Structured Clifford+T Circuits for Efficient Generation of Quantum Chaos

TL;DR

This paper demonstrates that deterministic Clifford+T circuits with causal connectivity can efficiently generate quantum chaos and emulate properties like Wigner-Dyson statistics and OTOC decay, without relying on randomness or circuit depth.

Contribution

It introduces structured, deterministic Clifford+T circuit architectures that achieve quantum chaos, emphasizing causal connectivity as the key factor over randomness or depth.

Findings

Causal connectivity drives quantum chaos in Clifford+T circuits.

Polylogarithmic-depth circuits can approximate chaotic behavior.

Adding T-layers after Clifford evolution enhances chaos indicators.

Abstract

We investigate the emergence of quantum chaos and unitary T-design behavior in derandomized Clifford+T circuits using causal cover architectures. Motivated by the need for deterministic constructions that can exhibit chaotic behavior across diverse quantum hardware platforms, we explore deterministic Clifford circuit architectures (random Clifford circuits with causal cover, bitonic sorting networks, and permutation-based routing circuits) to drive quantum circuits toward Wigner-Dyson (WD) entanglement spectrum statistics and OTOC decay.Our experiments demonstrate that causal connectivity, not circuit depth or randomness, is a critical feature that drives circuits to chaos. We show that initializing with n T-states and adding a second T-layer after a causally covered Clifford evolution yields consistent OTOC decay and WD statistics. This also enables deeper understanding of the circuit structures that generate complex entanglement behavior. Notably, our work suggests polylogarithmic-depth deterministic circuits suffice to approximate chaotic behavior, highlighting that causal connectivity is sufficient for operator spreading to induce Wigner-Dyson entanglement statistics and OTOC decay.