Simulation of mesoscopic quantum systems by liquid-state NMR

在这个项目中，我们将依靠液态核磁共振，这似乎仍然是未来几年量子信息处理最强大的技术。为了开发新的量子寄存器，我们将识别具有合适的核自旋系统的分子。对于这些分子，我们将评估相关的核磁共振参数(共振频率、耦合常数和驰豫时间)，并设计适当的程序来有效地实现算法。作为第二个主要目标，我们计划使用这些中型量子处理器来模拟量子力学系统的特定性质，例如量子相变。在这些模拟中，目标系统的希尔伯特空间将被映射到量子寄存器的状态中，并且目标哈密顿量将通过合适的多个脉冲序列产生为有效的哈密顿量。利用这些量子模拟器，我们将探索目标系统的能级结构以及一些动力学方面，如相变附近的临界涨落。本项目旨在填补我们最近在大型量子寄存器模型(高达2000个量子比特)中的退相干尺度研究与全量子算法实现之间的空白，在全量子算法中，我们仅限于2-3个量子比特系统。从中等大小的量子寄存器开始，我们将逐步增加同时控制的量子比特的数量，并评估操作时间和平均退相干速率如何随量子寄存器大小的增加而变化。越来越多的量子门操作和不断增加的退相干速率将要求更有效的、更高保真度的门操作。因此，我们将研究如何优化控制机制，以便将量子信息保留在系统中足够长的时间。

Within this project, we will rely on liquid-state NMR, which appears to remain the most powerful technique for quantum information processing for the next few years. To develop the new quantum registers, we will identify molecules with suitable nuclear spin systems. For these molecules, we will evaluate the relevant NMR parameters (resonance frequencies, coupling constants, and relaxation times) and design suitable procedures for efficiently implementing algorithms. As the second major goal, we plan to use these medium-sized quantum processors for simulating specific properties of quantum mechanical systems, such as quantum phase transitions. For these simulations, the Hilbert space of the target system will be mapped into the states of the quantum register and the target Hamiltonian will be generated as an effective Hamiltonian by suitable multiple pulse sequences. Using these quantum simulators, we will explore the energy level structure of the target system as well as some dynamic aspects, like critical fluctuations near the phase transition. The present project aims to fill a gap between our recent studies on the scaling of decoherence in large quantum register models (up to 2000 qubits) and implementations of full quantum algorithms, where we were restricted to 2-3 qubit systems. Starting from moderate sized quantum registers, we will successively increase the number of qubits being controlled simultaneously and evaluate how the operation time and average decoherence rates change with increasing quantum register size. The increasing number of quantum gate operations and the increasing decoherence rate will require more efficient gate operations with higher fidelity. We therefore will study how control mechanisms can be optimized to retain the quantum information in the system for sufficiently long times.