High-Precision Fidelity Estimation with Common Randomized Measurements

Efficient fidelity estimation of multiqubit quantum states is crucial to many applications in quantum information processing. However, to estimate the infidelity $\epsilon$ with multiplicative precision, conventional estimation protocols require (order) $1/\epsilon^2$ different circuits in addition to $1/\epsilon^2$ samples, which is quite resource-intensive for high-precision fidelity estimation. Here we introduce an efficient estimation protocol by virtue of common randomized measurements (CRM) integrated with shadow estimation based on the Clifford group, which only requires $1/\epsilon$ circuits. Moreover, in many scenarios of practical interest, in the presence of depolarizing or Pauli noise for example, our protocol only requires a constant number of circuits, irrespective of the infidelity $\epsilon$ and the qubit number. For large and intermediate quantum systems, quite often one circuit is already sufficient. In the course of study, we clarify the performance of CRM shadow estimation based on the Clifford group and 4-designs and highlight its advantages over standard and thrifty shadow estimation.