Quantum Simulations on an NMR Quantum Computer

目前关于量子算法实现的大部分工作集中在因子分解和数据库搜索算法上。然而，从物理学的角度来看，费曼最初提出的量子处理器可能是有效模拟量子力学系统的唯一可能性，提供了一个更令人兴奋的观点。在这个项目中，我们计划使用液态核磁共振实现一些有趣的模拟算法。量子计算机上的量子模拟涉及两种类型的映射：要研究的物理系统的状态（或密度算符）必须映射到量子计算机的状态（或密度算符）上，并且物理系统的哈密顿量必须在量子计算机中实现。量子计算机通常是一个量子比特系统（自旋1/2），而物理系统可能是一个自旋系统，一个玻色子或费米子系统。因此，寻找合适的映射通常是一项非常重要的任务。我们预计量子模拟在介观物理领域具有最大的潜力，在这个领域，经典计算机不够强大，无法进行精确计算，而且渐近解也不成立。作为起点，我们计划实现BCS超导理论的耦合哈密顿量。在最初的实验中使用两个和三个粒子实现，我们将研究将计算扩展到更大系统所涉及的问题，这可能在未来几代量子计算机中可用。对于这个初步的工作，我们将集中在统一的演化，结合绝热变化的哈密顿。在未来的阶段，通过包含非单一演化将模拟扩展到开放系统将是一件有趣的事情。

Most of the current work on implementations of quantum algorithms concentrates on the algorithms for factoring and database searching. From a physics perspective, however, the original suggestion by Feynman, that quantum processors may be the only possibility to efficiently simulate quantum mechanical systems, offers a more exciting perspective. In this project, we plan to implement some interesting simulation algorithms using liquid state NMR. Quantum simulations on quantum computers involve two types of mapping: The state (or density operator) of the physical system to be studied must be mapped onto the state (or density operator) of the quantum computer, and the Hamiltonian of the physical system must be implemented in the quantum computer. The quantum computer typically is a system of qubits (spins 1/2), while the physical system may be a spin system, a boson- or fermion system. Finding a suitable mapping is therefore often a nontrivial task. We expect that quantum simulations hold the biggest potential in the field of mesoscopic physics, where classical computers are not powerful enough for exact calculations and asymptotic solutions do not hold. As a starting point, we plan to implement the coupling Hamiltonian of the BCS theory of superconductivity. Using two- and three particle implementations for the initial experiments, we will study the issues involved in scaling the computation to larger systems, which may become available in future generations of quantum computers. For this initial work, we will concentrate on unitary evolutions, combined with adiabatic variation of the Hamiltonian. In a future phase, it will be interesting to extend the simulation to open systems by including non-unitary evolution.