Efficient Fidelity Estimation of General Quantum Resource States via Clifford Circuits

Abstract

Fidelity estimation is a fundamental tool for assessing quantum resource states across quantum information science. For small infidelity $ε$, tomography and direct fidelity estimation (DFE) have worst-case sample complexity $O(1/ε^2)$ at fixed relative accuracy and confidence. Direct target projections achieve $O(1/ε)$ but generally require non-Clifford operations whose reliability depends on the resource states that are typically the target of benchmarking. Here, we introduce the Bell--coherence fidelity estimation (BCFE) with optimal sample complexity $Θ(1/ε)$ using only Clifford gates and Pauli measurements. We prove that BCFE is applicable to arbitrary pure targets, possibly multi-qubit, with the statistical error of the single-copy coherence part explicitly controlled. To evaluate BCFE in a practical setting, we apply BCFE to analog rotation resource states in the candidate early-FTQC architecture called the Space-Time Efficient Analog Rotations (STAR) architecture. In the simulations using surface codes, BCFE is estimated to require up to approximately $27$ times fewer resource states than DFE for the same standard error in the infidelity estimate, while its estimates remain close to reference values despite circuit-level noise in the additional Bell measurement operations. These results support efficient resource benchmarking within fault-tolerant quantum computing.