Role of scrambling and noise in temporal information processing with quantum systems

TL;DR

This paper investigates how scrambling and noise affect the ability of quantum systems to process temporal information, revealing exponential decay of memory with system size and noise, and introducing new proof techniques for quantum models.

Contribution

It provides a comprehensive analysis of temporal information processing in quantum reservoirs, including effects of scrambling, noise, and scalability, with new mathematical bounds and insights.

Findings

Measurement readouts concentrate exponentially with reservoir size.

Memory of inputs decays exponentially with size and iterations.

Noise causes exponential decay of memory over time.

Abstract

Scrambling quantum systems have attracted attention as effective substrates for temporal information processing. Here we consider a quantum reservoir processing framework that captures a broad range of physical computing models with quantum systems. We examine the scalability and memory retention of the model with scrambling reservoirs modelled by high-order unitary designs in both noiseless and noisy settings. In the former regime, we show that measurement readouts become exponentially concentrated with increasing reservoir size, yet strikingly do not worsen with the reservoir iterations. Thus, while repeatedly reusing a small scrambling reservoir with quantum data might be viable, scaling up the problem size deteriorates generalization unless one can afford an exponential shot overhead. In contrast, the memory of early inputs and initial states decays exponentially in both reservoir size and reservoir iterations. In the noisy regime, we also prove that memory decays exponentially in time for local noisy channels. These results required us to introduce new proof techniques for bounding concentration in temporal quantum models.