Level Generation with Quantum Reservoir Computing

TL;DR

This work investigates applying Quantum Reservoir Computing (QRC) to real-time procedural level generation in games, aiming to leverage the fixed dynamics of a quantum reservoir on NISQ devices to produce diverse SMB levels and Roblox obby courses with a lightweight trainable output layer. By encoding levels as sequential features and tuning hyperparameters like the temperature $T$ and qubit count $q$, the approach balances novelty and structural coherence, outperforming simple baselines for short sequences and maintaining large-scale structure. The study examines ideal and noisy hardware scenarios, highlighting that noise can erode QRC advantages and motivating hardware-aware design and noise-robust training. The Roblox analysis demonstrates practical feasibility with a 6-qubit configuration, achieving reasonable save-point regularity and lower broken-transition rates, while acknowledging the need for hardware deployment and further noise mitigation in real devices.

Abstract

Reservoir computing is a form of machine learning particularly suited for time series analysis, including forecasting predictions. We take an implementation of \emph{quantum} reservoir computing that was initially designed to generate variants of musical scores and adapt it to create levels of Super Mario Bros. Motivated by our analysis of these levels, we develop a new Roblox \textit{obby} where the courses can be generated in real time on superconducting qubit hardware, and investigate some of the constraints placed by such real-time generation.

Figures (7)

• Figure 1: Diagram and quantum circuits of the quantum reservoir computing algorithm used in this paper. The input $x_t$ at step $t$ is encoded as parameters of a complex quantum circuit whose measurement outcome is fed to a FNN to sample the next feature.
• Figure 2: The original level, with a selection of QRC-generated variants.
• Figure 3: The rate of new sequences of a certain length for the uncorrelated generator (dotted dashed line), the Markov chain generator (dashed line) and QRC generator for different values of the temperature $T$ (dots). An ideal generator will have an originality rate higher than the Markov chain for short sequences but lower for long sequences, ensuring a balance of novelty and familiarity.
• Figure 4: Rate of transitions that break gameplay. In blue we highlight the region in which the temperature gives the best result, upper bounded by the condition that the error rate remains relatively low (below 5%), and lower bounded by the restriction that the levels are not found to be too repetitive. Inset: examples of three broken transitions.
• Figure 5: The originality metric when training and generating under different noise models. The depolarizing noise (dots) has the controlled depolarization rate $p$ with typical quantum hardware operating around 3% depolarization rate. The noise model based on IQM's Garnet process (crosses) is comparable to Markov and compatible with the specified mean polarization of 2%-3%.