标题： 用量子计算机模拟金融期权定价的非厄米动力学 显示英文标题

标题： Simulating the non-Hermitian dynamics of financial option pricing with quantum computers

摘要： 薛定谔方程描述了量子态如何根据系统的哈密顿量演化。 对于物理系统，我们有哈密顿量必须是一个厄米特算符，以确保幺正动力学。 对于反厄米特哈密顿量，薛定谔方程则模型化量子态在虚时间中的演化。 这种虚时间演化过程已被成功用于计算量子系统的基态。 尽管虚时间演化是非幺正的，但可以通过量子虚时间演化（QITE）算法在量子计算机上模拟该演化的归一化动力学。 在本文中，我们通过去除QITE对其仅限于反厄米特哈密顿量的限制，拓宽了QITE的应用范围，使我们能够求解任何与具有任意非厄米特哈密顿量的薛定谔方程等价的偏微分方程（PDE）。 此类PDE的一个例子是著名的布莱克-舒尔斯方程，它用于模型化金融衍生品的价格。 我们将展示如何通过使用我们的广义QITE方法来对根据布莱克-舒尔斯方程建模的各种欧式期权合约进行定价，从而证明该方法在现实世界应用中的可行性。 显示英文摘要

摘要： The Schrodinger equation describes how quantum states evolve according to the Hamiltonian of the system. For physical systems, we have it that the Hamiltonian must be a Hermitian operator to ensure unitary dynamics. For anti-Hermitian Hamiltonians, the Schrodinger equation instead models the evolution of quantum states in imaginary time. This process of imaginary time evolution has been used successfully to calculate the ground state of a quantum system. Although imaginary time evolution is non-unitary, the normalised dynamics of this evolution can be simulated on a quantum computer using the quantum imaginary time evolution (QITE) algorithm. In this paper, we broaden the scope of QITE by removing its restriction to anti-Hermitian Hamiltonians, which allows us to solve any partial differential equation (PDE) that is equivalent to the Schrodinger equation with an arbitrary, non-Hermitian Hamiltonian. An example of such a PDE is the famous Black-Scholes equation that models the price of financial derivatives. We will demonstrate how our generalised QITE methodology offers a feasible approach for real-world applications by using it to price various European option contracts modelled according to the Black-Scholes equation.