Operator space fragmentation in perturbed Floquet-Clifford circuits

TL;DR

This paper investigates how operator localisation and chaos emerge in perturbed Floquet-Clifford circuits, revealing stable localisation, operator fragmentation, and spectral properties relevant for current quantum devices.

Contribution

It introduces a model showing operator space fragmentation and emergent local integrals of motion in perturbed Floquet-Clifford circuits, with analytical stability analysis and spectral characterization.

Findings

Operators remain localized for 0 ≤ p < 1 due to wall configurations.

Operator spreading length is tunable by the perturbation probability p.

Spectral form factor indicates a fragmentation time scale before chaos sets in.

Abstract

Floquet quantum circuits are able to realise a wide range of non-equilibrium quantum states, exhibiting quantum chaos, topological order and localisation. In this work, we investigate the stability of operator localisation and emergence of chaos in random Floquet-Clifford circuits subjected to unitary perturbations which drive them away from the Clifford limit. We construct a nearest-neighbour Clifford circuit with a brickwork pattern and study the effect of including disordered non-Clifford gates. The perturbations are uniformly sampled from single-qubit unitaries with probability $p$ on each qubit. We show that the interacting model exhibits strong localisation of operators for $0 \le p < 1$ that is characterised by the fragmentation of operator space into disjoint sectors due to the appearance of wall configurations. Such walls give rise to emergent local integrals of motion for the circuit that we construct exactly. We analytically establish the stability of localisation against generic perturbations and calculate the average length of operator spreading tunable by $p$. Although our circuit is not separable across any bi-partition, we further show that the operator localisation leads to an entanglement bottleneck, where initially unentangled states remain weakly entangled across typical fragment boundaries. Finally, we study the spectral form factor (SFF) to characterise the chaotic properties of the operator fragments and spectral fluctuations as a probe of non-ergodicity. In the $p = 1$ model, the emergence of a fragmentation time scale is found before random matrix theory sets in after which the SFF can be approximated by that of the circular unitary ensemble. Our work provides an explicit description of quantum phases in operator dynamics and circuit ergodicity which can be realised on current NISQ devices.