Uncertainty Evaluation for Quantum Chemistry Simulations

量子计算机有潜力成为解决化学和材料科学中重大问题的宝贵工具，这些问题与从新药设计到先进材料工程等领域的工业应用有关。然而，当前和近期的机器对微小的扰动非常敏感，这些微小的扰动会给它们的输出带来误差，降低它们的精度。由于这些计算对于传统计算机来说是不可行的，因此不可能简单地检查答案：我们需要构建量子计算机的数学模型及其算法来计算结果的精确度。因此，需要系统地研究误差来源及其对计算精度的相对影响。我们项目的目的是基于量子器件的可测量误差参数来估计这种不确定性的程度。为了在量子计算机上模拟物理系统，其数学描述被分解为量子硬件对量子存储器(量子比特)执行的一系列原始操作(门)。当前和近期的机器虽然大到足以执行有用的计算，但还不够大，不足以包含纠错以保护模拟不受门中的不精确和量子比特中的错误的影响。考虑到这些器件的极端敏感性，模拟结果不可避免地会由于量子计算机中的噪声而产生一定程度的误差。量子计算机中有许多误差来源：门定时误差、量子比特退相干、热噪声和测量误差等。这些方法中的每一个都会给计算过程带来不需要的噪声项，从而在最终结果中产生不确定性。量子计算机可能基于各种不同的物理效应--例如微波脉冲或磁场--每种误差类型的贡献将相应地改变。量子计量学可以确定给定设备的每个误差源的大小，但关键的测量挑战是通过计量学分析和不确定性传播将不同误差对最终结果的不确定度的贡献联系起来。为了满足这一需求，我们将开发一个分析和数值框架，来解释量子计算机中的所有误差源，并将它们与在其上运行的算法的结果联系起来。这个项目的成功将使更好的算法能够提高量子计算机上物理模拟的准确性。

"Quantum computers have the potential to be an invaluable tool to solve major problems in chemistry and materials science, which are relevant for industrial applications in areas ranging from the design of new drugs to the engineering of advanced materials. However, current and near-term machines are very sensitive to small perturbations that introduce error into their outputs and reduce their accuracy. Since these calculations are infeasible for a conventional computer, it's impossible to simply check the answer: we need to construct a mathematical model of the quantum computer and its algorithm to calculate how accurate the results are. Therefore, systematic studies of the sources of error and their relative impact on the accuracy of the computation are needed. The aim of our project is to estimate the degree of this uncertainty based on the measurable error parameters of the quantum device.To simulate a physical system on a quantum computer its mathematical description is decomposed into a sequence of primitive operations (gates) which the quantum hardware performs on the quantum memory (qubits). Current and near-term machines, while large enough to perform useful calculations, are not large enough to incorporate error correction to protect the simulation from imprecision in the gates and errors in the qubits. Given the extreme sensitivity of these devices, the results of the simulation will inevitably have some degree of error due to noise in the quantum computer.There are many sources of error within a quantum computer: gate timing errors, qubit decoherence, thermal noise, and measurement errors, among others. Each of these contributes an undesirable noise term to the computation process which produces uncertainty in the final result. Quantum computers may be based on a variety of different physical effects -- microwave pulses or magnetic fields for example -- and the contribution of each error type will vary accordingly. Quantum metrology can determine the magnitude of each error source for a given device, but the key measurement challenge is to link, via metrological analysis and uncertainty propagation, the contributions of the different errors to the uncertainty of the final result.To address this need we will develop an analytical and numerical framework that accounts for all the sources of error within a quantum computer and relates them to the results of the algorithm running on it. The success of this project will enable better algorithms that will improve the accuracy of physical simulations on quantum computers."