Crystalline Quantum Circuits

TL;DR

This paper constructs and analyzes deterministic, translation-invariant Clifford quantum circuits on 2D lattices, revealing classes with efficient scrambling, error-correcting codes, and fractal dynamics, inspired by random quantum circuits.

Contribution

It introduces nonrandom, crystalline Clifford circuits with translation invariance and classifies their operator spreading and entanglement properties.

Findings

Identified a nonfractal good scrambling class with dense operator spreading.

Discovered circuits with linear code distance and high erasure error performance.

Extended the model to include fractal dynamics with measurements.

Abstract

Random quantum circuits continue to inspire a wide range of applications in quantum information science and many-body quantum physics, while remaining analytically tractable through probabilistic methods. Motivated by an interest in deterministic circuits with similar applications, we construct classes of \textit{nonrandom} unitary Clifford circuits by imposing translation invariance in both time and space. Further imposing dual-unitarity, our circuits effectively become crystalline spacetime lattices whose vertices are SWAP or iSWAP two-qubit gates and whose edges may contain one-qubit gates. One can then require invariance under (subgroups of) the crystal's point group. Working on the square and kagome lattices, we use the formalism of Clifford quantum cellular automata to describe operator spreading, entanglement generation, and recurrence times of these circuits. A full classification on the square lattice reveals, of particular interest, a "nonfractal good scrambling class" with dense operator spreading that generates codes with linear contiguous code distance and high performance under erasure errors at the end of the circuit. We also break unitarity by adding spacetime-translation-invariant measurements and find a class of such circuits with fractal dynamics.