How Quantum Algorithms Address Real-World Challenges

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

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

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.

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

Everybody’s asking about the 𝗸𝗶𝗹𝗹𝗲𝗿 𝗮𝗽𝗽 𝗳𝗼𝗿 𝗾𝘂𝗮𝗻𝘁𝘂𝗺 𝗰𝗼𝗺𝗽𝘂𝘁𝗲𝗿𝘀. But when a team actually uses one to explore 𝗳𝘂𝗻𝗱𝗮𝗺𝗲𝗻𝘁𝗮𝗹 𝗽𝗵𝘆𝘀𝗶𝗰𝘀 in a way we couldn't before, the 𝘀𝗶𝗹𝗲𝗻𝗰𝗲 from the broader community is deafening. Really? I’ve talked about using quantum computers for exploring physics before. I get it - 𝗶𝘁'𝘀 𝗻𝗼𝘁 𝘁𝗵𝗲 𝗶𝗺𝗺𝗲𝗱𝗶𝗮𝘁𝗲, 𝗱𝗶𝘀𝗿𝘂𝗽𝘁𝗶𝘃𝗲 𝗮𝗽𝗽𝗹𝗶𝗰𝗮𝘁𝗶𝗼𝗻 𝘁𝗵𝗮𝘁 𝗩𝗖𝘀 𝗮𝗻𝗱 𝗺𝗮𝗿𝗸𝗲𝘁 𝗮𝗻𝗮𝗹𝘆𝘀𝘁𝘀 𝘄𝗮𝗻𝘁 𝘁𝗼 𝗵𝗲𝗮𝗿 𝗮𝗯𝗼𝘂𝘁. 𝗕𝘂𝘁 𝗜 𝗳𝗶𝗻𝗱 𝗶𝘁 𝗮𝗯𝘀𝗼𝗹𝘂𝘁𝗲𝗹𝘆 𝗮𝗺𝗮𝘇𝗶𝗻𝗴 𝘁𝗵𝗮𝘁 𝘄𝗲'𝗿𝗲 𝗳𝗶𝗻𝗮𝗹𝗹𝘆 𝗯𝘂𝗶𝗹𝗱𝗶𝗻𝗴 𝘁𝗼𝗼𝗹𝘀 𝘁𝗵𝗮𝘁 𝗮𝗹𝗹𝗼𝘄 𝘂𝘀 𝘁𝗼 𝘂𝗻𝗱𝗲𝗿𝘀𝘁𝗮𝗻𝗱 𝗼𝘂𝗿 𝘄𝗼𝗿𝗹𝗱 𝗼𝗻𝗲 𝗹𝗮𝘆𝗲𝗿 𝗱𝗲𝗲𝗽𝗲𝗿. A new paper from Google 𝗤𝘂𝗮𝗻𝘁𝘂𝗺 𝗔𝗜 & 𝗰𝗼𝗹𝗹𝗮𝗯𝗼𝗿𝗮𝘁𝗼𝗿𝘀, is a perfect case in point. The team tackled a monster of a problem in condensed matter physics: 𝗵𝗼𝘄 𝘁𝗼 𝘀𝗶𝗺𝘂𝗹𝗮𝘁𝗲 𝘀𝘆𝘀𝘁𝗲𝗺𝘀 𝘄𝗶𝘁𝗵 𝗱𝗶𝘀𝗼𝗿𝗱𝗲𝗿. Classically, this is a brute-force nightmare: You have to simulate thousands or even millions of different disorder configurations one by one, which can take an exponential amount of time. 𝗜𝗻𝘀𝘁𝗲𝗮𝗱 𝗼𝗳 𝘀𝗶𝗺𝘂𝗹𝗮𝘁𝗶𝗻𝗴 𝗼𝗻𝗲 𝗰𝗼𝗻𝗳𝗶𝗴𝘂𝗿𝗮𝘁𝗶𝗼𝗻 𝗮𝘁 𝗮 𝘁𝗶𝗺𝗲, 𝗚𝗼𝗼𝗴𝗹𝗲 𝘂𝘀𝗲𝗱 𝘁𝗵𝗲𝗶𝗿 𝟴𝟭-𝗾𝘂𝗯𝗶𝘁 𝗾𝘂𝗮𝗻𝘁𝘂𝗺 𝗽𝗿𝗼𝗰𝗲𝘀𝘀𝗼𝗿 𝘁𝗼 𝗽𝗿𝗲𝗽𝗮𝗿𝗲 𝗮 𝘀𝘁𝗮𝘁𝗲 𝘁𝗵𝗮𝘁 𝗶𝘀 𝗮 𝘀𝘂𝗽𝗲𝗿𝗽𝗼𝘀𝗶𝘁𝗶𝗼𝗻 𝗼𝗳 𝗮𝗹𝗹 𝗽𝗼𝘀𝘀𝗶𝗯𝗹𝗲 𝗱𝗶𝘀𝗼𝗿𝗱𝗲𝗿 𝗰𝗼𝗻𝗳𝗶𝗴𝘂𝗿𝗮𝘁𝗶𝗼𝗻𝘀. Then they gave it a tiny kick of energy in one spot, and watched what happened. The result? The energy stayed put. It refused to spread. This is a phenomenon called 𝗗𝗶𝘀𝗼𝗿𝗱𝗲𝗿-𝗙𝗿𝗲𝗲 𝗟𝗼𝗰𝗮𝗹𝗶𝘇𝗮𝘁𝗶𝗼𝗻 (𝗗𝗙𝗟). Even though the system's evolution and the initial state were perfectly uniform and disorder-free, the underlying superposition over different "backgrounds" caused the system to localize. 𝗜𝘁’𝘀 𝗮 𝘀𝘁𝘂𝗻𝗻𝗶𝗻𝗴 𝗱𝗲𝗺𝗼𝗻𝘀𝘁𝗿𝗮𝘁𝗶𝗼𝗻 𝗼𝗳 𝗾𝘂𝗮𝗻𝘁𝘂𝗺 𝗺𝗲𝗰𝗵𝗮𝗻𝗶𝗰𝘀 𝗮𝘁 𝘄𝗼𝗿𝗸 𝗼𝗻 𝗮 𝘀𝗰𝗮𝗹𝗲 𝘁𝗵𝗮𝘁’𝘀 𝗶𝗻𝗰𝗿𝗲𝗱𝗶𝗯𝗹𝘆 𝗱𝗶𝗳𝗳𝗶𝗰𝘂𝗹𝘁 𝗳𝗼𝗿 𝗰𝗹𝗮𝘀𝘀𝗶𝗰𝗮𝗹 𝗰𝗼𝗺𝗽𝘂𝘁𝗲𝗿𝘀 𝘁𝗼 𝗵𝗮𝗻𝗱𝗹𝗲, 𝗲𝘀𝗽𝗲𝗰𝗶𝗮𝗹𝗹𝘆 𝗶𝗻 𝟮𝗗. But this isn't just a cool physics experiment. This work carves out a concrete path to quantum advantage. The team proposed an 𝗮𝗹𝗴𝗼𝗿𝗶𝘁𝗵𝗺 based on this technique that offers a 𝗽𝗼𝗹𝘆𝗻𝗼𝗺𝗶𝗮𝗹 𝘀𝗽𝗲𝗲𝗱𝘂𝗽 𝗳𝗼𝗿 𝘀𝗮𝗺𝗽𝗹𝗶𝗻𝗴 𝗱𝗶𝘀𝗼𝗿𝗱𝗲𝗿𝗲𝗱 𝘀𝘆𝘀𝘁𝗲𝗺𝘀. So yes, let's keep working toward fault-tolerant machines that can break RSA and optimize your portfolio. But let's not ignore the incredible science happening right now. 📸 Credits: Google 𝗤𝘂𝗮𝗻𝘁𝘂𝗺 𝗔𝗜 & 𝗖𝗼𝗹𝗹𝗮𝗯𝗼𝗿𝗮𝘁𝗼𝗿𝘀 (arXiv:2410.06557) Pedram Roushan

