Hardware-Agnostic Modeling of Quantum Side-Channel Leakage via Conditional Dynamics and Learning from Full Correlation Data

TL;DR

This paper develops a hardware-agnostic, machine learning-based method to model and decode quantum side-channel leakage from full correlation data, enabling better understanding and mitigation of quantum information leaks during quantum gate sequences.

Contribution

It introduces a sequential probe framework for quantum side-channel analysis, deriving a depth-dependent leakage model and a universal decoder that generalizes across noise and coupling variations.

Findings

Leakage envelope predicts optimal coupling band at each depth

Decoder accurately recovers gate sequences near the predicted band

Performance degrades predictably with decoherence and finite shots

Abstract

We study a sequential coherent side-channel model in which an adversarial probe qubit interacts with a target qubit during a hidden gate sequence. Repeating the same hidden sequence for $N$ shots yields an empirical full-correlation record: the joint histogram $\widehat{P}_g(b)$ over probe bit-strings $b\in\{0,1\}^k$, which is a sufficient statistic for classical post-processing under identically and independently distributed (i.i.d.) shots but grows exponentially with circuit depth. We first describe this sequential probe framework in a coupling- and measurement-agnostic form, emphasizing the scaling of the observation space and why exact analytic distinguishability becomes intractable with circuit depth. We then specialize to a representative instantiation (a controlled-rotation probe coupling with fixed projective readout and a commuting $R_x$ gate alphabet) where we (i) derive a depth-dependent leakage envelope whose maximizer predicts a "Goldilocks" coupling band as a function of depth, and (ii) provide an operational decoder, via machine learning, a single parameter-conditioned map from $\widehat{P}_g$ to Alice's per-step gate labels, generalizing across coupling and noise settings without retraining. Experiments over broad coupling and noise grids show that strict sequence recovery concentrates near the predicted coupling band and degrades predictably under decoherence and finite-shot estimation.