A quantum simulation of heterogeneous matter, designed by Algorithmiq and executed on IBM quantum computers, continues to compete with the world's leading classical simulation methods eight months after its debut on the Quantum Advantage Tracker.

The work addresses one of quantum computing's central challenges: how to trust a result when no classical computer can verify it.

Algorithmiq is also releasing a new benchmark for quantum advantage claims, making its best classical method for simulating molecular ground states available to the research community.

Jul 30, 2026

YORKTOWN HEIGHTS, N.Y. and MILAN – July 30, 2026 — Today, Algorithmiq and IBM (NYSE: IBM) announced a major milestone in the development of quantum computing: a joint demonstration of quantum advantage with the simulation of a heterogeneous quantum material, achieved with a new framework that establishes trust in quantum computations when classical verification is unavailable.

Eight months after this problem and results were first released through the launch of the Quantum Advantage Tracker, no classical method has been able to reliably produce results across the full problem regime studied in this work. It demonstrates that quantum computers can provide trusted solutions more efficiently, more cheaply, or more accurately than leading classical compute methods — which has long been considered a key milestone in the field.

Studying Information Flow in Heterogenous Quantum Matter

Real materials, including catalysts and battery electrolytes, are defined not by perfect crystalline order but by irregular structures, interfaces, and local variations that strongly influence how information, energy, and particles move through the system. To study these effects, a team led by senior scientist Sergey Filippov in Algorithmiq’s R&D division, which is headed by co-founder & Chief Scientific Officer Guillermo García-Pérez, developed a model of heterogeneous quantum matter in which information propagates through regions with different local properties. The resulting dynamics were deliberately positioned in a regime that is experimentally accessible on today's quantum hardware but demanding for leading classical simulation techniques.

The model, when executed on an IBM Quantum Heron processor, effectively captured a programmable quantum material whose microscopic couplings could be tuned and reconfigured at will, so that researchers can control where information flows, localizes, or interferes, as it would in a real material.

Solving Quantum Computing's Trust Problem

Quantum results have traditionally earned trust the same way: by checking them against a classical simulation. To do so, Algorithmiq’s software engineering team collaborated with world-leading classical simulation researchers to explore different simulation approaches. The various classical methods produced conflicting predictions among themselves for the same quantities. In the absence of an exact solution, the challenge was not only to outperform classical computation, but also to determine which result could be trusted.

To address this challenge, the team developed a new framework for trusted quantum computation in the beyond-classical era, laying down a blueprint for scientific discovery. A central part of this strategy was noise manipulation and building a representative model of the underlying noise in the device. Researchers deliberately changed the noise affecting the quantum circuits, including through controlled noise injection, modified gate calibrations, and execution on multiple IBM Quantum processors. This showed that the quantum results remained stable — providing evidence that the quantum computers were producing consistent solutions. With extensively tested noise models, they also demonstrated a path to stand-alone validation using unbiased error mitigation techniques with quantified uncertainty.

Open Sourcing the Benchmark

Algorithmiq is also today releasing monoprop, which makes its best classical method for simulating molecular ground states available to the wider research community — the same techniques it has used to test and challenge quantum advantage claims, including its own. The package is designed to let any research group, quantum or classical, stress-test future advantage claims rather than take them on faith.

Supporting Commentary

Sabrina Maniscalco, co-founder and CEO, Algorithmiq: “For an exponential technology like quantum computing, a verified, openly contested instance of advantage is the inflection point: proof the curve is real, not projected. Demonstrating quantum advantage is an ongoing process, not a single moment, but we believe these results represent our strongest claim published to date and will come to be seen as a major milestone in the evolution of quantum computing.”

Matteo Rossi, co-founder and CTO, Algorithmiq: “This collaboration with IBM has realized an idea first proposed by Richard Feynman in 1982. By simulating quantum matter using a digital quantum processor built from the same physics, we’re able to give researchers a tunable, physically interesting model open to anyone who wants to try to disprove it classically. It is a demanding test case, and it has withstood open challenge for eight months and counting.”

Jay Gambetta, Director of IBM Research and IBM Fellow: “Quantum computers have reached the point at which they can show evidence of the fundamental criteria for advantage: they can outperform leading classical methods, and they can simultaneously produce results that we can trust. I look forward to continued benchmarking of these results by the community on the Quantum Advantage Tracker, and progress towards rigorous error bars for quantum methods.This is a pivotal milestone in the future of quantum computers as we look towards scaling well beyond what could ever be possible with classical computers alone — and further explore new realms of physics, materials, life sciences, and much more.”

More Demonstrations of Quantum Advantage Emerge

Today, alongside this milestone from IBM and Algorithmiq, partners from across IBM’s ecosystem are announcing more demonstrations of quantum advantage with trusted computations. To learn more, visit https://www.ibm.com/quantum/blog/quantum-advantage.

About Algorithmiq

Algorithmiq programs quantum computers to solve the world's hardest problems. From medicine to materials, from AI to complex industrial challenges, the company develops the software that makes quantum computers useful for enterprises, today. Headquartered in Milan, Italy, with operations in Finland, the UK, and Ireland, Algorithmiq is led by CEO & and co-founder Dr Sabrina Maniscalco, CSO and co-founder Dr Guillermo García-Pérez, CTO and co-founder Dr Matteo Rossi and Lead Researcher and Co-Founder Dr Boris Sokolov. Algorithmiq has raised over $41 million to date, backed by United Ventures, institutional investor CDP and Inventure VC.

About IBM

IBM is a leading provider of global hybrid cloud and AI, and consulting expertise. We help clients in more than 175 countries capitalize on insights from their data, streamline business processes, reduce costs, and gain a competitive edge in their industries. Thousands of governments and corporate entities in critical infrastructure areas such as financial services, telecommunications and healthcare rely on IBM's hybrid cloud platform and Red Hat OpenShift to affect their digital transformations quickly, efficiently and securely. IBM’s breakthrough innovations in AI, quantum computing, industry-specific cloud solutions and consulting deliver open and flexible options to our clients. All of this is backed by IBM’s long-standing commitment to trust, transparency, responsibility, inclusivity, and service. Visit www.ibm.com for more information.

Media contacts:

Kirsten Nehr
COO
Algorithmiq Inc.
kirsten@algorithmiq.fi

Brittany Forgione
IBM 
Brittany.Forgione@ibm.com

Erin Angelini
IBM
edlehr@us.ibm.com