On Adaptive Verification of Quantum States

Assessing whether a state <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\rho$</tex> experimentally obtained from a procedure matches certain desired target state <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\psi$</tex> is a critical procedure in verifying the behaviour of a quantum circuit. Recent work has developed methods for verifying quantum states based on randomized single-qubit Pauli measurements labeled Randomized Pauli Certification (RPC). Our paper analyzes extends this line of research by showing existence of states which cannot be certified efficiently using single-qubit Pauli measurement under any static protocol. Further, we propose a transformer based based adaptive protocol which empirically adapts the standard RPC protocol.