Yuan Xiao, Sun Jinzhao, Liu Junyu, Zhao Qi, Zhou You
Center on Frontiers of Computing Studies, Department of Computer Science, Peking University, Beijing 100871, China.
Stanford Institute for Theoretical Physics, Stanford University, Stanford, California 94305, USA.
Phys Rev Lett. 2021 Jul 23;127(4):040501. doi: 10.1103/PhysRevLett.127.040501.
Tensor network theory and quantum simulation are, respectively, the key classical and quantum computing methods in understanding quantum many-body physics. Here, we introduce the framework of hybrid tensor networks with building blocks consisting of measurable quantum states and classically contractable tensors, inheriting both their distinct features in efficient representation of many-body wave functions. With the example of hybrid tree tensor networks, we demonstrate efficient quantum simulation using a quantum computer whose size is significantly smaller than the one of the target system. We numerically benchmark our method for finding the ground state of 1D and 2D spin systems of up to 8×8 and 9×8 qubits with operations only acting on 8+1 and 9+1 qubits, respectively. Our approach sheds light on simulation of large practical problems with intermediate-scale quantum computers, with potential applications in chemistry, quantum many-body physics, quantum field theory, and quantum gravity thought experiments.
张量网络理论和量子模拟分别是理解量子多体物理的关键经典和量子计算方法。在此，我们引入了混合张量网络框架，其构建块由可测量量子态和经典可收缩张量组成，继承了它们在高效表示多体波函数方面的独特特征。以混合树张量网络为例，我们展示了使用一台规模远小于目标系统的量子计算机进行高效量子模拟。我们通过数值方法对我们的方法进行了基准测试，该方法用于寻找分别具有多达8×8和9×8个量子比特的1D和2D自旋系统的基态，操作仅分别作用于8 + 1和9 + 1个量子比特。我们的方法为使用中规模量子计算机模拟大型实际问题提供了思路，在化学、量子多体物理、量子场论和量子引力思想实验等方面具有潜在应用。
