核磁共振多态相体系的开展研究及其量子纠缠测量

Nuclear magnetic resonance quantum computing platform is a controllable many-body nuclear spin quantum system, which consists mainly of nuclear spin and two-body interactions. Currently, there are still so many challenges in the following aspects for high-dimensional many-body nuclear spin quantum systems, such as, high sensitivity of liquid crystal quantum systems, highly accurate selective control and precise quantum measurement and readout. Facing such tough problems, we exploringly develop and study many-body nuclear spin quantum system with different states of matter, to realize the experimental preparation, coherent control and experiemental measurements of entanglement states of many-body nuclear spin systems, further to study the functions of symmetry of quantum entanglement states in the quantum information area. At present, it is still believed that the efficient measurement of quantum entanglement strongly depends on complicated quantum states reconstruction, whose complexity increases exponentially with the dimensionality of quantum systems. In the face of such a scientific trouble, we investigate and test the possibility of equivalently measuring quantum entanglement using the polynomial ancillary qubits instead of exponential quantum state reconstruction. We further test the effectiveness and expandability of the new method in experiments, and properly extend to open many-body nuclear spin quantum system to realize more far-ranging applications.

核磁共振量子计算平台基于原子核自旋以及两体相互作用而形成的可控多体核自旋量子系统，目前高维度的多体核自旋体系在以下方面仍存在难题，如液晶体系的高灵敏性、高精度选择性操控、精密的量子测量和读出等。介于存在的这些棘手问题，我们探索性开展并研究多态相的多体核自旋量子体系，以实现多体核自旋纠缠态的实验制备、相干控制以及实验测量，从而来研究量子纠缠态对称性在量子信息领域中的作用。当前量子纠缠的测量仍旧依赖于繁琐的量子态重构过程，而量子态重构过程的复杂度随着系统维度指数增加，面对这样一个瓶颈性的科学问题，我们调研并尝试牺牲多项式的辅助比特资源，来替代指数式的量子态重构过程去等效实现量子纠缠的测量。我们将进一步在实验上验证这种量子纠缠测量新方法的有效性和扩展性，并将其适当推广到开放多体量子体系，以实现更加广泛的应用。

量子计算作为经典计算机与量子物理学的新兴交叉领域，为实现更加强大计算和模拟能力提供了新的思路与方向。近年来基于量子计算机模拟各种量子现象，开发不同的量子算法已经成为重要的研究热点。在本项目中，我们基于核磁共振量子计算平台实现了多种量子系统和量子算法的演示和模拟，包括四维杨巴斯特方程，全息纠缠熵的量子引力，线性方程组的绝热算法，以及非厄米宇称-时间对称与宇称-时间反对称系统，双粒子BBH模型中的量子相变过程等；提出了利用核磁共振噪声注入技术有效模拟任意谱密度光合作用的方法，提出普适量子逻辑门框架下的求解线性微分方程组的量子算法,发展了可变参数的量子梯度下降算法。这些研究对加深量子体系理解，模拟不同微观体系，操控量子计算机以实现实际问题求解具有重要的理论与实践意义。

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