non-markovian-kerr-feedback-qrc

name

non-markovian-kerr-feedback-qrc

description

Proves unbounded computational superiority of Kerr nonlinear feedback over Gaussian linear reservoirs in continuous-variable quantum reservoir computing. Single Kerr mode with feedback depth D replaces up to ~100 linear modes. Use when: CV-QRC design, non-Markovian reservoir computing, Kerr nonlinear optics, cross-time nonlinear correlations, quantum reservoir capacity analysis, Gaussian limitations, time-delay feedback.

Overview

This methodology proves that a single Kerr nonlinear element in a time-delayed feedback loop can outperform arbitrarily many linear optical modes in continuous-variable quantum reservoir computing (QRC). It establishes a fundamental limit on Gaussian reservoirs and shows how one nonlinear mode replaces ~100 linear ones.

Paper: Soh (2026). "Computational Superiority of Non-Markovian Kerr Feedback in Continuous-Variable Quantum Reservoir Computing." arXiv:2606.06689 [quant-ph, math-ph].

Core Problem: The Gaussian Ceiling

Why Linear Optical Reservoirs Fail

A linear optical medium can delay, mix, and superpose light pulses — but cannot multiply. Cross-time nonlinear correlations (products of input at different past times) are essential for many temporal computations, yet Gaussian reservoirs cannot form genuine products within the reservoir. They can only:

1. Store each past input separately
2. Multiply them in the readout layer
3. This forces an exponentially harder high-order measurement

The Hardware Ceiling

Theorem (Cross-Time Nonlinear Rank):

• N-mode Gaussian reservoir: maximum cross-time nonlinear rank = 2N (hard ceiling)
• Single Kerr mode with feedback depth D: rank = D (no ceiling)

The Kerr Solution

Time-Delayed Feedback Architecture

Input → Kerr Element → Feedback Loop → Readout
          ↑               ↓
          └── Delay ──────┘