Anticoncentration in Clifford Circuits and Beyond: From Random Tensor Networks to Pseudomagic States

A central question in quantum computing is how quantum circuits generate randomness, since this property underlies complexity, chaos, and the potential for computational advantage. A key concept is anticoncentration, which measures how evenly a quantum state spreads across all possible outcomes. In this work, we study anticoncentration in Clifford circuits and tensor networks, which play a central role in error correction and fault-tolerant quantum computation.

We calculate the overlap distribution for random stabilizer states, giving a precise description of how Clifford circuits anticoncentrate. Our analysis shows that Clifford tensor networks whose bond dimension grows like some power of the system fully anticoncentrate, as do Clifford circuits with only logarithmic depth. We then go beyond Clifford dynamics by introducing non-Clifford, or “magic,” resources. By adding only a logarithmic number of special quantum states known as 𝑇 states, we find that circuits transition to fully chaotic behavior.

These results reveal the fine balance between Clifford operations, which are structured and efficiently simulable, and non-Clifford resources, which push circuits into the regime of quantum complexity. Understanding this transition informs strategies for quantum sampling, provides new tools for benchmarking devices, and points to resource requirements for true quantum advantage.

Publication: Anticoncentration in Clifford Circuits and Beyond: From Random Tensor Networks to Pseudomagic States. Beatrice Magni, Alexios Christopoulos, Andrea De Luca and Xhek Turkeshi. Phys. Rev. X 15, 031071 – Published 15 September, 2025 
DOI: https://doi.org/10.1103/p8dn-glcw

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