Quantum Computing Solutions for Complex Problem Classes

Thought you knew which #quantumcomputers were best for #quantum optimization? The latest results from Q-CTRL have reset expectations for what is possible on today's gate-model machines. Q-CTRL today announced newly published results that demonstrate a boost of more than 4X in the size of an optimization problem that can be accurately solved, and show for the first time that a utility-scale IBM quantum computer can outperform competitive annealer and trapped ion technologies. Full, correct solutions at 120+ qubit scale for classically nontrivial optimizations! Quantum optimization is one of the most promising quantum computing applications with the potential to deliver major enhancements to critical problems in transport, logistics, machine learning, and financial fraud detection. McKinsey suggests that quantum applications in logistics alone are worth over $200-500B/y by 2035 – if the quantum sector can successfully solve them. Previous third-party benchmark quantum optimization experiments have indicated that, despite their promise, gate-based quantum computers have struggled to live up to their potential because of hardware errors. In previous tests of optimization algorithms, the outputs of the gate-based quantum computers were little different than random outputs or provided modest benefits under limited circumstances. As a result, an alternative architecture known as a quantum annealer was believed – and shown in experiments – to be the preferred choice for exploring industrially relevant optimization problems. Today’s quantum computers were thought to be far away from being able to solve quantum optimization problems that matter to industry. Q-CTRL’s recent results upend this broadly accepted industry narrative by addressing the error challenge. Our methods combine innovations in the problem’s hardware execution with the company’s performance-management infrastructure software run on IBM’s utility-scale quantum computers. This combination delivered improved performance previously limited by errors with no changes to the hardware. Direct tests showed that using Q-CTRL’s novel technology, a quantum optimization problem run on a 127-qubit IBM quantum computer was up to 1,500 times more likely than an annealer to return the correct result, and over 9 times more likely to achieve the correct result than previously published work using trapped ions These results enable quantum optimization algorithms to more consistently find the correct solution to a range of challenging optimization problems at larger scales than ever before. Check out the technical manuscript! https://lnkd.in/gRYAFsRt

We are pursuing quantum computing because there’s evidence that quantum can solve certain problems exponentially faster than any classical computer. I’m excited to share a new algorithm from our team with the potential for an exponential speedup in a real-world use case: simulating electric circuits. Circuits built from resistors, inductors, and capacitors — RLC circuits — show up across engineering, from power grids to analog filters to integrated circuit design. Predicting how voltages and currents evolve in these systems is routine. But as circuits grow large and complex, those simulations can become increasingly expensive on classical hardware. What makes RLC circuits so challenging to simulate is that they aren’t described by ordinary differential equations (ODEs), but by differential-algebraic equations (DAEs): systems that combine equations describing time evolution with constraints that must be satisfied at every instant. In the case of RLC circuits, we must solve Kirchhoff’s laws of charge and voltage conservation at every junction, but standard ODE solvers struggle to handle this mixed structure. A new paper authored by Arkopal Dutt, Anirban Chowdhury, Kristan Temme, and Hari Krovi, presents the first quantum algorithm tailored to DAEs of this kind. The approach separates the circuit’s state into two parts: one that evolves dynamically over time, and another that is fixed by the constraints. Each part is then handled with the appropriate technique. The result is an algorithm that prepares a quantum state encoding the circuit’s full time evolution, with a runtime that scales only polylogarithmically in the number of nodes — an exponential improvement over the polynomial worst-case scaling of classical methods. This speedup applies to well-conditioned networks where the circuit can be queried in superposition, meaning its structure is accessed as a function that returns entries on demand, rather than being read out element by element. From the quantum computer’s output state (the state encoding the full solution), physically meaningful quantities, like the energy stored in a set of capacitors or dissipated across a set of resistors, can be extracted directly. Interestingly, the authors also show that this energy-estimation task is as powerful as quantum computation itself: a quantum computer can solve it efficiently, and any problem that admits an efficient quantum solution can be reduced to an instance of it. In complexity-theoretic terms, this implies that, under standard assumptions, no classical algorithm can match a quantum computer on this task. Classical circuit simulation has been a workhorse of electronic design for decades. Demonstrating a provable quantum advantage on a problem this practical is an exciting step, and it lines up closely with IBM Quantum’s broader goal of identifying where quantum computing can deliver real value in engineering and industrial settings.   Full paper: https://lnkd.in/ekTFap64

