Extending Classically Simulatable Bounds of Clifford Circuits with Nonstabilizer States via Framed Wigner Functions

Area of Science:

• Quantum Information Science
• Quantum Computing
• Computational Physics

Background:

• The Wigner function formalism is crucial for analyzing quantum states' nonclassical properties and classical simulatability.
• Negativity issues in the Wigner function limit its application to qubit Clifford circuits.

Purpose of the Study:

• To propose a novel classical simulation method for qubit Clifford circuits.
• To address the limitations of the Wigner function formalism in quantum computing.

Main Methods:

• Utilizing a framed Wigner function, an extension of the Wigner function with an added phase degree of freedom.
• Developing a graph-theoretical approach to identify classically simulatable marginal outcomes.
• Implementing an outcome probability estimation scheme with the framed Wigner function.

Main Results:

• Clifford gates do not induce negativity in the framed Wigner function, allowing positive representation of nonstabilizer states.
• Efficient polynomial-time and memory sampling of marginal outcomes for Clifford circuits with nonstabilizer states.
• Identification of classically simulatable marginal outcomes in log-depth random Clifford circuits.

Conclusions:

• The framed Wigner function provides a new framework for classical simulation of quantum circuits.
• This approach enables efficient sampling and probability estimation for specific quantum circuit outcomes.
• Opens new research avenues for using quasiprobabilities in classically simulatable quantum computation.