Recent Advances in Quantum Optimization

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

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.

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

Let's look at the new paper from IonQ and Airbus researchers exploring practical #quantumcomputing applications in aviation logistics. Their research tackles the aircraft loading optimization problem—selecting and placing cargo containers within operational constraints like maximum payload capacity, center of gravity requirements, and fuselage shear limits. This is computationally demanding, as it's NP-Hard (similar to the knapsack problem) with classical algorithms scaling exponentially as the problem size increases. What makes this paper worth your time: 1. The researchers developed a Multi-Angle Layered Variational Quantum Algorithm (MALVQA) that uses fewer two-qubit gates than standard QAOA approaches, making it viable on current quantum hardware.     2. They implemented a novel cost function handling inequality constraints without introducing slack variables—significantly reducing qubit requirements while maintaining algorithmic effectiveness.     3. Testing on IonQ's Aria and Forte trapped-ion quantum processors demonstrated optimal solutions for problems requiring 12-28 qubits, representing real aircraft loading scenarios with up to 7 containers across 4 cargo positions. The business implications are "directionally promising", as my old boss would say when I was Supply Chain Analyst back at Peabody. We were wrangling coal shipments, not boxes on planes, so this is another order of complexity and really quite fascinating. Efficient aircraft loading directly impacts airline profitability by maximizing revenue-generating payload while minimizing fuel consumption—a primary operating cost and environmental concern. Especially now as global trade gets more... unpredictable. While practical quantum advantage for full-scale commercial operations will require further hardware advances, the research demonstrates progress in exploring quantum computing to meaningful logistics challenges. I appreciated the focus on evolving near-term quantum algorithms in a constrained but critical problem space (versus the "ten septillion years" or "invented new matter" or "calculating in other universes" press releases of late). I've shared the link to the source paper in the comments below (because LinkedIn algo). PS: I wrote more about this on the private list, touching on additional resources, like the previous Airbus explorations (using QUBO and a D-Wave annealer), the Airbus quantum computing challenge the preceded these efforts, the IEEE survey into quantum technology in aerospace, McKinsey's report for IATA on airline value chains, etc. DM me or reply "I want that" and I'll add you.

Excellent paper this morning: "Quantum optimization using a 127-qubit gate-model IBM quantum computer can outperform quantum annealers for nontrivial binary optimization problems" by Natasha Sachdeva, Gavin S. Hartnett, Smarak Maity, Samuel Marsh, Yulun Wang, Adam Winick, Ryan Dougherty, Daniel Canuto, You Quan Chong, Michael Hush, Pranav S. Mundada, Christopher D. B. Bentley, Michael J. Biercuk, and Yuval Baum the Q-CTRL team Abtrstect: We introduce a comprehensive quantum solver for binary combinatorial optimization problems on gate-model quantum computers that outperforms any published alternative and consistently delivers correct solutions for problems with up to 127 qubits. We provide an overview of the internal workflow, describing the integration of a customized ansatz and variational parameter update strategy, efficient error suppression in hardware execution, and overhead-free post-processing to correct for bit-flip errors. We benchmark this solver on IBM quantum computers for several classically nontrivial unconstrained binary optimization problems -- the entire optimization is conducted on hardware with no use of classical simulation or prior knowledge of the solution. First, we demonstrate the ability to correctly solve Max-Cut instances for random regular graphs with a variety of densities using up to 120 qubits, where the graph topologies are not matched to device connectivity. Next, we apply the solver to higher-order binary optimization and successfully search for the ground state energy of a 127-qubit spin-glass model with linear, quadratic, and cubic interaction terms. Use of this new quantum solver increases the likelihood of finding the minimum energy by up to ∼1,500×  relative to published results using a DWave annealer, and it can find the correct solution when the annealer fails. Furthermore, for both problem types, the Q-CTRL solver outperforms a heuristic local solver used to indicate the relative difficulty of the problems pursued. Overall, these results represent the largest quantum optimizations successfully solved on hardware to date, and demonstrate the first time a gate-model quantum computer has been able to outperform an annealer for a class of binary optimization problems. Link: https://lnkd.in/eHeEK8MT #quantummachinelearning #research #quantumcomputing

Conventional wisdom suggests that the Quantum Approximate Optimization Algorithm (QAOA) and quantum annealing differ fundamentally, especially when QAOA uses angles that do not vanish with problem size. In our new work (led by Sami Boulebnane), we rigorously show that, for certain “constant‐angle” schedules, QAOA does replicate linear‐time quantum annealing behavior—precisely in the regime where QAOA achieves its best performance. • We prove this equivalence for the Sherrington‐Kirkpatrick (SK) model, a classical spin‐glass benchmark, and provide evidence that the same reasoning may extend to other constrained optimization problems. • Because QAOA can approximate annealing without tiny Trotter steps, we reduce the required circuit depth by a factor linear in the number of variables. • Our analysis employs a novel series expansion for QAOA observables at arbitrary depth, providing new tools to study how QAOA scales. Special thanks to the great team: Sami Boulebnane, James Sud, and Marco Pistoia. Link: https://lnkd.in/eBfCrffj

⚛️ 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

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 computing for financial mathematics A key paper published in 2023 by Jack Jacquier, Oleksiy Kondratyev, Gordon Lee, and Mugad Oumgari reviews the state of quantum computing in financial mathematics and leaves a clear message: the value is not in waiting for the perfect machine, but in how we manage the transition with what we already have. Three application lines highlighted by the authors - Portfolio optimization with variational algorithms (QAOA, VQE), where hybrid approaches already help explore scenarios that scale poorly in the classical world. - Quantum Machine Learning, with generative and discriminative models (QGANs, QNNs, Quantum Circuit Born Machines) applied to market data generation, credit scoring, and detection of distribution shifts. - Quantum Monte Carlo, with algorithms achieving a quadratic speedup in expectation estimation, useful for high-dimensional derivative pricing. Other areas mentioned The paper also points to the potential of Quantum Semidefinite Programming (QSDP) for robust risk management and portfolio optimization under uncertainty. The key takeaway The authors emphasize: it’s not just about speed, it’s about thinking differently. - Use quantum algorithms to accelerate critical steps of classical pipelines. - Develop hybrid and quantum-inspired schemes. - Prepare data structures and methodologies that can scale once hardware matures. Ultimately: the real race lies in turning current limitations into opportunities for integration and new value models, while technological acceleration follows its own path. Link https://lnkd.in/d-CPDkN9 Imperial College London Abu Dhabi Investment Authority (ADIA) Lloyds Banking Group

QUANTUM INFORMATION GEOMETRY: QUANTUM NATURAL GRADIENT Review of Quantum Gradient Descent Algorithm and its use in different Quantum Optimization Algorithms Sangram Deshpande https://lnkd.in/eJ9WVNcu Abstract This review explores the quantum gradient descent algorithm, highlighting its distinctive advantages over classical gradient descent methods. Unlike the classical approach, which requires O(n) complexity for gradient computation, the quantum version achieves a remarkable complexity of O(1) through the principles of quantum superposition and entanglement. A particular focus is given to the Variational Quantum Eigensolver (VQE), a hybrid quantum-classical framework that utilizes parameterized quantum circuits combined with classical optimization routines. By replacing the classical optimizer with a quantum gradient descent optimizer, significant performance enhancements are realized, including faster convergence and reduced resource requirements. This work examines the implementation of quantum gradient methods within the VQE algorithm and emphasizes their potential to revolutionize optimization in quantum computing by providing exponential advantages in specific applications. The findings underscore the transformative role of quantum algorithms in advancing computational efficiency for complex optimization tasks.