基于采样的环面码相变变分模拟：能量、全局纠缠与噪声鲁棒性
Shot-based variational simulation of the toric code phase transition: Energy, global entanglement, and noise resilience
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中文总结 AI 辅助
本研究利用基于采样的变分量子电路模拟环面码在磁场下的拓扑相变，通过能量和全局纠缠探测相变点，并验证了拓扑相对门噪声的线性鲁棒性。
中文摘要 AI 辅助
我们研究了变分量子电路在探测均匀磁场下环面码模型中拓扑相变的能力。该探测通过基于采样的基态能量和全局纠缠计算来实现。我们首先采用成熟的量子化重整化技术构建一个能够精确表示周期性边界条件下纯环面码的量子电路。随后对该电路进行参数化，以实现存在磁场时基态的基于采样的变分模拟。我们的结果表明，即使对于最小晶格尺寸和有限数量的测量采样，基态能量在相变点处也表现出明显的奇异性，并且可以通过有限尺寸标度分析可靠地近似。此外，我们引入了一个辅助变分电路来计算所生成基态的全局纠缠。我们观察到全局纠缠及其条件对应量在相变点处均表现出预期的定性行为，与相变的拓扑性质一致。为了评估我们的变分方法在实际量子硬件上的实用可行性，我们系统地研究了门噪声对分析的负面影响。我们发现拓扑相表现出对噪声的显著鲁棒性，表现为相变点随噪声强度增加而线性下降。
英文摘要
We investigate the capability of variational quantum circuits in detecting a topological phase transition within the toric code model subjected to a uniform magnetic field. The detection is carried out via shot-based computations of both the ground state energy and the global entanglement. We begin by employing well-established renormalization techniques to construct a quantum circuit that accurately represents the pure toric code under periodic boundary condition. This circuit is subsequently parameterized to enable a shot-based variational simulation of the ground state in the presence of the magnetic field. Our results demonstrate that even for the minimal lattice sizes and a finite number of measurement shots, the ground state energy exhibits a distinct singularity at the transition point which can be reliably approximated through finite-size scaling analysis. Furthermore, we introduce a secondary variational circuit designed to compute the global entanglement of the generated ground state. We observe that both global entanglement and its conditional counterpart display the expected qualitative behavior at the transition point, consistent with the topological nature of the phase transition. To evaluate the practical viability of our variational approach on real quantum hardware, we systematically examine the detrimental effects of gate noise on the analysis. We find that the topological phase exhibits a notable robustness against noise, manifesting as a linear decrease in the transition point with increasing noise strength.
发表机构
- Physics Department, College of Sciences, Shiraz University（设拉子大学理学院物理系）
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