Three-Dimensional Hamiltonian Problems

Daniel R. Bes

Eardley, Jon

Hamiltonians

Zoltán Papp

Alexander N. Kvinikhidze, Boris Blankleider

We formulate three-dimensional equations for the finite temperature in-matter three-body problem. Our approach takes into account the full infinite series for the effective pair-interaction kernel, so that all possible two-body sub-processes allowed by the underlying Hamiltonian are retained.

Jinyuan Dong, yao zhao, Zhiqiang Li +3 more

Abstract The three-dimensional matching problem is a classic NP-complete problem in combinatorial optimization, with wide applications in resource allocation, task scheduling, and many other practical scenarios. Traditional algorithms for solving the three-dimensional matching problem face the challenge of high time complexity, making it difficult to solve large-scale problems within a reasonable time frame. To improve the solution efficiency, a quantum circuit solution based on the Quantum Approximate Optimization Algorithm (QAOA) is proposed. By constructing a mathematical model of the three-dimensional matching problem, the corresponding Hamiltonian expression is derived. A QAOA-based quantum circuit is designed and the parameters of the parameterized quantum gates are optimized using the classical optimization algorithm COBYLA. Simulation experiments are performed using IBM's quantum development framework Qiskit. The experimental results show that the solution to the three-dimensional matching problem can be obtained with 84% probability in polynomial time, verifying the feasibility and effectiveness of solving the three-dimensional matching problem based on the Quantum Approximate Optimization Algorithm.

Edward L. Hill