Variational Quantum Brushes

TL;DR

The paper advances quantum art by presenting two variational brushes, Steerable and Chemical, that leverage $H(t)=H_0+\sum_i u_i(t) H_i$ dynamics and VQE-inspired circuits to produce novel visual effects. Steerable employs quantum geometric control to smoothly interpolate between two canvases via a learnable time-dependent circuit, while Chemical visualizes the ground-state evolution of a molecule through a parametric circuit family $U(\boldsymbol{\eta})$ applied to stroke pixels, using a DUCC-inspired ansatz. Key contributions include a concrete optimization framework with fidelity and energy terms, a second-order splitting circuit implementation, SVD-based color encoding, and precomputation of VQE circuit families to enable real-time painting; together they demonstrate new modes of artistic expression at the intersection of quantum computing and the visual arts. The work highlights practical considerations for NISQ-era quantum-augmented art, including extrapolation in Steerable, gray-decay artifacts, and the need to precompute for complex molecules in Chemical, offering a path toward broader adoption and experimentation. The open-source release at $https://github.com/moth-quantum/QuantumBrush$ further facilitates exploration and extension by practitioners.

Abstract

Quantum brushes are computational arts software introduced by Ferreira et al (2025) that leverage quantum behavior to generate novel artistic effects. In this outreach paper, we introduce the mathematical framework and describe the implementation of two quantum brushes based on variational quantum algorithms, Steerable and Chemical. While Steerable uses quantum geometric control theory to merge two works of art, Chemical mimics variational eigensolvers for estimating molecular ground energies to evolve colors on an underlying canvas. The implementation of both brushes is available open-source at https://github.com/moth-quantum/QuantumBrush and is fully compatible with the original quantum brushes.

Figures (10)

• Figure 1: Steerable effect applied to Renoir's Bal du moulin de la Galette using a red parrot as target image.
• Figure 2: Diagram summarizing the learning process behind Steerable.
• Figure 4: Visualization of the steering effect for 2 qubits.
• Figure 5: Fidelity evolution over time and the control amplitudes $u_1$ and $u_2$.
• Figure 6: Target for the application of the Steerable brush for generating Figure \ref{['fig: renoir']}.