论文标题
路径非依赖性量子控制的代数结构
Algebraic structure of path-independent quantum control
论文作者
论文摘要
最近已经提出了非依赖性（PI）量子控制以整合量子误差校正和量子控制[Phys。莱特牧师。 125，110503（2020）]，针对Ancilla误差实现易于断层的量子门。在这里，我们揭示了PI量子对照的潜在代数结构。 PI Hamiltonians和繁殖者恰好位于代数的同构中，我们称之为Pi Matrix代数。 PI矩阵代数定义在复合系统的Hilbert空间（包括Ancilla系统和中央系统），是对Ancilla系统希尔伯特空间上定义的基质代数的同构。通过将PI矩阵代数扩展到复合系统的Hilbert-Schmidt空间，我们为针对Ancilla噪声的PI量子控制提供了精确而统一的条件。
Path-independent (PI) quantum control has recently been proposed to integrate quantum error correction and quantum control [Phys. Rev. Lett. 125, 110503 (2020)], achieving fault-tolerant quantum gates against ancilla errors. Here we reveal the underlying algebraic structure of PI quantum control. The PI Hamiltonians and propagators turn out to lie in an algebra isomorphic to the ordinary matrix algebra, which we call the PI matrix algebra. The PI matrix algebra, defined on the Hilbert space of a composite system (including an ancilla system and a central system), is isomorphic to the matrix algebra defined on the Hilbert space of the ancilla system. By extending the PI matrix algebra to the Hilbert-Schmidt space of the composite system, we provide an exact and unifying condition for PI quantum control against ancilla noise.
