Quantum Mechanics Applications in Algorithm Development

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

"Researchers from USC and Johns Hopkins used two IBM Eagle quantum processors to pull off an unconditional, exponential speedup on a classic “guess-the-pattern” puzzle, proving—without assumptions—that quantum machines can now outpace the best classical computers." "What makes a speedup “unconditional,” Lidar explains, is that it doesn’t rely on any unproven assumptions. Prior speedup claims required the assumption that there is no better classical algorithm against which to benchmark the quantum algorithm. Here, the team led by Lidar used an algorithm they modified for the quantum computer to solve a variation of “Simon’s problem,” an early example of quantum algorithms that can, in theory, solve a task exponentially faster than any classical counterpart, unconditionally." https://lnkd.in/ec39PXwv "The goal of demonstrating an algorithmic quantum speedup, i.e., a quantum speedup that scales favorably as the problem size grows, is central to establishing the utility of quantum computers. Simon’s problem is an early example of the Abelian hidden subgroup problem and a precursor to Shor’s factoring algorithm. It requires exponential time to solve on a classical computer but only linear time on a noiseless quantum computer, assuming we count oracle queries but do not account for the actual resources spent on executing the oracle. Here, we studied a modified version of Simon’s problem, which restricts the allowed Hamming weight of the hidden bitstring to 𝑤 ≤𝑛. The classical solution of this version scales as 𝑛𝑤/2. Our goal was to determine whether NISQ devices are capable of providing an algorithmic quantum speedup in solving this version of Simon’s problem. We ran restricted-HW Simon’s algorithm demonstrations on the IBM Quantum platform and demonstrated that two 127-qubit devices, Sherbrooke and Brisbane, exhibited an exponential algorithmic quantum speedup, which extended to larger HW values when we incorporated suitably optimized DD protection." DOI: 10.1103/PhysRevX.15.021082

Many of you will have seen the news about HSBC’s world-first application of quantum computing in algorithmic bond trading. Today, I’d like to highlight the technical paper that explains the research behind this milestone. In collaboration with IBM, our teams investigated how quantum feature maps can enhance statistical learning methods for predicting the likelihood that a trade is filled at a quoted price in the European corporate bond market. Using production-scale, real trading data, we ran quantum circuits on IBM quantum computers to generate transformed data representations. These were then used as inputs to established models including logistic regression, gradient boosting, random forest, and neural networks. The results: • Up to 34% improvement in predictive performance over classical baselines. • Demonstrated on real, production-scale trading data, not synthetic datasets. • Evidence that quantum-enhanced feature representations can capture complex market patterns beyond those typically learned by classical-only methods. This marks the first known application of quantum-enhanced statistical learning in algorithmic trading. For full technical details please see our published paper: 📄 Technical paper: https://lnkd.in/eKBqs3Y7 📰 Press release: https://lnkd.in/euMRbbJG Congratulations to Philip Intallura Ph.D , Joshua Freeland Freeland and all HSBC colleagues involved — and huge thanks to IBM for their partnership.

A new paper, now published in Nature Computational Science, introduces "Quantum Approximate Multi-Objective Optimization," a breakthrough from researchers at IBM, Los Alamos National Laboratory, and Zuse Institute Berlin. This work represents one of the most promising proposals for near-term demonstrations of quantum advantage in combinatorial optimization, with enormous relevance across industry and science: https://lnkd.in/ew7Pe2K5 Multi-objective optimization is a branch of mathematical optimization that deals with problems involving multiple often conflicting goals—e.g., constructing financial portfolios that minimize risk while maximizing returns. These problems can be extremely challenging for classical methods as the number of objective functions increases, even in cases where the single-objective version of the problem is easily solvable. The study demonstrates how quantum computers can approximate the optimal Pareto front, i.e., the set of all optimal trade-offs between conflicting objectives, showing better scaling than classical algorithms. Sampling good solutions from vast solution spaces is a task at which quantum computers excel, and the researchers take full advantage of that in their work. This marks an important step toward practical quantum advantage in optimization, and shows the value of exploring quantum capabilities beyond conventional problem classes. The paper is the latest outcome from our quantum optimization technical working group, and I encourage you to have a look.

