Nonstabilizerness via Matrix Product States in the Pauli Basis

Area of Science:

• Quantum Information Science
• Quantum Computing
• Condensed Matter Physics

Background:

• Nonstabilizerness, or "magic," is vital for quantum computing advantage but poorly understood in many-body systems.
• Current methods for computing nonstabilizerness are limited in scalability, hindering research.

Purpose of the Study:

• To develop a scalable method for evaluating nonstabilizerness in quantum systems.
• To connect nonstabilizerness to many-body physics phenomena through efficient computation.

Main Methods:

• Developed a novel approach using matrix product states (MPS) by expressing them directly in the Pauli basis.
• Implemented calculations for stabilizer Rényi entropies, stabilizer nullity, and Bell magic within the MPS framework.

Main Results:

• Successfully computed nonstabilizerness measures for ground states of Ising and XXZ spin chains.
• Analyzed nonstabilizerness in dynamics of quantum circuits realized in Rydberg atom arrays.
• Provided benchmarks for future experiments on logical qubits up to twice current scales.

Conclusions:

• The novel MPS-based framework enables efficient and scalable computation of nonstabilizerness.
• This method facilitates the study of quantum magic in complex quantum systems and circuits.
• The findings offer practical benchmarks for advancing quantum computing experiments.