Estimating Non-Stabilizerness Dynamics Without Simulating It

TL;DR

The paper presents ICCR, a new method to efficiently analyze non-stabilizerness dynamics in quantum circuits by transforming circuits into Clifford form and renormalizing initial states, avoiding expensive simulations.

Contribution

ICCR introduces an iterative circuit renormalization technique that enables efficient evaluation of non-stabilizerness dynamics without direct simulation.

Findings

Successfully evaluated non-stabilizerness for systems up to N=1000.

Validated ICCR results against tensor network simulations.

Observed measurement-induced transition in a magic purification circuit.

Abstract

We introduce the Iterative Clifford Circuit Renormalization (ICCR), a novel technique designed to efficiently handle the dynamics of non-stabilizerness (a.k.a. quantum magic) in generic quantum circuits. ICCR iteratively adjusts the starting circuit, transforming it into a Clifford circuit where all elements that can alter the non-stabilizerness, such as measurements or T gates, have been removed. In the process the initial state is renormalized in such a way that the new circuit outputs the same final state as the original one. This approach embeds the complex dynamics of non-stabilizerness in the flow of an effective initial state, enabling its efficient evaluation while avoiding the need for direct and computationally expensive simulation of the original circuit. The initial state renormalization can be computed explicitly using a matrix-product state approximation that can be systematically improved. We implement the ICCR algorithm to evaluate the non-stabilizerness dynamics for systems of size up to N = 1000. We validate our method by comparing it to tensor networks simulations. Finally, we employ the ICCR technique to study a magic purification circuit, where a measurement-induced transition is observed.