利用GKP稳定化在玻色模式中编码紧致U(1)规范场
Encoding Compact U(1) Gauge Fields in Bosonic Modes with GKP Stabilization
- The University of Tennessee（田纳西大学）
- Stony Brook University（石溪大学）
- CERN（欧洲核子研究组织）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究提出利用GKP稳定器的一一对应编码，将紧致U(1)规范场编码到玻色量子硬件的振子模式，应用于紧致QED₃并通过单格点示例和实时光谱学验证了方法的有效性。
AI中文摘要：
紧致格点规范理论以角变量和整数电通量构建，而玻色量子硬件提供具有连续、无界正交分量的振子模式。我们通过一一对应编码弥合这一差距。在求解高斯定律后，每个剩余的规范自由度由单个振子模式承载，其相互作用由三角函数门构建，而Gottesman-Kitaev-Preskill（GKP）型稳定器提供硬件不具备的紧致性。该编码在无限压缩极限下是精确的，在有限压缩下，主要缺陷表现为物理可观测量的可计算小偏移，而非不受控的泄漏。我们将该构造应用于紧致QED₃，推导有限压缩下的误差预算，以闭式形式表征主要误差，并表明它们可被校正、减去或外推消除。我们构建了症候提取协议，用于检测和移除光子损失的位移分量，界定其未触及的噪声，比较两种动力学变量选择，并汇总模式数、门数和测量成本的标度关系。单格点示例重现了精确的紧致转子动力学，且通过受控外推的实时光谱学以百分比级精度恢复了电荷区之间指数小的能级分裂，该分裂是理论单极子物理的核心。
英文摘要：
Compact lattice gauge theories are formulated in terms of angular variables and integer electric fluxes, while bosonic quantum hardware provides oscillator modes with continuous, unbounded quadratures. We bridge this gap with a one-to-one encoding. After Gauss's law is solved, each remaining gauge degree of freedom is carried by a single oscillator mode, with its interactions built from trigonometric gates, and a Gottesman--Kitaev--Preskill (GKP)-type stabilizer provides the compactness that the hardware does not. The encoding becomes exact in the limit of infinite squeezing, and at finite squeezing, the leading imperfections act as small, computable shifts of physical observables rather than uncontrolled leakage. We apply the construction to compact QED$_3$ and derive the error budget at finite squeezing, characterizing the leading errors in closed form, and showing that they can be corrected, subtracted, or extrapolated away. We construct syndrome-extraction protocols that detect and remove the displacement component of photon loss, delimit the noise it does not reach, compare two choices of dynamical variables, and collect the scaling of mode count, gate count, and measurement cost. A one-plaquette example reproduces the exact compact-rotor dynamics, and real-time spectroscopy with controlled extrapolations recovers the exponentially small energy splitting between charge sectors, the seed of the monopole physics of the theory, at the percent level against its exact value.
