Simulating the dynamic evolution of physical and molecular systems in a quantum computer is of fundamental interest in many applications. The implementation of dynamics simulation requires efficient quantum algorithms. The Lie-Trotter-Suzuki approximation algorithm, also known as the Trotterization, is basic in Hamiltonian dynamics simulation. A multi-product algorithm that is a linear combination of multiple Trotterizations has been proposed to improve the approximation accuracy. However, implementing such multi-product Trotterization in quantum computers remains challenging due to the requirements of highly controllable and precise quantum entangling operations with high success probability. Here, we report a programmable integrated-photonic quantum simulator based on a linear combination of unitaries, which can be tailored for implementing the linearly combined multiple Trotterizations, and on the simulator we benchmark quantum simulation of Hamiltonian dynamics. We modify the multi-product algorithm by integrating it with oblivious amplitude amplification to simultaneously reach high simulation precision and high success probability. The quantum simulator is devised and fabricated on a large-scale silicon-photonic quantum chip, which allows the initialization, manipulation, and measurement of arbitrary four-qubit states and linearly combined unitary gates. As an example, the quantum simulator is reprogrammed to emulate the dynamics of an electron spin and nuclear spin coupled system. This work promises the practical dynamics simulations of real-world physical and molecular systems in future large-scale quantum computers.

中文翻译：

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基于酉线性组合的可编程硅光子量子模拟器


在量子计算机中模拟物理和分子系统的动态演化在许多应用中具有根本意义。动力学模拟的实现需要高效的量子算法。 Lie-Trotter-Suzuki 近似算法（也称为 Trotterization）是哈密顿动力学模拟的基础。提出了一种多乘积算法，该算法是多个 Trotterization 的线性组合，以提高逼近精度。然而，由于需要高度可控、精确的量子纠缠操作以及高成功概率，在量子计算机中实现这种多产品 Trotterization 仍然具有挑战性。在这里，我们报告了一种基于酉线性组合的可编程集成光子量子模拟器，它可以定制用于实现线性组合的多个Trotterization，并且在模拟器上我们对哈密顿动力学的量子模拟进行了基准测试。我们修改了多乘积算法，将其与不经意的幅度放大相结合，以同时达到高模拟精度和高成功概率。量子模拟器是在大规模硅光子量子芯片上设计和制造的，它允许初始化、操纵和测量任意四量子位态和线性组合的单一门。例如，量子模拟器被重新编程以模拟电子自旋和核自旋耦合系统的动力学。这项工作有望在未来的大规模量子计算机中对现实世界的物理和分子系统进行实用的动力学模拟。