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, 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.

Quantinuum and Qpurpose are jointly exploring the application of Quantinuum’s advanced quantum computing capabilities to demonstrate quantum advantage in low-dimensional topology, specifically by performing Topological Quantum Field Theory (TQFT) computations beyond the reach of classical systems, while also investigating the error-correction properties of various TQFT-based codes.

Qpurpose and Pasqal are collaborating to reformulate permutation-based optimization problems as Maximum Weight Independent Set (MWIS) instances tailored to Pasqal’s neutral-atom quantum platform, with the aim of developing quantum-native solutions to real-world industrial optimization challenges.

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.

QPurpose is collaborating with Orca Quantum to solve Gaussian weighted integrals on the ORCA PT Series photonic quantum computing platforms.

At QM, we developed a quantum algorithm, native to photonic technologies, with an exponential speedup over classical Monte Carlo methods. Together with Orca Quantum, we are exploring its integration with photonic quantum computing hardware.

In collaboration with Sparrow Quantum, QM and QPurpose are developing quantum algorithms tailored to Sparrow’s world leading deterministic single photon sources.

While the quantum algorithm developed at QM is based on Gaussian boson sampling, which uses squeezed light, we expect that a similar exponential speedup over Monte Carlo methods exists for boson sampling.

To achieve quantum advantage with boson sampling over classical methods, we need deterministic, high efficiency, indistinguishable single photons, as well as ultra low-loss optical components, which, in principle, are within reach of current photonic integrated circuit technology.

In collaboration with researchers at Microsoft, both QM and Qpurpose are developing cutting-edge quantum error correction protocols inspired by topological methods for use on a variety of quantum hardware platforms, but especially for Magne.

Magne is a new powerful quantum computer owned and operated by QuNorth on Danish soil, with hardware provided by Atom Computing, software provided by Microsoft, and financing provided by EIFO and the Novo Nordisk Foundation.