耗散自旋-1/2海森堡链的大规模量子模拟
Large-scale quantum simulations of dissipative spin-1/2 Heisenberg chains
- North Carolina State University（北卡罗来纳州立大学）
- Oak Ridge National Laboratory（橡树岭国家实验室）
- Georgetown University（乔治城大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本研究在ibm_kingston超导处理器上模拟50格点耗散海森堡链，通过Stinespring膨胀实现Lindblad动力学，绘制117点相图，解决长期相图争议，证明量子计算机可研究耗散量子系统。
AI中文摘要：
与环境耦合的量子多体系统会弛豫到非平衡稳态，这种稳态可以维持平衡态中不存在的有序性。计算这种稳态比封闭系统动力学更为困难，因为密度矩阵问题使希尔伯特空间维度平方化，且没有自由能来选择稳态。耗散自旋-1/2海森堡链是非平衡稳态物理的基准示例；各种方法都计算了其相图但结果不一致，在大系统尺寸下的受控确定仍然遥不可及。在这里，我们在超导处理器ibm_kingston上模拟了多达50个格点链的Lindblad动力学——100个同时活跃的量子比特，纠缠门深度高达1700——通过Stinespring膨胀实现耗散。系统的耗散演化是一种自校正机制，能有效擦除错误，因此硬件噪声仅作为弱的竞争耗散器进入。我们测量静态结构因子，分辨出铁磁、反铁磁、自旋密度波和顺磁稳态，在$J_x$–$J_y$平面上用117个量子硬件数据点绘制相图。我们揭示了一个丰富的非平衡相图，其中有序相仅保留平均场序的残余，尖锐转变让位于一维中预期的交叉行为。我们还发现存在一个初生的（Trotter诱导的）自旋密度波相，突显了受控Trotter化作为在耗散自旋系统中工程化各种磁相的工具的潜力。我们的量子模拟在很大程度上解决了关于该基准系统正确相图的长期不确定性。此外，它们表明量子计算机现在是解决涉及耗散量子系统的科学问题的可行工具。
英文摘要：
A quantum many-body system coupled to an environment relaxes to a nonequilibrium steady state that can sustain order with no equilibrium counterpart. Computing such steady states is harder than closed-system dynamics as the density matrix problem squares the Hilbert-space dimension, and no free energy selects the steady state. The dissipative spin-1/2 Heisenberg chain is a benchmark example for nonequilibrium steady state physics; various methods have each calculated its phase diagram but do not agree, and a controlled determination at large system size has remained out of reach. Here we simulate the Lindblad dynamics of chains of up to 50 sites on the superconducting processor ibm_kingston -- 100 simultaneously active qubits at up to 1700 entangling-gate depths -- realizing the dissipation via Stinespring dilation. The system's dissipative evolution is a self-correcting mechanism that effectively erases errors, so hardware noise enters only as a weak competing dissipator. We measure static structure factors and resolve ferromagnetic, antiferromagnetic, spin-density-wave, and paramagnetic steady states, mapping the phase diagram with 117 quantum hardware data points across the $J_x$--$J_y$ plane. We uncover a rich non-equilibrium phase diagram of ordered phases with only remnants of the mean-field order, and where sharp transitions give way to the crossovers expected in one dimension. We also find the existence of an incipient (Trotter-induced) spin density wave phase, highlighting the potential of controlled Trotterization as a tool to engineer various magnetic phases in dissipative spin systems. Our quantum simulations largely settle the lingering uncertainty regarding the correct phase diagram of this benchmark system. Moreover, they show that quantum computers are now a feasible tool for addressing scientific questions involving dissipative quantum systems.
