2021/02/19 by Raúl O. Vallejos, Raul O. Vallejos, Fernando de Melo +1
Computer Science · Mathematics · Physics and Astronomy · #Combinatorics #Controlled NOT gate #Discrete mathematics #Electronic circuit #Majorization #Mathematics #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum entanglement #Quantum many-body systems #Quantum mechanics #Quantum network #Topology (electrical circuits) #quant-ph
paper · pdf · doi:10.1103/physreva.104.012602
published as Phys. Rev. A 104, 012602 (2021) · 8 pages, 4 figures
arxiv created 2021/02/19 · openalex publication_date 2021/07/07 · arxiv updated 2021/07/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We test the principle of majorization J. I. Latorre and M. A. Mart'\in-Delgado, Phys. Rev. A 66, 022305 (2002). in random circuits. Three classes of circuits were considered: (i) universal, (ii) classically simulatable, and (iii) neither universal nor classically simulatable. The studied families are: cnot, H, T, cnot, H, not, cnot, H, S (Clifford), matchgates, and IQP (instantaneous quantum polynomial-time). We verified that all the families of circuits satisfy on average the principle of decreasing majorization. In most cases the asymptotic state (number of gates \ensuremath→\ensuremath∞) behaves like a random vector. However, clear differences appear in the fluctuations of the Lorenz curves associated with asymptotic states. The fluctuations of the Lorenz curves discriminate between universal and nonuniversal classes of random quantum circuits, and they also detect the complexity of some nonuniversal but not classically efficiently simulatable quantum random circuits. We conclude that majorization can be used as an indicator of complexity of quantum dynamics, as an alternative to, e.g., entanglement spectrum and out-of-time-order correlators.