Introducing a Novel Quantum Sampling based Hybrid algorithm for #Peer2Peer Energy trading In our recent preprint “Boosting Sparsity in Graph Decompositions with QAOA Sampling” together with STFC Hartree Centre and IBM Quantum, we developed an algorithm that aims to leverage a quantum computers solution variety as an advantage, rather than a hinderance. Mathematically, we studied the problem of decomposing a graph into a weighted sum of a small number of graph matchings. This problem is called the #MinimumBirkhoffDecomposition, and is known to be extremely hard classically, even for small instances. In fact, it is one of the 10 problems presented in the companion paper “Quantum Optimization Benchmarking Library: The Intractable Decathlon” (👉 https://lnkd.in/dU3EC5M9). This is one of the underlying #mathproblems for decentralized peer-2-peer energy auctioning algorithms. We show that: - The algorithm works at #utilityscale where we experimentally demonstrated it using up to 111 qubits - Most interestingly, for large heavy-hex graphs with 50 and 70 nodes, our approach also #outperforms the best classical heuristics in terms of approximation error. - Inching towards #quantumadvantage: MPS simulation of our algorithm provides the best overall performance (up to the 76 qubit case we could run), yet our hardware results are quite close at utility scale. This work marks an important step towards #samplingbased optimization solvers and demonstrates the value of collaboration as it was a spinoff project of the IBM Quantum Optimization Working Group. ❗️Paper link here 👉 https://lnkd.in/dVJmvE-g Thanks to all the wonderful collaborators and looking forward to the next steps on this one! George Pennington Naeimeh Mohseni Oscar Wallis, Francesca Schiavello, Stefano Mensa, PhD MBCS, Giorgio Cortiana, Víctor Valls E.ON Digital Technology E.ON #quantumcomputing #quantumoptimization

Quantum whispers in the GPU roar For Wall Street, more AI means more GPUs, more datacenters, more cloud contracts. And OpenAI–NVIDIA $100B deal locks it in. But quieter signals from research point to a second axis of scaling: not just more metal, but smarter math. It’s about quantum. Let me give you some notable examples from the last week research: 1. Compression: QKANs and quantum activation functions Paper: Quantum Variational Activation Functions Empower Kolmogorov-Arnold Networks Offers replacing fixed nonlinearities with single-qubit variational circuits (DARUANs). These tiny activations generate exponentially richer frequency spectra → so we get same power with exponentially fewer parameters. Quantum KANs (QKANs), built on this idea, already outperformed MLPs and KANs with 30% fewer parameters. 2. Exactness: Coset sampling for lattice algorithms Paper: Exact Coset Sampling for Quantum Lattice Algorithms Proposes a subroutine that cancels unknown offsets and produces exact, uniform cosets, making subsequent Fourier sampling provably correct. Injecting mathematically guaranteed steps into probabilistic workflows means precision: fewer wasted tokens, fewer dead-end paths, less variance in cost per query. 3. Hybridization: quantum-classical models in practice Paper: Hybrid Quantum-Classical Model for Image Classification These models dropped small quantum layers into classical CNNs, showing that they can train faster and use fewer parameters than classical versions. ▪️ What does this mean for inference scaling? Scaling won’t only mean bigger clusters for bigger models. It might also be about: - extracting more from each parameter - cutting errors at the source - and blending quantum and classical strengths. Notably, this direction is not lost on the companies like NVIDIA. There are several signs: • NVIDIA's CUDA-Q – an open software platform for hybrid quantum-classical programming. • NVIDIA also launched DGX Quantum, a reference architecture linking quantum control systems directly into AI supercomputers.  • They are opening a dedicated quantum research center with hardware partners. • Jensen Huang is aggressively investing into quantum startups like PsiQuantum (just raised $1B, saying it’s computer will be ready in two years), Quantinuum, and QuEra through NVentures - a major strategic shift in 2025, validating quantum's commercial timeline. ▪️ So what we will see:  GPUs will remain central. But quantum ideas will be slipping into the story of inference scaling. They are still early, but it's the new axis worth paying attention to. What do you think about it?

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.