⚛️ Sequential Quantum Computing 📑 We propose and experimentally demonstrate sequential quantum computing (SQC), a paradigm that utilizes multiple homogeneous or heterogeneous quantum processors in hybrid classical-quantum workflows. In this manner, we are able to overcome the limitations of each type of quantum computer by combining their complementary strengths. Current quantum devices, including analog quantum annealers and digital quantum processors, offer distinct advantages, yet face significant practical constraints when individually used. SQC addresses this by efficient inter-processor transfer of information through bias fields. Consequently, measurement outcomes from one quantum processor are encoded in the initial-state preparation of the subsequent quantum computer. We experimentally validate SQC by solving a combinatorial optimization problem with interactions up to three-body terms. A D-Wave quantum annealer utilizing 678 qubits approximately solves the problem, and an IBM’s 156-qubit digital quantum processor subsequently refines the obtained solutions. This is possible via the digital introduction of non-stoquastic counterdiabatic terms unavailable to the analog quantum annealer. The experiment shows a substantial reduction in computational resources and improvement in the quality of the solution compared to the standalone operations of the individual quantum processors. These results highlight SQC as a powerful and versatile approach for addressing complex combinatorial optimization problems, with potential applications in quantum simulation of many-body systems, quantum chemistry, among others. ℹ️ Romero et al - 2025

NotebookLM: "Overcoming Finite-Size Barriers in Quantum Systems: The tensor network method provides a methodology to accurately solve quantum many-body problems that feature exponentially large Hilbert spaces. By compressing incredibly dense objects—such as the many-body density matrix—into a tensor network, the required memory scales logarithmically rather than quadratically with the system size. This computational compression allows researchers to model exceptionally large electronic systems, scaling up to hundreds of millions of sites (micron-scale domains), which far exceeds the capabilities of conventional methodologies. Characterizing Topological Quantum Materials: The method is critical for computing real-space topological markers in complex quantum materials that lack translational symmetry, such as 2D quasicrystals and supermoiré matter. By utilizing a Chebyshev tensor network algorithm, scientists can map out local topological domains, Chern mosaics, and chiral edge modes, which are essential for connecting local topological features to emergent macroscopic functionalities. Simulating Quantum Algorithms: Tensor network contraction can be efficiently parallelized to simulate quantum computation directly. This includes the ability to simulate fundamental quantum algorithms—such as the quantum Fourier transform, Grover's algorithm, and the quantum counting algorithm—in environments with limited entanglement. Advancing Quantum Error Correction: Tensor networks provide structural frameworks for error correction, specifically enabling the parallel decoding of multiple logical qubits within tensor-network codes. Enhancing Machine Learning and Complex Dynamics: Beyond core quantum many-body physics, tensor network techniques have been extended to improve data compression for quantum machine learning, unsupervised generative modeling, complex fluid dynamics, and ultraprecise function integration." https://lnkd.in/epCHzkGY watch: https://lnkd.in/e76jqWZ9

