Ryotaro Suzuki - Unitary designs and complexity in structured random quantum circuits

Wed, 17 Sep 2025 00:00:00 +0000

Unitary designs and complexity in structured random quantum circuits

This seminar, given by Ryotaro Suzuki, will happend on 17 September 2025, at 12:0. It will take place in Room Not specified.

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Abstract

Random quantum circuits have emerged as powerful tools in quantum information science and many-body physics, serving as minimal models for understanding randomness generation, scrambling, and computational complexity in quantum systems. In the first part, I will present results on structured random circuits with non-Haar local gates, showing they can generate more global randomness than Haar random circuits [1]. By mapping the second-moment operator to a Kitaev chain, we exactly determine its spectrum and find larger spectral gaps, leading to improved bounds for shallow 2-design generation and randomized benchmarking. In the second part, we study the circuit complexity of monitored random circuits, consisting of random gates and measurements [2]. We prove a phase transition in quantum state complexity: below a critical rate, complexity grows linearly in time and saturates exponentially in system size and above it, complexity remains polynomial. The proof uses percolation theory and algebraic geometry to bound complexity growth. [1] Ryotaro Suzuki, Katsura, Mitsuhashi, Soejima, Eisert, Yoshioka, arXiv:2410.24127 (2024) [2] Ryotaro Suzuki, Jonas Haferkamp, Jens Eisert, and Philippe Faist, Quantum 9, 1627 (2025)

Ryotaro Suzuki | LIP6 - QI Team

Ryotaro Suzuki - Unitary designs and complexity in structured random quantum circuits

Unitary designs and complexity in structured random quantum circuits

Abstract