Overview
The group develops mathematically grounded research projects in quantum computing and related areas. Our aim is to connect quantum algorithms with concrete questions in applied mathematics, numerical analysis, optimization, data analysis, and scientific computing.
Research Themes
Quantum Algorithms & Numerical Methods
Linear algebra, differential equations, approximation, spectral methods, QSVT and algorithmic complexity.
Quantum Machine Learning
Hybrid quantum-classical models, robustness, reproducibility, benchmarking and data encoding.
Quantum Compilation
Gate reduction, high-level quantum instructions, topology-aware compilation and resource estimation.
Quantum Data & Imaging
Quantum databases, image representations, state preparation, finite-shot effects and reconstruction quality.
Current Research Projects
Topology-aware high-level quantum compilation
We study whether algebraic gate-count reductions remain advantageous after transpilation to realistic hardware connectivity. The project compares CNOT/SWAP counts, depth, two-qubit depth and noise-sensitive performance across several coupling graphs.
Reproducibility and robustness of quantum machine learning for malware analysis
A controlled study of hybrid QCNN/QMLP models under repeated training, alternative encodings, circuit depths, noise models and classical baselines.
Finite-shot stability of quantum image representations
Mathematical and numerical analysis of reconstruction error for FRQI and related image encodings, including shot complexity, noise propagation and image-quality metrics.
Approximation error and circuit complexity in QSVT
We investigate the trade-off between polynomial approximation degree, approximation error, circuit depth and resource requirements in QSVT-based algorithms.
Quantum Computing Research Notes · 2026
Student research notes developed in the 2026-1 edition of Introduction to Quantum Computing. The series distinguishes expository work from reproducible research and ongoing research projects.
Operational Framework for a Quantum Database
Catalina Velásquez Ortiz
Quantum databases, QRAM, dynamic database operations, no-cloning/no-deleting limitations and operational models for quantum data structures.
Optimizing Quantum Compilation via High-Level Quantum Instructions
Juan Giraldo
Tensor-explicit reformulation of compiler optimization theorems, together with a local reproduction and extension of CNOT-count results for V-chain decompositions.
Quantum Singular Value Transformation: Unification and Applications
Nicolás Bello
Mathematical foundations of block-encoding and QSVT, with emphasis on polynomial transformations and applications to credit-risk estimation.
Towards Quantum Machine Learning for Malicious Code Analysis
Santiago Rocha Pachón
Theoretical review and practical recreation of hybrid QMLP and QCNN experiments for malware classification, with attention to reproducibility and dataset accessibility.
Quantum Image Analysis
Mateo Santiago Cardona Ayala
Comparison of FRQI, NEQR, GQIR, BRQI and OQIM, emphasizing qubit requirements, circuit depth, finite-shot measurement and reconstruction metrics.
Reproducible Research
Whenever possible, research notes are accompanied by scripts, notebooks, benchmark tables and experiment logs. Repositories will be linked here as they are curated and versioned.
Quantum compilation repository QML reproducibility repository Quantum imaging repository
People
Principal Investigator
Dr. Diego Gerardo Roldán
Department of Mathematics, Universidad Nacional de Colombia
Current Research Students
Julian Sierra · Applied Mathematics
Jose Fidel Casas · Applied Mathematics
Mateo Cardona · Data Analytics
Nicolas Bello · Data Analysis
Laura Pineda · Applied Mathematics
2026 Student Contributors
Catalina Velásquez Ortiz · Quantum databases
Juan Giraldo · Quantum compilation
Nicolás Bello · QSVT and quantum algorithms
Santiago Rocha Pachón · Quantum machine learning
Mateo Santiago Cardona Ayala · Quantum image analysis
Outreach & Teaching Resources
2026
Add poster preview here
Quantum Computing — An Introduction
Introductory material covering Hilbert spaces, qubits, quantum operators, HHL, Shor's algorithm and key historical milestones in quantum computing.
Collaborations
Centro de Excelencia en Cálculo Científico (CECC), Universidad Nacional de Colombia.