CAREER: A Roadmap for Quantum Simulation

量子理论和计算机可以说是二十世纪最深刻的两个科学发展。量子力学是每一门基础物理科学的基础。计算对生活的几乎每一个领域都产生了深远的影响，科学也不例外，计算机模拟扩展了我们从流体力学到基因组学等领域的理解。然而，当我们将计算应用于量子系统的研究时，由于经典物理和量子物理之间的差异，我们面临着根本的限制。量子力学提出了严重的概念挑战，取代了物理现实的基本经典概念，如牛顿运动的确定性轨迹。这意味着，对量子系统进行精确的计算机模拟通常需要同时跟踪许多可能的结果，这需要随着系统的规模而迅速增长的资源。然而，这也意味着，根据量子力学运行的计算机应该具有与现有经典计算机不同的能力--特别是，它们应该能够有效地模拟量子系统。因此，对其他量子系统的模拟是量子计算最有前途的应用之一。实现这些算法所需的量子比特(量子比特)的数量在数百个，即使对于经典计算之外的应用也是如此。这项计划资助的工作将提供详细实验的理论路线图，带领我们从今天的几个量子比特量子计算机到几十到几百个量子比特的应用，这些应用可以与当前科学兴趣的计算相竞争。我们专注于与化学相关的应用，特别是分子能量的计算和化学反应的模拟。即使是用于量子模拟的中型量子计算机的发展也将是一项相当重要的技术壮举。在这个项目中所做的工作将使这一目标更接近。这项工作的许多方面将以量子模拟的数值工具包的形式传播，将在量子模拟中轻松设计实验的能力交到实验小组手中。将量子模拟应用于量子化学意味着，此类实验将被引导到能够在物理科学的许多领域进行具有广泛影响的量子模拟的设备的开发。这笔拨款将支持哈弗福德学院的博士后学者和本科生，从而改善哈弗福德学院本科生的研究环境。哈弗福德学院将通过为非专业学生开发一门关于量子力学基础问题的新课程，来加强非物理专业学生的教育经验。这项工作的影响还将通过与这门新课程相关的一系列公开讲座延伸到学生社区之外。

Quantum theory and the computer were arguably the two most profound scientific developments of the twentieth century. Quantum mechanics underpins every fundamental physical science. Computation has made a profound impact on almost every area of life, and science is no exception, with computer simulation extending our understanding in fields ranging from from fluid mechanics to genomics. However, when we apply computation to the study of quantum systems we face fundamental limitations arising from the difference between classical and quantum physics. Quantum mechanics presents serious conceptual challenges, displacing basic classical notions of physical reality such as the deterministic trajectories of Newtonian motion. This means that exact computer simulation of quantum systems often requires tracking many possible outcomes simultaneously, requiring resources which grow rapidly with the size of the system. However, this also implies that computers which operate according to quantum mechanics should have different capabilities than existing classical computers - in particular, they should allow effcient simulation of quantum systems. Simulation of other quantum systems is therefore one of the most promising applications of quantum computing. The number of quantum bits (qubits) required to implement these algorithms is in the few hundreds even for applications beyond the reach of classical computation. The work funded in this proposal will provide a theoretical roadmap of detailed experiments leading us from the few qubit quantum computers of today to the applications on few tens to few hundreds of qubits which can compete with current calculations of scientific interest. We focus on applications of relevance to chemistry, specifically the calculation of molecular energies and simulation of chemical reactions.The development of even a medium scale quantum computer for quantum simulation would be a technological feat of considerable importance. The work performed in this project will bring this goal closer. Many aspects of this work will be disseminated in the form of a numerical toolkit for quantum simulation, placing the ability to easily design experiments in quantum simulation in the hands of experimental groups. The focus on quantum simulation applied to quantum chemistry means that such experiments will be guided towards the development of devices capable of performing quantum simulations with broad impact in many areas of physical science. The grant will support postdoctoral scholars and undergraduate students at Haverford college and so enhance the research environment for undergraduate students at Haverford college. The educational experience of students outside the physical sciences at Haverford College will be enhanced through the development of a new course for non-majors on foundational questions in quantum mechanics. The impact of this work will also extend beyond the student community through a set of public lectures connected to this new course.