Related papers: Bootstrapping Matrix Quantum Mechanics
Supersymmetric quantum mechanics is well known to provide, together with the so-called shape invariance condition, an elegant method to solve the eigenvalue problem of some one-dimensional potentials by simple algebraic manipulations. In…
We propose the variational quantum singular value decomposition based on encoding the elements of the considered { $N\times N$} matrix into the state of a quantum system of appropriate dimension. This method doesn't use the expansion of…
Conventional weak-coupling perturbation theory suffers from problems that arise from resonant coupling of successive orders in the perturbation series. Multiple-scale perturbation theory avoids such problems by implicitly performing an…
Quantum renormalization group scheme provides a microscopic understanding of holography through a general mapping between the beta functions of underlying quantum field theories and the holographic actions in the bulk. We show that the…
A finite dimensional system with a quadratic Hamiltonian constraint is Dirac quantized in holomorphic, antiholomorphic and mixed representations. A unique inner product is found by imposing Hermitian conjugacy relations on an operator…
Stochastic nonequilibrium exclusion models are treated using a real space scaling approach. The method exploits the mapping between nonequilibrium and quantum systems, and it is developed to accommodate conservation laws and duality…
The measurement process for hidden-configuration formulations of quantum mechanics is analysed. It is shown how a satisfactory description of quantum measurement can be given in this framework. The unified treatment of hidden-configuration…
We describe the application of the quantum mechanical bootstrap to the solution of one-dimensional scattering problems. By fixing a boundary and modulating the Robin parameter of the boundary conditions we are able to extract the reflection…
Fundamental matrix operations and solving linear systems of equations are ubiquitous in scientific investigations. Using the "Sender-Receiver" model, we propose quantum algorithms for matrix operations such as matrix-vector product,…
Supersymmetric quantum gauge theories are important mathematical tools in high energy physics. As an example, supersymmetric matrix models can be used as a holographic description of quantum black holes. The wave function of such…
Matrix scaling and matrix balancing are two basic linear-algebraic problems with a wide variety of applications, such as approximating the permanent, and pre-conditioning linear systems to make them more numerically stable. We study the…
With the decline of the Copenhagen interpretation of quantum mechanics and the recent experiments indicating that quantum mechanics does actually embody 'objective reality', one might ask if a 'mechanical', conceptual model for quantum…
We develop a novel numerical bootstrap for unitary, crossing-symmetric conformal field theories, focusing on moment observables defined as weighted averages over conformal data. Providing a global and coarse-grained probe of the operator…
Equations of motion of large N quantum mechanics are solved for infinite N in the case of unbroken global O(N) symmetry. It is shown that the only correction to the action is a change in the potential. All characteristics of the motion…
We introduce new representations to formulate quantum mechanics on noncommutative coordinate space, which explicitly display entanglement properties between degrees of freedom of different coordinate components and hence could be called…
Tailoring many-body interactions among a proper quantum system endows it with computing ability by means of static quantum computation in the sense that some of the physical degrees of freedom can be used to store binary information and the…
A bootstrap program is presented for algebraically solving the $R$-matrix of a generic integrable quantum spin chain from its Hamiltonian. The Yang-Baxter equation contains an infinite number of seemingly independent constraints on the…
We derive out a complete series expression of Hamiltonian eigenvalues without any approximation and cut in the general quantum systems based on Wang's formal framework \cite{wang1}. In particular, we then propose a calculating approach of…
We investigate a stochastic approach to non-equilibrium quantum spin systems based on recent insights linking quantum and classical dynamics. Exploiting a sequence of exact transformations, quantum expectation values can be recast as…
It is shown that the Hamilton equations in supersymmetric quantum mechanics can be presented in nonassociative form, where the Hamiltonian is decomposed into two nonassociative factors.