Supanut Thanasilp

If you ever wonder during the night whether you have forgotten the effect of shot-noise in your BP-free strategy analysis ... maybe this could help 😁 Also, congrats to @reyhanehaghaeisaem.bsky.social for her first work 🙌🥳

Congrasts Kasidit on his first arxiv 🙌🥳 such a talented and hard working master student. He's sure going to do amazing things in the quantum world ⚛️

Thanks so much to my co-authors Weijie Xiong @qzoeholmes.bsky.social @aangrisani.bsky.social Yudai Suzuki @thipchotibut.bsky.social It's real fun to work with you all 😃🙌

Also, special thanks to @mvscerezo.bsky.social Martin Larocca for their valuable insight on correlated Haar random unitaries 🌮

So yes, big question for future QRP design: how to pick your circuit depth or interaction time so that you remain powerful without going full random.

You want that “just right” level of chaos: enough to get expressive states, not so much that it all washes out.

Episode 4: New Hope

Not everything is gloom and doom. We found that for moderate scrambling (like shallow random circuits or chaotic Ising with short evolution), you don’t get lethal exponential concentration.

a close up of thanos ' face in avengers infinity war . ALT: a close up of thanos ' face in avengers infinity war .

Episode 3: Noise erases memo...

We also studied QRP under local unital or non-unital noise. While there are work that argue dissipation as a resource for QRP, we prove noise also forces your reservoir to forget states from the distant past exponentially quickly

Episode 2: Oh what ! I forgot now

We prove that in extreme-scrambling QRPs, old inputs or initial states get forgotten exponentially fast (in both time steps and system size !). Too much scrambling -> you effectively “MIB” zap each past input.

Hence our new results show that, while chaotic (extreme-scrambling) reservoirs are fine for processing information in small setups as people have studied, they suffer from scalability issue to larger models doomed by their own chaoticity.

Episode 1: Scalability barrier

Based on the unrolled form, we prove the exponential concentration of QRP output. In a large scale setting, the trained QRP model becomes input-insensitive leading to poor generalization despite trainability guarantee.

To address this challenge, we apply tensor-diagram approaches to unroll multi-step QRP into a single high-moment Haar integral on a larger dimension amenable for scalability and memory analysis.

Episode 0: Temporal correlation hinders standard analytical techniques.

While related techniques already establish scalability barriers for other quantum models, the QRP protocol is much more demanding: a fixed reservoir repeatedly interleaves with a stream of input time-series.

Our key messages can be summarized as

🎯 Big scrambling in quantum reservoirs helps at small sizes but kills input-sensitivity at large scale
🎯 Memory of older states decays exponentially (in both time steps and system size !)
🎯 Noise can make us forget even faster

The QRP model processes input time series of quantum states. Here we model the extreme scrambling reservoir as an instance drawn from a high-order design unitary ensemble.

Once upon a time a myth in Quantum Reservoir Processing (QRP) goes by “more chaos = richer feature map = better”

Doomed by their own chaotic dynamics, QRP may not scale in the extreme scrambling limit.

Check out our new Star Wa… I mean paper on arxiv: scirate.com/arxiv/2505.1...