Smarter Usage of Measurement Statistics Can Greatly Improve Continuous Variable Quantum Reservoir Computing

TL;DR

The paper tackles the limitations of Gaussian-state quantum reservoir computing by introducing two practical enhancements for CV photonic implementations: sampling the cumulative distribution function (CDF) of measurement outcomes to augment nonlinear processing, and storing past measurements in classical memory to boost memory and mitigate finite-ensemble noise. Using a seven-mode photonic reservoir with squeezing and χ^(2) interactions, the authors demonstrate that CDF-based readouts—especially multivariate CDFs—significantly increase information processing capacity (IPC) and improve NARMA task performance beyond covariance-only approaches, even in the ideal measurement limit. In realistic finite-ensemble scenarios, these gains persist, with classical memory further enhancing performance and sometimes surpassing ideal covariance benchmarks for modest ensemble sizes. Collectively, the results establish a new Gaussian-resource benchmark for CV-QRC and suggest broader applicability of CDF-based processing in CV quantum learning and DV-CV hybrids.

Abstract

Quantum reservoir computing is a machine learning scheme in which a quantum system is used to perform information processing. A prospective approach to its physical realization is a photonic platform in which continuous variable (CV) quantum information methods are applied. The simplest CV quantum states are Gaussian states, which can be efficiently simulated classically. As such, they provide a benchmark for the level of performance that non-Gaussian states should surpass in order to give a quantum advantage. In this article we propose two methods to extract more performance from Gaussian states compared to previous protocols. We consider better utilization of the measurement distribution by sampling its cumulative distribution function. We show it provides memory in areas that conventional approaches are lacking, as well as improving the overall processing capacity of the reservoir. We also consider storing past measurement results in classical memory, and show that it improves the memory capacity and can be used to mitigate the effects of statistical noise due to finite measurement ensemble.

Figures (6)

• Figure 1: Schematic of the photonic reservoir computer and its use. The reservoir is a physical ensemble of optical modes circulating in a fiber loop. The classical input modulates squeezed vacua which are injected through a beam splitter, which is also responsible for output extraction. $\chi^{(2)}$-crystals are responsible for creating correlations. Conventionally, homodyne measurements of the $x$-quadratures of each mode are used to estimate the expected variance $\langle x^2\rangle$ of the normally distributed measurement outcomes which become the computational nodes. Here we introduce the use of the cumulative distribution function (CDF) to form the nodes. It can be sampled for each measured observable at various points $c$ by evaluating the probability that a measurement outcome is at most $c$. In both cases tasks are accomplished as is typically done, i.e. by forming the optimal linear combination of the computational nodes.
• Figure 2: Performance in the NARMA task using the CDF.
• Figure 3: Information processing capacity of the CDF schemes by degree. Compared to the covariances-only approach the CDF schemes lead to substantially higher nonlinearity in terms of the degree reached as well as higher overall capacity.
• Figure 4: Information processing capacity of the classical memory schemes by degree. The black stars indicate the number of computational nodes, which corresponds to the theoretical upper bound on the IPC. Averaged over 50 realizations.
• Figure 5: Information processing capacity of the different schemes with finite ensembles of various sizes and the ideal case of an infinite ensemble. The dashed black line shows the covariances-only performance when $M \to \infty$. Averaged over 50 realizations.