Most enterprises treat quantum computing as a nerdy R&D curiosity. A mistake. Critical business problems, which are fundamentally constrained by classical computing today, are likely to be solved by 2030. With a hybrid combination of high performance computing and quantum approaches. Three sectors stand out: Pharma, Life & Material Sciences: Drug discovery is essentially a molecular simulation challenge. Classical systems approximate. Quantum systems are designed around quantum mechanics itself. Thus, it is not just about faster research, but the ability to model molecular interactions with higher fidelity. For protein folding, compound optimization, personalized therapeutics. Reaching quantum advantage first in pharma won’t merely accelerate pipelines — it will redefine them. Financial Services: Banks, insurers, stock exchanges operate enormous optimization, transaction or probability engines. E.g., for risk simulations, or fraud detections. Many of these problems scale exponentially in complexity. Quantum algorithms are particularly promising where classical Monte Carlo simulations hit practical limits. And, quantum computing is becoming a cybersecurity challenge. Post-quantum cryptography migration will likely be one of the largest infrastructure transitions the financial sector has seen for decades. Complex Logistics & Supply Chains: Airlines, shipping companies, manufacturers, energy grids, and global retailers all face combinatorial optimization problems. These systems already operate at scales where small efficiency gains create major business impact. Enterprises operating in these segments should get „quantum-ready“ now: • Identify quantum-relevant business problems • Work with quantum partners who advocate an open approach • Build internal quantum literacy • Develop hybrid workflows • Prepare your security stack for the post-quantum era. Additionally we need quantum computing companies delivering at production scale. IQM Quantum Computers calls this Production Quantum. Which is the delivery of a production-ready full stack solution rather than just a scientific solution for a specific problem. This is the same pattern we saw with #AI. The competitive gap formed before the technology fully matured. #Quantum readiness is becoming a strategic capability and critical timing question. For an increasing number of enterprises. Not only for R&D departments.

Can quantum computing revolutionize computational mechanics? In our paper "Towards Quantum Computational Mechanics", we introduce a PDE solver that achieves exponential speedup, reducing the complexity of representative volume element (RVE) computations from O(Nᶜ) in classical computing to O((log N)ᶜ). This exponential acceleration over classical solvers brings concurrent multiscale computing one step closer to practicality. https://lnkd.in/ebxTBG4Z Our research, recently accepted in Computer Methods in Applied Mechanics and Engineering, is a joint effort by Burigede Liu, Michael Ortiz, and myself.

Excited to announce a new #QuantumComputing result from JPMorganChase's Global Technology Applied Research, titled “Fast Convex Optimization with Quantum Gradient Descent,” which has just appeared on arXiv! Convex #optimization is a fundamental subroutine in #MachineLearning, engineering, and #DataScience, with many applications in financial engineering. We develop new #QuantumAlgorithms in the “derivative-free” setting where the algorithm only uses the function value and not its gradient. We show that #quantum algorithms without gradient access can match the convergence of classical gradient-descent methods, which do assume gradient access! In the derivative-free setting, this translates to an exponential speedup in terms of the dimension.   Our results also have applications outside the black-box setting. By leveraging a connection between semi-definite programming and eigenvalue optimization, we develop algorithms that exhibit the best known quantum or classical runtimes for semi-definite programming, linear programming, and zero-sum games, which are the three most well-studied classes of structured convex optimization problems. These classes model many practical problems of interest, including portfolio optimization and least-squares regression problems. Coauthors: Brandon Augustino, Dylan Herman, Enrico Fontana, Junhyung Lyle Kim, Jacob Watkins, Shouvanik Chakrabarti, and Marco Pistoia. Link to the article: https://lnkd.in/eMtqXM-r