Is this the first real-world use case for quantum computers? True randomness is hard to come by. And in a world where cryptography and fairness rely on it, “close enough” just doesn’t cut it. A new paper in Nature claims to present a demonstrated, certified application of quantum computing, not in theory or simulation, but in the real world. Led by Quantinuum, JPMorganChase, Argonne National Laboratory, Oak Ridge National Laboratory, and The University of Texas at Austin, the team successfully ran a certified randomness expansion protocol on Quantinuum’s 56-qubit H2 quantum computer, and validated the results using over 1.1 exaflops of classical computing power. TL;DR is certified randomness--the kind of true, verifiable unpredictability that’s essential to cryptography and security--was generated by a quantum computer and validated by the world’s fastest supercomputers. Here’s why that matters: True randomness is anything but trivial. Classical systems can simulate randomness, but they’re still deterministic at the core. And for high-stakes environments such as finance, national security, or fairness in elections, you don’t want pseudo-anything. You want cold, hard entropy that no adversary can predict or reproduce. Quantum mechanics is probabilistic by nature. But just generating randomness with a quantum system isn’t enough; you need to certify that it’s truly random and not spoofed. That’s where this experiment comes in. Using a method called random circuit sampling, the team: ⚇ sent quantum circuits to Quantinuum’s 56-qubit H2 processor, ⚇ had it return outputs fast enough to make classical simulation infeasible, ⚇ verified the randomness mathematically using the Frontier supercomputer ⚇ while the quantum device accessed remotely, proving a future where secure, certifiable entropy doesn’t require trusting the hardware in front of you The result? Over 71,000 certifiably random bits generated in a way that proves they couldn’t have come from a classical machine. And it’s commercially viable. Certified randomness may sound niche—but it’s highly relevant to modern cryptography. This could be the start of the earliest true “quantum advantage” that actually matters in practice. And later this year, Quantinuum plans to make it a product. It’s a shift— from demos to deployment from supremacy claims to measurable utility from the theoretical to the trustworthy read more from Matt Swayne at The Quantum Insider here --> https://lnkd.in/gdkGMVRb peer-reviewed paper --> https://lnkd.in/g96FK7ip #QuantumComputing #CertifiedRandomness #Cryptography

