Quantinuum
Quantinuum and QM are collaborating on implementing TQFTs and TQC on Quantinuums hardware. Together we will work on 4 projects 1) Computing Quantum Invariants and Probing Conjectures, 2) Benchmarking QPUs with Quantum Invariants, 3) Implementing universal Topological Quantum Codes, providing error corrected universal Quantum computers and 4) Developing Quantum Computing-assisted Machine Learning Approach to Quantum Invariants.
IBM
In collaboration with IBM, we are developing quantum algorithms for solving partial differential equations (PDEs). In earlier work, we focused on the advection–diffusion equation (link: https://arxiv.org/abs/2512.22163), aiming to construct quantum circuits that are implementable on near-term hardware, particularly IBM’s superconducting quantum devices. Our approach is based on the quantum singular value transformation in combination with efficient block-encodings of high-order finite-difference approximations of spatial derivatives. A key objective is to assess the extent to which higher-order methods outperform their lower-order counterparts in a quantum computing setting.
Atom Computing
In collaboration with Atom Computing, QM and Qpurpose are working to implement important quantum algorithms in topological quantum computing on the powerful neutral-atom platform provided by Atom Computing. The relevant algorithms are BQP-complete, and their implementation will enable researchers to probe longstanding conjectures in mathematics. The project has deep connections to schemes for universal fault-tolerant quantum computing based on TQFT gates. In particular, it is closely related to topological error-correcting codes and the mathematical aspects of topological phases of matter. Part of the project involves rewriting the quantum algorithms in terms of the native gate set of neutral-atom processors, where the controlled-Z gate is the essential two-qubit building block.