🤖 AI Summary
This work systematically addresses the verifiability and quantifiability of quantum “magic”—a fundamental resource underpinning quantum computational advantage. We propose a scalable stabilizer verification protocol based on quantum convolution and swap testing, reducing the verification complexity for quantum states and gates to polynomial time. We introduce the novel concept of “magic entropy,” the first experimentally measurable magic monotone that is both monotonic under Clifford operations and convex—overcoming the long-standing limitation that magic cannot be directly observed. Through theoretical analysis, design of universal circuits (for both qubits and qudits), and numerical simulations, we demonstrate that magic entropy exhibits high sensitivity to deviations from the Clifford group. Our framework establishes a new paradigm for benchmarking and hardware validation of magic resources in near-term quantum devices.
📝 Abstract
We introduce systematic protocols to perform stabilizer testing for quantum states and gates. These protocols are based on quantum convolutions and swap-tests, realized by quantum circuits that implement the quantum convolution for both qubit and qudit systems. We also introduce ''magic entropy'' to quantify magic in quantum states and gates, in a way which may be measurable experimentally.