Real use-case, real-data set, real quantum computer! We published a white paper together with Deutsche Bahn, assigning trains to scheduled services in a way that minimizes operational cost while satisfying a range of hard constraints. Using a real operational dataset from Deutsche Bahn, a schedule of 190 trips across five German cities translating into roughly 98,500 possible cycles, IQM Quantum Computers and DB developed and tested a hybrid quantum-classical algorithm designed for enterprise-scale optimization problems. There are two reasons why I like this use-case: 1) It is a recurring use-case: trains are running on a daily schedule with changing boundary conditions. Meaning the optimization task is not going to go away. This is different from, for example, molecular simulations, where you run the simulation once until you have the desired outcome. 2) It benefits the broader society: running critical infrastructure like a national train system in an efficient way impacts a large group of people. It is important to showcase that a new technology like quantum computing is not only relevant for a small group of experts but will have wider impact on society. Thanks Manfred Rieck, Martin Leib, Jiri Guth Jarkovsky and teams for this nice collaboration! Press release: https://iqm.tech/press-releases/iqm-and-deutsche-bahn-demonstrate-quantum-algorithm-for-railway-scheduling-on-real-operational-data/ Scientific paper: https://arxiv.org/pdf/2606.11383 White paper: https://iqm.tech/wp-content/uploads/2026/07/IQM-DB-RailwayOptimization-Whitepaper.pdf Inés De Vega Dimitrios P. Sylwia Barthel de Weydenthal Craig Ciesla Soren Hein Juha Vartiainen Tomi Riipinen Juha Hassel Jan Kuerschner Blair Robertson Mark Falcon Pasi Kivinen

We have started to use quantum computing to solve real engineering problems, especially for optimization, if you map the problem into a Quadratic unconstrained binary optimization (QUBO) formula (basically an Ising model). However, QUBO only includes 2nd-order interactions, limiting its ability to express complex optimization landscapes. Collaborating with Sanghyo Hwang, Prof. Eungkyu Lee from Kyung Hee University, and Dr. Seongmin Kim from Oak Ridge National Lab, we developed a 3rd-order model for higher-order binary optimization (HOBO) problems. https://rdcu.be/eKcgB

Our R&D team at Stellium Inc. has recently been diving deep into concepts like quantum machine learning and quantum PCA, with the goal of identifying the best levers out there to address supply chain challenges with emerging tech. After our most recent midmonth Innov8 workshop, I’m no longer surprised by the fact that the market size for quantum computing is projected to grow at a CAGR of 18+% during the forecast period 2025-2032. The modern supply chain, as we all know, forms a sophisticated network of interconnected elements, where decision-making amid complexity often involves significant uncertainty. Effective management hinges on processing vast streams of real-time data to minimize costs and fulfill customer demands. As these global systems expand, classical computing approaches are reaching their limits in processing speed and handling intricate modeling. Enter Quantum Computing: 🎱 Quantum solutions are exceptionally positioned to tackle the most demanding challenges in logistics, including route optimization, operational efficiency, and emissions reduction. This capability stems from foundational quantum mechanics principles such as Superposition, Interference and Entanglement, that are redefining computational processes. For supply chain executives, this really boils down to resolving complex problems more rapidly than classical algorithms, including those on supercomputers. The aim is to develop responsive analytics through dramatically reduced computation times. Large scale supply chain optimization problems are no longer going to need hrs or days but rather seconds. Industry researchers and a few enterprises are already applying techniques such as the Quantum Approximate Optimization Algorithm (QAOA) and Quantum Annealing. These methods reformulate combinatorial challenges, like the traveling salesman problem in transportation logistics into quantum frameworks, identifying optimal solutions by reaching the ‘minimum energy state’. We are now seeing progress beyond conceptual stages to practical Proofs of Concept (PoCs): • BMW Group applied recursive QAOA to address partitioning issues in supply chain resource allocation. • Volkswagen demonstrated real-time optimal routing through urban traffic variations. • Coca-Cola Bottlers Japan Inc. utilized quantum computing to refine their logistics for a network exceeding 700,000 vending machines. Quantum-powered logistics and supply chain innovations are poised for substantial growth in the years ahead. Forward-thinking organizations recognize the impending transformation and are proactively preparing to become quantum-ready. At Stellium Inc., we are in our early R&D stage when it comes to exploring quantum use cases and strategic partnerships. I am bullish about the impact it’s going to have on supply chain and recognize the need to invest in it right now. DM if you’re interested to discuss more over coffee at Dubai this coming week or at SAP Connect early October in Vegas.