Quantum State Designs with Clifford Enhanced Matrix Product States

2024/04/29 by Guglielmo Lami, Tobias Haug, Lami, Guglielmo +3 · 8 citations
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.2404.18751

openalex publication_date 2024/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Nonstabilizerness, or `magic', is a critical quantum resource that, together with entanglement, characterizes the non-classical complexity of quantum states. Here, we address the problem of quantifying the average nonstabilizerness of random Matrix Product States (RMPS). RMPS represent a generalization of random product states featuring bounded entanglement that scales logarithmically with the bond dimension χ. We demonstrate that the 2-Stabilizer Rényi Entropy converges to that of Haar random states as N/χ², where N is the system size. This indicates that MPS with a modest bond dimension are as magical as generic states. Subsequently, we introduce the ensemble of Clifford enhanced Matrix Product States (CMPS), built by the action of Clifford unitaries on RMPS. Leveraging our previous result, we show that CMPS can approximate 4-spherical designs with arbitrary accuracy. Specifically, for a constant N, CMPS become close to 4-designs with a scaling as χ^-2. Our findings indicate that combining Clifford unitaries with polynomially complex tensor network states can generate highly non-trivial quantum states.

Cited by

• Prospects for quantum advantage in machine learning from the representability of functions
• Magic of the Well: assessing quantum resources of fluid dynamics data
• Efficient certification of intractable quantum states with few Pauli measurements
• Quantum State Designs via Magic Teleportation
• Spin versus Magic: Lessons from Gluon and Graviton Scattering
• Operational interpretation of the Stabilizer Entropy
• Stabilizer Rényi Entropy Encodes Fusion Rules of Topological Defects and Boundaries
• Disentangling strategies and entanglement transitions in unitary circuit games with matchgates

Related

• Magic-protected entanglement and Clifford-irreducible structure in magic state space
• Quantum Magic via Perfect Pauli Sampling of Matrix Product States
• Quantum State Designs via Magic Teleportation
• Efficient mutual magic and magic capacity with matrix product states
• Classical simulability of Clifford+T circuits with Clifford-augmented matrix product states