# Algebraic structure of path-independent quantum control

@article{Ma2022AlgebraicSO, title={Algebraic structure of path-independent quantum control}, author={Wen-Long Ma and Shu-Shen Li and Liang Jiang}, journal={Physical Review Research}, year={2022} }

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…

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