Magic in quantum trajectory unravelings of noisy random quantum circuits
Abstract
The quantum-trajectory description of a noisy quantum circuit is not unique: every Kraus representation of the noise channel defines a different unraveling, i.e., a different ensemble of pure states that averages to the same density matrix. While all unravelings share the same expectation values of observables, they generally differ in the amount of quantum resources carried by the individual trajectories. Here we study non-stabilizerness, or magic, quantified by the stabilizer Rényi entropy, in quantum-trajectory unravelings of Haar-random and T-doped random Clifford brickwork circuits subject to local dephasing noise of strength p. The canonical unraveling in terms of Pauli jumps is Clifford and leaves magic untouched, so that trajectories retain the Haar-random value of non-stabilizerness. Exploring the full two-parameter family of minimal unravelings, we find that the trajectory-averaged magic can be substantially reduced by a state-independent choice of Kraus operators, and that the optimal choice is not in general the projective-measurement unraveling, but a two-outcome generalized measurement in which the Kraus operators correspond to a weak measurement of the noisy qubit. The optimal unraveling reduces the extensive magic density of the trajectories by a p-dependent factor without altering its linear scaling with system size. At the same time, it produces a very broad distribution of magic over trajectories, with a sizable fraction of trajectories retaining Haar-random magic. Since the cost of stabilizer-based classical simulation grows exponentially with the magic of the state, these high-magic trajectories, rather than the average, control the simulation cost. Our results delineate the potential and the limitations of unraveling optimization as a route to the classical simulation of noisy quantum dynamics with stabilizer methods.
Related
- Quantum magic dynamics in random circuits
- Random quantum circuits, chaos and quantum thermalization
- Rare-History Transitions in Temporally Random Integrable Quantum Circuits
- One Gate at a Time: Complexity Growth in Random Quantum Circuits
- On the Distortion of Partitioning Performance by Random Quantum Circuits
BibTeX
@misc{santos2026magic,
title = {{Magic in quantum trajectory unravelings of noisy random quantum circuits}},
author = {Sara Santos and Alessio Paviglianiti and Vincenzo Savona},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.22318},
eprint = {2610.22318},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.22318},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Magic in quantum trajectory unravelings of noisy random quantum circuits
AU - Sara Santos
AU - Alessio Paviglianiti
AU - Vincenzo Savona
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2610.22318
UR - https://arxiv.org/abs/2610.22318
AB - The quantum-trajectory description of a noisy quantum circuit is not unique: every Kraus representation of the noise channel defines a different unraveling, i.e., a different ensemble of pure states that averages to the same density matrix. While all unravelings share the same expectation values of observables, they generally differ in the amount of quantum resources carried by the individual trajectories. Here we study non-stabilizerness, or magic, quantified by the stabilizer Rényi entropy, in quantum-trajectory unravelings of Haar-random and T-doped random Clifford brickwork circuits subject to local dephasing noise of strength p. The canonical unraveling in terms of Pauli jumps is Clifford and leaves magic untouched, so that trajectories retain the Haar-random value of non-stabilizerness. Exploring the full two-parameter family of minimal unravelings, we find that the trajectory-averaged magic can be substantially reduced by a state-independent choice of Kraus operators, and that the optimal choice is not in general the projective-measurement unraveling, but a two-outcome generalized measurement in which the Kraus operators correspond to a weak measurement of the noisy qubit. The optimal unraveling reduces the extensive magic density of the trajectories by a p-dependent factor without altering its linear scaling with system size. At the same time, it produces a very broad distribution of magic over trajectories, with a sizable fraction of trajectories retaining Haar-random magic. Since the cost of stabilizer-based classical simulation grows exponentially with the magic of the state, these high-magic trajectories, rather than the average, control the simulation cost. Our results delineate the potential and the limitations of unraveling optimization as a route to the classical simulation of noisy quantum dynamics with stabilizer methods.
ER -