通过共轭哈密顿量演化的乘积生成随机酉算子

中文摘要 AI 辅助

随机酉操作是量子信息处理的基本资源，然而，利用实验上可用的控制手段来可证明地生成它们仍然具有挑战性。现有方法通常需要计算高阶算子期望值，并依赖于实验哈密顿量谱的统计假设以使这些计算易于处理。我们展示了如何通过由固定哈密顿量生成的演化序列（该哈密顿量被全局控制算子共轭）来实现随机酉算子。我们给出了一个几何论证，该论证确立了在均匀参数采样下，当序列长度超过我们限定的有限阈值时，可访问酉群上的指数收敛到均匀随机（Haar）测度。我们证明了当由共轭哈密顿量生成的连通李子群是闭合的时，这一结论成立。因此，本征动力学和全局控制为均匀随机性提供了一条建设性途径，适用于许多实验平台，包括里德伯原子、光晶格中的玻色子和费米子、超导量子比特（transmon）以及 trapped ions（囚禁离子）。

英文摘要

Random unitary operations are a fundamental resource for quantum information processing, yet provably generating them with experimentally available controls remains challenging. Existing approaches often require calculating higher-order operator expectation values, relying on statistical assumptions about the experimental Hamiltonian's spectrum to make these calculations tractable. We show how to implement random unitaries by a sequence of evolutions generated by a fixed Hamiltonian conjugated by a global control operator. We give a geometric argument that establishes exponential convergence to the uniform random (Haar) measure on the accessible unitary group under uniform parameter sampling, beyond a finite sequence-length threshold that we bound. We show this holds when the connected Lie subgroup generated by the conjugated Hamiltonians is closed. Native dynamics and global control thus provide a constructive route to uniform randomness, with applications to many experimental platforms including Rydberg atoms, bosons and fermions in optical lattices, transmons, and trapped ions.

发表机构

• University of Oxford（牛津大学）
• University of Cambridge（剑桥大学）

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