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

Lockheed and IBM Use Quantum Computing to Solve Chemistry Puzzle Once Thought Impossible Introduction: Cracking a Chemical Code with Quantum Power In a breakthrough for quantum chemistry, Lockheed Martin and IBM have successfully used quantum computing to model the complex electronic structure of an “open-shell” molecule—a challenge that has defied classical computing for years. This marks the first application of the sample-based quantum diagonalization (SQD) method to such systems and signals a significant advance in the practical application of quantum computing for scientific research. Key Highlights from the Collaboration • The Molecule: Methylene (CH₂): • Methylene is an open-shell molecule, meaning it has unpaired electrons that lead to complex quantum behavior. • These molecules are notoriously difficult to simulate accurately because electron correlations create exponentially growing complexity for classical algorithms. • The Innovation: Sample-Based Quantum Diagonalization (SQD): • The team used IBM’s quantum processor to implement SQD for the first time in an open-shell system. • SQD is a hybrid algorithm that leverages quantum sampling to solve eigenvalue problems in quantum chemistry, reducing computational burdens. • Why Classical Methods Fall Short: • Traditional high-performance computing (HPC) platforms struggle with electron correlation in multi-electron systems. • Approximation techniques become prohibitively expensive as system size increases, especially for reactive or radical species like methylene. • Quantum Advantage in Practice: • Quantum processors can represent electron configurations using entangled qubits, offering more scalable solutions. • By simulating the electronic structure directly, quantum methods could help scientists design new materials, catalysts, and pharmaceuticals faster and more efficiently. Why It Matters: Pushing Past the Limits of Classical Chemistry • Industrial and Scientific Impact: • Simulating open-shell systems is vital for battery design, combustion processes, and metalloprotein modeling. • The success of SQD opens the door to accurate modeling of previously inaccessible molecules, potentially accelerating innovations in energy, health, and aerospace. • Defense and Aerospace Relevance: • Lockheed Martin’s involvement reflects strategic interest in applying quantum computing to defense-grade materials and mission-critical chemistry. • Quantum Chemistry as a Flagship Use Case: • This achievement underscores how quantum computing is beginning to deliver real results in scientific domains where classical methods hit their ceiling. • As quantum hardware improves, the number of solvable molecular systems will expand exponentially. Quantum computing just helped humanity take a critical step into the chemical unknown, proving its value not just in theory—but in practice. Keith King https://lnkd.in/gHPvUttw

⚛️ 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

This image is from an Amazon Braket slide deck that just did the rounds of all the Deep Tech conferences I've been at recently (this one from Eric Kessler). It's more profound than it might seem. As technical leaders, we're constantly evaluating how emerging technologies will reshape our computational strategies. Quantum computing is prominent in these discussions, but clarity on its practical integration is... emerging. It's becoming clear however that the path forward isn't about quantum versus classical, but how quantum and classical work together. This will be a core theme for the year ahead. As someone now on the implementation partner side of this work, and getting the chance to work on specific implementations of quantum-classical hybrid workloads, I think of it this way: Quantum Processing Units (QPUs) are specialised engines capable of tackling calculations that are currently intractable for even the largest supercomputers. That's the "quantum 101" explanation you've heard over and over. However, missing from that usual story, is that they require significant classical infrastructure for: - Control and calibration - Data preparation and readout - Error mitigation and correction frameworks - Executing the parts of algorithms not suited for quantum speedup Therefore, the near-to-medium term future involves integrating QPUs as accelerators within a broader classical computing environment. Much like GPUs accelerate specific AI/graphics tasks alongside CPUs, QPUs are a promising resource to accelerate specific quantum-suited operations within larger applications. What does this mean for technical decision-makers? Focus on Integration: Strategic planning should center on identifying how and where quantum capabilities can be integrated into existing or future HPC workflows, not on replacing them entirely. Identify Target Problems: The key is pinpointing high-value business or research problems where the unique capabilities of quantum computation could provide a substantial advantage. Prepare for Hybrid Architectures: Consider architectures and software platforms designed explicitly to manage these complex hybrid workflows efficiently. PS: Some companies like Quantum Brilliance are focused on this space from the hardware side from the outset, working with Pawsey Supercomputing Research Centre and Oak Ridge National Laboratory. On the software side there's the likes of Q-CTRL, Classiq Technologies, Haiqu and Strangeworks all tackling the challenge of managing actual workloads (with different levels of abstraction). Speaking to these teams will give you a good feel for topic and approaches. Get to it. #QuantumComputing #HybridComputing #HPC

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

The Schrödinger Equation Gets Practical: Quantum Algorithm Speeds Up Real-World Simulations Quantum computing has taken a major leap forward with a new algorithm designed to simulate coupled harmonic oscillators, systems that model everything from molecular vibrations to bridges and neural networks. By reformulating the dynamics of these oscillators into the Schrödinger equation and applying Hamiltonian simulation methods, researchers have shown that complex physical systems can be simulated exponentially faster on a quantum computer than with traditional algorithms. This breakthrough demonstrates not only a practical use of the Schrödinger equation but also the deep connection between quantum dynamics and classical mechanics. The study introduces two powerful quantum algorithms that reduce the required resources to only about log(N) qubits for N oscillators, compared to the massive computational demands of classical methods. This exponential speedup could transform fields such as engineering, chemistry, neuroscience, and material science, where coupled oscillators serve as the backbone of real-world modeling. By bridging theory and application, this research underscores how quantum computing is redefining problem-solving in physics and beyond. With proven exponential advantages and the ability to simulate systems once thought computationally impossible, this quantum algorithm marks a milestone in quantum simulation, Hamiltonian dynamics, and real-world physics applications. The findings point toward a future where quantum computers can accelerate scientific discovery, optimize engineering designs, and even open new frontiers in AI and computational neuroscience. #QuantumComputing #SchrodingerEquation #HamiltonianSimulation #QuantumAlgorithm #CoupledOscillators #QuantumPhysics #ComputationalScience #Neuroscience #Chemistry #Engineering