Zero and Low Energy Thresholds in Quantum Simulation

Abstract

Quantum simulation is the process of simulating a quantum mechanical system using either a quantum or a classical computer. Because quantum mechanical systems contain a large number of entangled particles, they are hard to simulate on a classical computer. It is the task of computational complexity theorists to estimate the amount of resources to do the same number of operations on either classical or quantum devices. This report first summarizes the state of the art in the field of quantum computing, and gives an example of a model of quantum computer and examples of quantum algorithms that are currently being researched. Then our own research about k-local quantum Hamiltonians is discussed. We developed programs to determine if a particular kind of k-local Hamiltonian has zero-energy solutions. First, to familiarize ourselves with quantum algorithms, we implemented a recently discovered polynomial-time 2-QSAT algorithm called SolveQ. Then we wrote several versions of brute force 7-variable 3-QSAT solvers and conducted experiments for the threshold of satisfiability. We empirically determined that the thresholds for the four versions, Versions 3, 4, 5, and 6, are 0.741, 1.714, 1.714, and 0.571, respectively. In addition, experiments were conducted involving the 6-qubit Ising model, working on which caused us to realize how inefficient the classical computer really is at simulating quantum mechanical systems. Our conclusion is that quantum simulation is much less feasible than classical simulation on a classical computer