The intertwined action of non-Gaussianity, symplectic coherence, noise rate, and energy determine the boundary between quantum and classical regimes.
Balancing these quantum resources — not just reducing noise — will be key to future demonstrations of bosonic quantum advantage.

This interplay yields striking phase diagrams: in the blue regions, bosonic circuits are classically simulable with runtime linear in depth, ruling out quantum advantage. Intriguingly, both too low (bottom row) and too high (top and middle rows) cubic gate rates can destroy advantage under noise.

Using this tool, we uncover a surprising result:
quantum resources usually linked to bosonic advantage — non-Gaussianity and symplectic coherence — can actually make classical simulation easier in the presence of noise.

To this end, we introduce the displacement propagation algorithm—a continuous-variable analogue of Pauli propagation. It uses Markov chain Monte Carlo methods to propagate displacement operators through noisy circuit layers, revealing when bosonic circuits are classically simulable.

Can your quantum device still provide quantum advantage in the presence of noise? This is well-studied for spin systems, but less so for bosonic systems—photonics, superconducting resonators, or motional modes of trapped ions and atoms. We address this question in our new paper!

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Excited to share that this paper is now published in @quantum-journal.bsky.social !

Thrilled to announce that our work on classical simulation via Pauli Propagation was accepted for an oral presentation at TQC! See you in Bengaluru!

Our approach leverages a new Pauli Propagation algorithm, specifically tailored to this setting, which stochastically prunes the Pauli tree.

In arXiv:2501.13050, we relax the random circuit assumption by using a fixed ansatz with Clifford gates and Pauli rotations at random angles.

Our approach is highly scalable, as shown by @quantummanuel.bsky.social’s numerics for a Hamiltonian variational ansatz on a 6×6 lattice (below) and real-time dynamics on an 11×11 lattice.

Pauli propagation algorithms work by computing an approximate Heisenberg evolution of the observable in the Pauli basis, iteratively forming a Pauli tree and pruning it with a case-dependent truncation rule.

Crucially, the Quantum Refrigerator scheme shows that carefully designed circuits with non-unital noise can evade efficient classical simulation. However, we prove that average-case circuits can still be efficiently simulated using Pauli propagation algorithms!

Our noise model is highly general, covering arbitrary incoherent single-qubit noise. Unlike many prior works focusing on depolarizing-like noise, we extend to non-unital (e.g., amplitude damping) and dephasing-like noise, pushing the boundaries further!

In arXiv:2501.13101, we explore a broad class of noisy circuits across all geometries, significantly relaxing the strict assumptions on geometric locality and noise models imposed by prior works.