10 million containers. Thousands of trucks. Hundreds of cranes. One impossible scheduling problem. Welcome to the Port of Los Angeles—the largest container port in the US and a critical node in global supply chains. The bottleneck: Every day, Pier 300 (one of the port's largest terminals) faces a computational nightmare: - Which truck goes to which crane? - When do arrivals shift due to delays? - How do you balance load across equipment? - What happens when conditions change every few minutes? Classical scheduling systems couldn't keep up: ⏱️ Long truck wait times (sometimes 2+ hours) 🏗️ Inefficient crane utilization 📉 Reduced throughput during peak periods 💰 Millions in lost productivity Then they deployed quantum optimization. Working with quantum computers, Pier 300 built a system that: 🔬 Simulates 100,000+ cargo-handling scenarios 🎯 Optimizes truck-to-crane assignments in real-time 🔄 Updates every few minutes across two daily shifts ⚡ Runs with 99.999% availability The results: ✅ ~40% reduction in crane usage → Lower labor and equipment costs ✅ ~60% increase in container deliveries per crane → Massive productivity gain ✅ 10 minutes reduced per truck visit → Up to 2 hours in some cases ✅ Tens of millions in annual savings → Plus increased terminal asset value Why this matters: This isn't theory. This is a working terminal processing millions of containers with measurable, bottom-line impact. The shift: From "schedule and hope" to "optimize continuously." Classical algorithms could generate a schedule. Quantum systems generate the optimal schedule—and update it dynamically as reality changes. The insight for supply chain leaders: Port operations are some of the most complex scheduling challenges on the planet. If quantum optimization can handle this, what could it do for your: 📦 Warehouse operations? 🚚 Fleet routing? 📊 Inventory allocation? 🏭 Production scheduling? The computational barrier just fell. The logistics advantage is here. Question: What's the biggest bottleneck in your logistics operations that classical optimization can't crack? #QuantumComputing #Truckl #SupplyChain #Transportation #Innovation

At the intersection of AI and the real world -- can we solve some of science's greatest problems? Ever wondered how quantum computing could revolutionize our understanding of complex systems? Well, this article dives into how quantum computers can significantly speed up simulations compared to classical computers, especially when dealing with coupled classical oscillators (think of them as swinging pendulums that affect each other's movement -- and which can be used to solve all kinds of physics problems). In simple terms, while traditional computers might take longer to calculate how these pendulums interact as their number increases, a quantum computer can do this much faster—achieving what's called an "exponential speedup." This means that as the problem grows bigger (more pendulums), the advantage of using quantum computers grows dramatically. The researchers, including experts from Google Quantum AI and several universities, demonstrate a theoretical framework where quantum algorithms outperform their classical counterparts. They provide a method that could be practically implemented on quantum devices in the near future, paving the way for more efficient simulations in physics, engineering, and beyond. This breakthrough not only highlights the potential of quantum computing to solve specific technical challenges but also gets us closer to realizing practical applications that were once thought to be decades away. It's an exciting peek into a future where quantum computing could become a key tool in scientific research and innovation. https://lnkd.in/gFmW8bEX

Quantum computing may still be in its early stages, but its ability to simulate molecular behavior so precisely is already making traditional trial-and-error approaches in drug and material research feel increasingly outdated. Quantum computing offers a radically different way to approach complex scientific challenges, particularly in chemistry and pharmaceuticals. By using qubits to process multiple possibilities simultaneously, researchers can simulate how molecules interact without relying on expensive and time-consuming lab experiments. This can accelerate drug discovery, enabling identification of viable compounds earlier in the development process. In materials science, it can guide the design of new alloys or polymers with tailored properties. However, current hardware and algorithm limitations mean that companies must still invest carefully and prepare for a long-term integration strategy. #QuantumComputing #DrugDiscovery #MaterialsScience #PharmaTech #DigitalTransformation

Joint work with Dhrumil Patel and Patrick Coles now published in Quantum - the open journal for quantum science: https://lnkd.in/g7vUGDjn Popular Summary: Many real-world problems in science and industry can be expressed as optimization problems, which involve finding the best solution while meeting specific constraints. Among these, a special class of optimization problems called semidefinite programming holds significance. They are widely used to model or approximate problems arising in various fields such as operations research, combinatorial optimization, control theory, and quantum information theory. For solving these programs, quantum algorithms have been proven to provide a quadratic speedup over classical algorithms. However, these quantum algorithms are not well-suited for current quantum devices, which are noisy and limited in their capabilities. In this work, we propose three quantum algorithms designed to run on these noisy devices. Our algorithms are hybrid quantum-classical algorithms that have a classical computer available for optimization, only calling a quantum computer for tasks that are not efficiently solvable by it. We rigorously analyze the performance of one of our algorithms, quantifying how rapidly it converges to the optimal value. Finally, to demonstrate their practicality, we numerically simulate our quantum algorithms for problems like MaxCut, a prominent graph theoretic problem. Our simulations showcase their effectiveness even in the presence of noise.