is normal almost everywhere. This fact enables us to generate a family of normal…
The aim of this paper is to derive a raw Bloch model for the interaction of light with quantum boxes in the framework of a two-electron-species (conduction and valence) description. This requires a good understanding of the one-species case…