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arXiv:2512.24173

Variational Quantum Brushes

Jui-Ting Lu, Henrique Ennes, Chih-Kang Huang, Ali Abbassi

quant-phcs.GRcs.LGmath.OCSubmitted Dec 30, 2025• Announced Dec 31, 2025• 0 citations
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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.

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quant-pharXiv:2609.17979•Sep 17, 2026
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.
Accurate prediction of binding affinities and efficient lead optimization remain central challenges in computational drug discovery, particularly for complex biological targets characterized by rugged energy landscapes, conformational heterogeneity, and high-dimensional interaction spaces. Classical computational methods—such as molecular docking, force-field–based simulations, and deep learning models—have made substantial progress, yet they often struggle to capture quantum-mechanical effects and long-range correlations critical to molecular recognition. This study explores a quantum-enhanced framework that integrates Variational Quantum Algorithms (VQAs), quantum-inspired Hamiltonian modeling, and hybrid quantum–classical optimization workflows to improve the fidelity and scalability of drug discovery pipelines. By encoding molecular interactions into parameterized quantum circuits, the framework leverages quantum superposition and entanglement to explore complex chemical space more efficiently, enabling refined estimation of binding energies and accelerated identification of high-quality leads. Preliminary simulations indicate that VQA-based estimators outperform classical baselines for challenging protein–ligand systems, reducing prediction error while maintaining computational tractability. These findings highlight the emerging potential of quantum technologies to enable more accurate, data-efficient, and mechanistically grounded drug discovery for next-generation therapeutics.
'In the past few years quantum computers have seen considerable interest from fields which have problems which are computationally expensive to solve with classical computers. One area that has been a major of source of this interest is the simulation of chemical systems. Materials are one type of system that is important to a variety of industries such as renewable energy and medicine. Among the obstacles faced in simulating materials, materials can have properties which are challenging to calculate on classical computers. The promise of quantum computing for improving the exactness of chemical calculations has been shown with a number of methods for a variety of systems. One such method which has previously been used for materials is the variational quantum eigensolver (VQE). However work doing this is still fairly scarce and also typically uses closed source/paid software or does not publish detailed code. The goal of this research is to implement VQE for materials using the python package Tangelo. This implementation will then be used to perform calculations on simple systems to compare this implementation with existing results.
Quantum mechanics has introduced a new theoretical framework for the study of molecules, enabling the prediction of properties and dynamics through the solution of the Schrödinger equation applied to these systems. However, solving this equation is computationally expensive, which has led to the development of various mathematical frameworks and computational methods designed to balance the available resources with the desired level of accuracy. In particular, quantum computers have emerged as a promising technology with the potential to address these problems more efficiently in the coming decades, whether through reductions in memory, time, and energy consumption, i. e.\textit{i. e.}i. e., reductions in computational complexity or by enhancing precision. This research field is known as Quantum Simulation. Given the current technological limitations of quantum computers, Variational Quantum Algorithms (VQAs), especially the Variational Quantum Eigensolver (VQE), stand out as a feasible approach to demonstrating advantages over classical methods in the near term. This feasibility arises from their lower demand for quantum gates and the reduced depth of the circuits required for their implementation. In this work, we present the application of quantum mechanics to the study of molecules, provide an introduction to the fundamentals of quantum computing, and explore the integration of these fields by employing the VQE in molecular simulations. Finally, we discuss the spatial and temporal complexity associated with the algorithm, highlighting its implications and challenges.
Abstract We propose a hybrid quantum-classical algorithm to compute approximate solutions of binary combinatorial problems. We employ a shallow-depth quantum circuit to implement a unitary and Hermitian operator that block-encodes the weighted maximum cut or the Ising Hamiltonian. Measuring the expectation of this operator on a variational quantum state yields the variational energy of the quantum system. The system is enforced to evolve toward the ground state of the problem Hamiltonian by optimizing a set of angles using normalized gradient descent. Experimentally, our algorithm outperforms the state-of-the-art quantum approximate optimization algorithm on random fully connected graphs and challenges D-Wave quantum annealers by producing good approximate solutions. Source code and data files are publicly available ( https://github.com/nkuetemeli/UQMaxCutAndIsing ).
Quantum simulation of chemical systems is one of the most promising near-term applications of quantum computers. The variational quantum eigensolver, a leading algorithm for molecular simulations on quantum hardware, has a serious limitation in that it typically relies on a pre-selected wavefunction ansatz that results in approximate wavefunctions and energies. Here we present an arbitrarily accurate variational algorithm that, instead of fixing an ansatz upfront, grows it systematically one operator at a time in a way dictated by the molecule being simulated. This generates an ansatz with a small number of parameters, leading to shallow-depth circuits. We present numerical simulations, including for a prototypical strongly correlated molecule, which show that our algorithm performs much better than a unitary coupled cluster approach, in terms of both circuit depth and chemical accuracy. Our results highlight the potential of our adaptive algorithm for exact simulations with present-day and near-term quantum hardware.
Estimating quantum state properties is essential across a wide range of applications, from studying quantum many-body physics to benchmarking quantum hardware. We present Qurrium, a Python package built on Qiskit that implements randomized measurement protocols for estimating purity, second-order Rényi entropy, expectation values of Pauli observables, and state overlap. In this paper, we focus on the classical shadow protocol and demonstrate two workflows in Qurrium. One is the end-to-end workflow that integrates quantum circuit preparation, simulation, measurement, and analysis. The other is the standalone estimation workflow that accepts pre-collected measurement data from any hardware platform in Qurrium's data format. We demonstrate both workflows through examples of a cluster state and an Ising time-evolved state. Furthermore, we report results obtained from a superconducting quantum processor developed by Academia Sinica and analyzed using the standalone estimation workflow. Qurrium is built on Qiskit, the dominant framework in quantum computing software, making it directly accessible to the large community of researchers already working with Qiskit. The source code is openly available at https://github.com/qurrium/qurrium and the example code is provided at https://github.com/qurrium/classical-shadow-examples.