Nearly Optimal T-Count for Symmetry-Based Quantum State Purification
This research investigates how many non-Clifford gates (T gates) are needed to implement a quantum state purification protocol called symmetric projection. The authors show an upper bound of Oe(n) T gates for this task and a lower bound of 2n-2 T gates, proving that the required resources scale nearly optimally with the number of input copies ($n$). This establishes fundamental limits on the cost of coherent symmetry projection in quantum state purification.