EMT/QIS: Robust Quantum Simulation Techniques for Fault-Tolerant Quantum Computation

与经典计算机相比，量子计算机提供了基本的算法优势，建造量子计算机将从根本上改变我们计算机的能力。然而，大规模量子计算机很难建造，很大程度上是因为量子系统与环境相互作用，很快就失去了量子本质。这个问题的解决方案，至少在理论上，是由容错量子计算理论提供的。容错量子计算理论虽然在原则上证明了量子计算机的可行性，但存在着需要具有严重复杂性开销的协议的问题。由于这些困难，人们一直在寻求另一种构建健壮量子计算机的方法，在这种方法中，多体量子系统通过以适当的受保护自由度对量子信息进行编码来保护这些信息。在这种方法中，系统的自然物理有助于保护量子信息。然而，出现了一个困难，部分原因是工程量子系统所需的复杂性。正在进行的研究旨在克服这一障碍，并为构建量子计算机的晶体管等价物开辟道路。在这里，研究人员研究了三种适合于保护量子信息的工程有效多体相互作用的方法。第一种方法涉及构建容错扰动小工具。这项研究涉及到研究扰动小工具的健壮性。第二种方法涉及使用量子电路来模拟哈密顿动力学。在该技术中，研究了容错仿真的新方法。NAL技术涉及到依赖于时间的哈密顿量的使用，该研究涉及到对这种依赖于时间的结构中的错误的详细研究。

Quantum computers offer fundamental algorithmic advantages over classical computers and building a quantum computer would fundamentally change the power of our computers. Large scale quantum computers, however, are difficult to build in large part due to the fact that quantum systems interact with their environment and quickly lose their quantum nature. The solution to this problem, at least in theory, was provided by the theory of fault-tolerant quantum computation. The theory of fault-tolerant quantum computation, while providing an in principle demonstration of viability of quantum computers, suffers from requiring protocols that have a severe complexity overhead. As a result of these difficulties, an alternative approach toward building a robust quantum computer has been pursued in which many-body quantum systems protect quantum information by encoding this information in suitable protected degrees of freedom. In this approach the natural physics of the system helps protect the quantum information. A difficulty arises, however, due in part to the complexity required of the engineered quantum system. The research being performed here seeks to overcome this obstacle and open the path for constructing the equivalent of a transistor for quantum computers.Here the investigators study three approaches to engineering effective many-body interactions suitable for protecting quantum information. The first approach involves the construction of fault-tolerant perturbation gadgets. This research involves studying the robustness of the perturbation gadgets. The second approach involves the use of quantum circuits to simulate Hamiltonian dynamics. In this technique, research is performed on new methods for fault-tolerant simulation. A final technique involves the use of time-dependent Hamiltonians and the research involves a detailed study of the errors in this time-dependent construction.