在具有线性深度电路的量子计算机上产生和操纵Laughlin型$ν=1/3$分数量子Hall态
Creating and manipulating a Laughlin-type $ν=1/3$ fractional quantum Hall state on a quantum computer with linear depth circuits
摘要：
本文提出了一种在数字化量子计算机上产生与Laughlin的$ν=1/3$分数量子Hall态等价的多体态的有效量子算法。我们的算法只使用作用于准一维设置中的相邻量子比特的量子门，并且其电路深度与量子比特的数量成线性关系，即，第二量化图像中朗道轨道的数量。我们确定关联函数，作为劳克林状态的签名，并讨论如何在量子计算机上获得它们。我们还讨论了在Laughlin态中产生准粒子的算法的推广。这为几个重要的研究铺平了道路，包括非平衡动力学的量子模拟和量子霍尔态准粒子的编织。
英文摘要：
Here we present an efficient quantum algorithm to generate an equivalent many-body state to Laughlin's $ν=1/3$ fractional quantum Hall state on a digitized quantum computer. Our algorithm only uses quantum gates acting on neighboring qubits in a quasi-one-dimensional setting, and its circuit depth is linear in the number of qubits, i.e., the number of Landau orbitals in the second quantized picture. We identify correlation functions that serve as signatures of the Laughlin state and discuss how to obtain them on a quantum computer. We also discuss a generalization of the algorithm for creating quasiparticles in the Laughlin state. This paves the way for several important studies, including quantum simulation of nonequilibrium dynamics and braiding of quasiparticles in quantum Hall states.
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