HUBO Optimization: The Quantum Leap?

Kipu Quantum just released in cooperation with IBM Quantum the Iskay Quantum Optimizer on IBM 's Qiskit Functions. The full press release can be found here. My colleagues Eric Michon and Gabriel Alvarado wrote a great Blog article about the potential applications of this heuristic solver. In their article about the solver it is discribed also as a HUBO solver. In this weeks 'Entangled Threads' newsletter I want to explain what HUBO optimization is and why it matters.

Higher-Order Unconstrained Binary Optimization (HUBO) should be a bigger deal than it is. And yet, outside a small circle of experts, few people are talking about it. But they should be—because HUBO isn't just an incremental improvement on the well-known QUBO (Quadratic Unconstrained Binary Optimization). It's a fundamental shift in how we think about optimization problems, especially in the era of quantum computing.

For years, QUBO has been the go-to framework for encoding optimization problems. It’s been great for solving problems with pairwise interactions, making it a favorite in fields like finance, logistics, and machine learning. But here’s the problem: real-world systems aren’t just about two-variable interactions. They’re messy, interconnected, and full of higher-order relationships.

HUBO fixes that. Instead of forcing everything into quadratic terms, HUBO allows optimization problems to be formulated with genuine higher-order interactions. No more kludgy workarounds. No more artificial constraints. Just a cleaner, more natural representation of complex problems.

Now, QUBO still has its place. It’s well-supported by classical and quantum annealing hardware, and there are plenty of algorithms optimized for it. But HUBO shines in specific scenarios where higher-order interactions are crucial. One advantage is reduced overhead—converting a higher-order problem into QUBO often requires introducing extra variables, increasing the problem size and computational complexity. HUBO eliminates this step, making computations more efficient.

Another key benefit is better model fidelity. Many real-world problems, such as combinatorial chemistry and MIMO signal processing, inherently involve multi-variable interactions. HUBO allows these problems to be modeled directly without losing crucial information.

Perhaps most importantly, HUBO offers a quantum-native formulation. Classical computers struggle with HUBO due to exponential scaling, but quantum systems are inherently better suited for these problems. The ability to process higher-order interactions directly gives HUBO a significant edge in the quantum computing landscape.

Classical solvers often need to approximate HUBO problems or transform them into QUBO, which negates many of HUBO’s advantages. But quantum computers, especially those leveraging higher-order Hamiltonians, can natively represent and process HUBO problems.

Recent breakthroughs illustrate its potential. Researchers of Kipu Quantum have successfully demonstrated HUBO optimization on quantum processors with up to 156 qubits, showing early signs of superior performance over classical heuristics. Quantum algorithms like Bias-Field Digitized Counterdiabatic Quantum Optimization (BF-DCQO), that also the Iskay Optimizer is based on, have been specifically designed to tackle HUBO problems, delivering stronger results compared to traditional approaches in benchmark tests. In telecommunications, HUBO-based MIMO detection has also outperformed classical methods in optimizing signal decoding, proving its relevance in real-world applications.

These advancements indicate that HUBO’s advantages are not just theoretical. As quantum hardware continues to evolve, HUBO is poised to play a critical role in solving complex optimization challenges more efficiently than ever before.

HUBO isn’t just another optimization technique—it’s a game-changer, especially in the quantum era. The problem? Adoption is lagging because too many optimization workflows are still stuck in a QUBO-first mindset. As quantum hardware continues to improve, expect to see more direct HUBO implementations rather than forcing everything through QUBO approximations.

This is one of those rare cases where the tech exists, the use cases are real, but the awareness just isn’t there yet. That won’t last forever. HUBO is coming. The only question is: Will you be ahead of the curve?

Read you next time.