Introducing Clifford Entropy for Unitary Operations
Published:Dec 28, 2025 19:26
•1 min read
•ArXiv
Analysis
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.
Key Takeaways
- •Introduces Clifford entropy as a new measure for quantifying the 'Clifford-ness' of unitary operations.
- •Establishes key properties of Clifford entropy, including invariance and subadditivity.
- •Connects Clifford entropy to stabilizer entropy and utilizes concentration of measure results.
- •Provides a potential lower bound on the depth of doped Clifford circuits.
- •Suggests directions for future research in quantum circuit complexity and optimization.
Reference
“The Clifford entropy vanishes if and only if a unitary is Clifford.”