Introducing Clifford Entropy for Unitary Operations

This paper introduces a new measure, Clifford entropy, to quantify how close a unitary operation is to a Clifford unitary. This is significant because Clifford unitaries are fundamental in quantum computation, and understanding the 'distance' from arbitrary unitaries to Clifford unitaries is crucial for circuit design and optimization. The paper provides several key properties of this new measure, including its invariance under Clifford operations and subadditivity. The connection to stabilizer entropy and the use of concentration of measure results are also noteworthy, suggesting potential applications in analyzing the complexity of quantum circuits.