Magic transition in measurement-only circuits

TL;DR

This paper investigates the transition of quantum magic in measurement-only circuits with Clifford and non-Clifford measurements, revealing a phase transition characterized by extensive magic and topological distinctions, using large-scale simulations.

Contribution

It introduces a detailed study of magic transitions in measurement-only circuits, highlighting the role of topological magic and critical behavior using scalable numerical methods.

Findings

Identifies a magic phase transition with extensive magic scaling.

Shows the presence of a critical point with entanglement-like scaling behavior.

Distinguishes phases by topological magic properties.

Abstract

Magic, also known as nonstabilizerness, quantifies the distance of a quantum state to the set of stabilizer states, and it serves as a necessary resource for potential quantum advantage over classical computing. In this work, we study magic in a measurement-only quantum circuit with competing types of Clifford and non-Clifford measurements, where magic is injected through the non-Clifford measurements. This circuit can be mapped to a classical model that can be simulated efficiently, and the magic can be characterized using any magic measure that is additive for tensor product of single-qubit states. Leveraging this observation, we study the magic transition in this circuit in both one- and two-dimensional lattices using large-scale numerical simulations. Our results demonstrate the presence of a magic transition between two different phases with extensive magic scaling, separated by a critical point in which the mutual magic exhibits scaling behavior analogous to entanglement. We further show that these two distinct phases can be distinguished by the topological magic. In a different regime, with a vanishing rate of non-Clifford measurements, we find that the magic saturates in both phases. Our work sheds light on the behavior of magic and its linear combinations in quantum circuits, employing genuine magic measures.