Nonstabilizerness via Perfect Pauli Sampling of Matrix Product States

Area of Science:

• Quantum Information Science
• Quantum Computing
• Many-Body Physics

Background:

• Nonstabilizerness quantifies the resource cost of quantum states.
• Evaluating nonstabilizerness, particularly via Stabilizer Rényi Entropies (SREs), is computationally challenging for large quantum systems.
• Matrix Product States (MPS) are a powerful tool for simulating one-dimensional quantum systems.

Purpose of the Study:

• To develop an efficient method for calculating the nonstabilizerness of N-qubit matrix product states (MPS).
• To leverage Stabilizer Rényi Entropies (SREs) for quantifying nonstabilizerness.
• To enable the study of nonstabilizerness in complex quantum scenarios, including dynamics.

Main Methods:

• Introduced a novel perfect sampling technique for many-body wave functions over Pauli string configurations.
• Utilized a new MPS-based approach to compute samples efficiently.
• Achieved a computational cost scaling of O(Nχ^3) for N qubits with bond dimension χ.

Main Results:

• Demonstrated an efficient method to evaluate SREs, overcoming exponential complexity.
• Successfully benchmarked the method on random magic states and the Ising chain ground state.
• Enabled access to the nonequilibrium dynamics of SREs after quantum quenches.

Conclusions:

• The developed MPS technique provides an efficient pathway to compute nonstabilizerness measures.
• This method significantly advances the study of quantum resources and dynamics in complex quantum systems.
• Opens new avenues for exploring quantum computational advantages and error correction.