Related papers: TBA Equations and Quantization Conditions
A formalism is developed to obtain the energy eigenvalues of spatially confined quantum mechanical systems in the framework of The usual WKB and MAF methods. The technique is applied to three different cases,viz one dimensional Harmonic…
The problem of quantum state preparation is one of the main challenges in achieving the quantum advantage. Furthermore, classically, for multi-level problems, our ability to solve the corresponding quantum optimal control problems is rather…
We develop a systematic procedure for constructing quantum many-body problems whose spectrum can be partially or totally computed by purely algebraic means. The exactly-solvable models include rational and hyperbolic potentials related to…
The Quantum Approximate Optimization Algorithm (QAOA) is a promising variational quantum algorithm introduced to tackle classically intractable combinatorial optimization problems. This tutorial offers a comprehensive, first-principles…
Quantum deformed potentials arise naturally in quantum mechanical systems of one bosonic coordinate coupled to $N_f$ Grassmann valued fermionic coordinates, or to a topological Wess-Zumino term. These systems decompose into sectors with a…
We prove the existence of topological quantum error correcting codes with encoding rates $k/n$ asymptotically approaching the maximum possible value. Explicit constructions of these topological codes are presented using surfaces of…
Analytic and approximate solutions for the energy eigenvalues generated by a confined softcore Coulomb potentials of the form a/(r+\beta) in d>1 dimensions are constructed. The confinement is effected by linear and harmonic-oscillator…
This paper proposes a trigonometric interpolation-based approach (TIBA) to approximate solutions of mixed boundary value problems of second-order ODEs. TIBA leverages the analytic attractiveness of a trigonometric polynomial to reformulate…
Quantum tunneling across multiple barriers as yet is an unsolved problem for barrier numbers greater than five. The complexity of the mathematical analysis even for small number of barriers pushed it into the realms of Numerical Analysis.…
We continue the study of a novel relation between quantum periods and TBA(Thermodynamic Bethe Ansatz)-like difference equations, generalize previous works to a large class of Calabi-Yau geometries described by three-term quantum operators.…
The truncated Wigner approximation (TWA) enables us to investigate bosonic quantum many-body dynamics, including open quantum systems described by the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) equation. In the TWA, the Weyl-Wigner…
Unbounded potentials are always utilized to strictly confine quantum dynamics and generate bound or stationary states due to the existence of quantum tunneling. However, the existed accurate Wigner solvers are often designed for either…
Semiclassical quantization is exact only for the so called \emph{solvable} potentials, such as the harmonic oscillator. In the \emph{nonsolvable} case the semiclassical phase, given by a series in $\hbar$, yields more or less approximate…
Quantum computing offers significant potential for solving NP-hard combinatorial (optimization) problems that are beyond the reach of classical computers. One way to tap into this potential is by reformulating combinatorial problems as a…
Recently the authors developed a scattering approach that allows for a complete description of the steady-state physics of quantum-impurities in and out of equilibrium. Quantum impurities are described using scattering eigenstates defined…
The classical WKB method (also known as the WKBJ method, the LG method, or the phase integral method) for solving singularly perturbed linear differential equations has never, as far as we know, been looked at from the structured backward…
Stabilizer-based simulation of quantum error-correcting codes typically relies on the Pauli-twirling approximation (PTA) to render non-Clifford noise classically tractable, but PTA can distort the behavior of physically relevant channels…
We show that supersymmetry is a simple but powerful tool to exactly solve quantum mechanics problems. Here, the supersymmetric approach is used to analyse a quantum system with periodic P\"oschl-Teller potential, and to find out the exact…
The problem of quantum particle moving in Dirac delta potential with instant changing well depth is studied by using formalism of tomographic representation of quantum mechanics.The bound state tomogram is given in terms of error…
Quantum error correction allows for faulty quantum systems to behave in an effectively error free manner. One important class of techniques for quantum error correction is the class of quantum subsystem codes, which are relevant both to…