I would expect that even for sampling tasks, very high values of quantum resources can make a quantum system more prone to noise. But the exact thresholds and phase diagrams will likely be different.

No — so far, we’ve only looked at estimating expectation values (like in heterodyne detection). Whether similar conclusions hold for sampling tasks is an interesting direction for future work

This was a truly funny project, merging different backgrounds: CV quantum information (@Varun, @ulyssechabaud.bsky.social) and simulation of DV circuits (@qzoeholmes.bsky.social and myself). Looking forward to other enriching collaborations in the future.
In the meantime, check out our preprint:

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.

In recent years, bosonic platforms have surged in importance, powering advances in quantum error correction, quantum machine learning, and quantum chemistry.
But their infinite-dimensional, continuous-variable (CV) nature makes them far harder to analyze or simulate.

quantum-journal.org/papers/q-202...

This work extends the theory of quantum statistical query (QSQ) learning to the task of learning unitary operators. One of the main advantages of this model is its robustness to noise — the proposed algorithms can handle both shot noise and certain systematic measurement errors.

If the noise is nonunital, there are at least two issues: (i) the output distribution is not anticoncentrated (arxiv.org/abs/2306.16659) and (ii) the noise creates additional Pauli paths, increasing the runtime of the previous sampling algorithm from polynomial to quasi-polynomial

Thanks :) Yes, Pauli-path methods can definitely be used for sampling from noisy random circuits, as shown in this pioneering work arxiv.org/abs/2211.03999. However, this result holds for local depolarizing noise and provided that the output distribution is anticoncentrated.

Taken together, these works close a gap in understanding the link between barren plateaus and classical simulability. While non-unital noise enhances trainability by avoiding barren plateaus, we also prove it enables efficient classical simulation of generic circuits!

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.

Check out the open-source library at github.com/MSRudolph/Pa...!

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.