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Path-independent (PI) quantum control has recently been proposed to integrate quantum error correction and quantum control [Phys.
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The reason we choose H 0 ( t ) H_{0}(t) to be diagonal in the ancilla eigenbasis is that it preserves the ancilla projection basis. When H 0 ( t ) H_{0}(t) contains off-diagonal terms in the ancilla eigenbasis (acting nontrivially on the central system), generallly it is not possible to guarantee a unitary operation on the central system when returning to the Schrödinger’s picture
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