The Quantum Mechanics Solver

Jean-Louis Basdevant, Jean Dalibard

Jean-Louis Basdevant, Jean Dalibard

John R. Hiller, Ian Johnston, Daniel F. Styer +3 more

Kristoffer Aronsen, Simon Sandell

In this report we examine the concept of PT -symmetric quantum mechanics and analyze two such systems. PT -symmetric quantum mechanics is a new branch of quantum mechanics, first proposed by Bender and Boettcher in 1998 and has been the subject of much research since then. Various important aspects of PT -symmetric quantum mechanics is explained, such as asymptotic behaviour of solutions of the Schrödinger equation, as well as the concept of the C operator that is unique to PT -symmetric quantum mechanics. We briefly discuss both the concept of broken and unbroken PT -symmetry, and the relation between PT -symmetric and Hermitian quantum mechanics through similarity transforms. We specifically direct our attention to two theoretical quantum mechanical systems described by Hamiltonians with the property of being PT -symmetric. For these systems we determine the energy levels, one by analytical means and the other by use of numerical methods. To determine the energy levels numerically we have used the builtin ODE-solver ode45 in MATLAB in conjunction with the equation solver fzero. Our results are compared to those of previous studies and our methods and results are discussed.

Beatrice Casey, Joanna C. S. Santos, Andrew Hennessee

Satisfiability Modulo Theory (SMT) solvers are a useful tool that can be applied to a variety of problems, such as configuring relationships in distributed systems, detecting race conditions, and program analysis. String constraints are particularly difficult for SMT solvers to navigate, as the search space is generally large. Often times, classical SMT solvers will have to quit generating a solution for string constraints because it takes too long to find the solution. Quantum computing offers the advantages of quantum mechanics (e.g., superposition), which allows a system to explore a large search space much more efficiently. In this work, we explore creating a quantum-enabled SMT solver for string theory by using quantum annealing and Quadratic Unconstrained Binary Optimization (QUBO). Our preliminary results demonstrate that it is feasible to transform these string constraints to QUBO, and generate solutions for given constraints.

Salvador Elías Venegas-Andraca, José Luis Gómez-Muñoz, Marco O. Lanzagorta +1 more