Average fidelity estimation of twirled noisy quantum channel using unitary 2<i>t</i>-design<xref rid="cpb_28_1_010304fn1" ref-type="fn">*</xref> <fn id="cpb_28_1_010304fn1"> <label>*</label> <p>Project supported by the National Natural Science Foundation of China (Grant Nos. 61372076 and 61701375), the 111 Project, China (Grant No. B08038), the Key Research and Development Plan of Shannxi Province, China (Grant No. BBD24017290001), and the Foundation of Science and Technology on Communication Networks Laboratory, China (Grant No. KX172600031).</p> </fn>

Average fidelity estimation of twirled noisy quantum channel using unitary 2t-design* *

Project supported by the National Natural Science Foundation of China (Grant Nos. 61372076 and 61701375), the 111 Project, China (Grant No. B08038), the Key Research and Development Plan of Shannxi Province, China (Grant No. BBD24017290001), and the Foundation of Science and Technology on Communication Networks Laboratory, China (Grant No. KX172600031).

Zhang Linxi^{1, 2, †}, Zhu Changhua¹, Pei Changxing¹

Moment superoperator of a d^2nt-dimensional space can be visualized as an array of 2nt qubits, so that t copies support a ket in the state space on nt qubits, and the remaining t copies support the corresponding bra. The ovals U_{i,i + 1} correspond to a unitary operator U that acts nontrivially on two neighboring qubits i and i + 1. The dashed rectangles indicate that the 2t qubits that correspond to a local moment space H_lt indicate the random circuit of two neighboring qubits that correspond to a d²-dimensional space.