Simulating Complex Quantum Systems for Research

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

Today in Science Magazine, work from our IBM team, in collaboration with The University of Manchester, University of Oxford, ETH Zürich, EPFL and the University of Regensburg, shows the creation and simulation of a new molecule with an electronic structure that has never existed before — a half‑Möbius topology: https://lnkd.in/eFU5s9qR. The molecule was assembled using scanning probe microscopy at temperatures just above absolute zero — building it one atom at a time using STM, atom manipulation, and AFM. The electronic orbitals of this half‑Möbius molecule twist by 90 degrees with every loop around the ring, completing a full turn only after four revolutions. Why is this also important for quantum computing? This work demonstrates, for the first time, that quantum computing calculations can provide decisive scientific guidance and powerful characterization capabilities to support the discovery of new complex chemical molecules. In close collaboration with leading experimental laboratories, quantum simulations can now contribute directly to interpreting experimental observations and to guiding the design and understanding of novel molecular systems. The calculations performed in this project go well beyond the regime accessible to brute-force classical simulations, although we do not exclude the possibility that approximate classical methods could also provide valuable insights. Nevertheless, the discovery process itself benefited from quantum simulation, and we chose to employ quantum computing because it offers a natural and scalable framework for tackling problems of this kind. In particular, by comparing Dyson orbitals measured with scanning tunneling microscopy (STM) with images reconstructed from electronic structure calculations performed on a quantum computer using the SqDRIFT algorithm, we were able, for the first time, to contribute directly to the discovery and characterization of a new molecule exhibiting entirely novel electronic structure properties. paper: https://lnkd.in/esg9sHqV

I am very proud of our new paper on simulations of scattering processes in (1+1)-dimensional quantum field theory. All the hard work was done by my co-authors Raghav Jha, Ash Milsted, Dominik Neuenfeld, and Pedro Vieira. https://lnkd.in/gr3rix7K Using tensor network methods, we studied wave-packet collisions in Ising field theory. These pictures depict various processes that occur. Time is on the vertical axis and spatial position is on the horizontal axis. The colors show the energy density relative to the vacuum state. The picture on the left shows an elastic scattering event. The particles emerge from the scattering region with a time delay that reveals information about how the scattering phase shift depends on the energy. The picture in the middle shows elastic scattering with total energy close to the mass of a narrow resonance. A lump of energy density appears, which gradually dissipates as the resonance decays to outgoing particles. By fitting the decay rate of the lump, we can determine the lifetime of the resonance. (Pairs of tracks are seen propagating outward in each direction due to a subtle interference effect that we explain in the paper.) The picture on the right shows a process in which both elastic and inelastic scattering occur. The outgoing tracks capture all of the possible final-state channels, which appear in superposition. Energy-density correlation functions clarify the interpretation of the final state. Seeing processes unfold in real time provides an edifying perspective, complementing the more conventional approach to scattering, which focuses on the relation between asymptotic in and out states rather than the dynamical evolution while the particles are interacting. Aside from generating pretty pictures, we obtain quantitative results that characterize the S-matrix of the theory. It would be instructive to do the same for other field theories in one dimension and beyond. These simulations are done using conventional computers. Someday (I can’t say when), we’ll be able to study more complex processes at higher energy using quantum computers!

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

The battle for quantum advantage just entered a new phase. While analog simulators have been showing incredible results in material modeling lately, a new breakthrough proves that digital (gate-based) quantum computers are not sitting still. A recent paper on arXiv (2603.06325) demonstrates the preparation of a complex 100-qubit Symmetry-Protected Topological (SPT) order on IBM hardware. IBM Quantum The secret? Not just better hardware, but smarter algorithms. They used a technique called Approximate Quantum Compiling (AQC), based on tensor networks, to "compress" deep quantum circuits into shallow ones. This allowed them to capture topological features with high fidelity before noise destroyed the computation. This is a game-changer for digital platforms. It proves that with the right software stack, we can simulate large, complex systems without waiting for fault tolerance. Do you think smart compilation will be the defining factor for practical digital quantum computing in the next 3 years? Let's discuss in the comments. #QuantumComputing #QuantumPhysics #IBMQuantum #DeepTech #MaterialScience #Physics #Innovation

Last week, we shared exciting new results studying operator dynamics on structured circuits designed by our collaborators at Algorithmiq. Our experiments on up to 70 qubit, high-fidelity, heavy-hex layouts, with heuristic error mitigation methods, produced accurate results at short depths that were verified with classical simulation. At larger circuit depths (up to 1872 CZ gates), the circuits were seen to be challenging for Belief propagation-based tensor network methods in the Schrödinger picture, even at fairly large bond dimensions, while the experiments produced data points that were within theoretical bounds. These experiments were enabled, in part, by a 10x reduction in median 2Q error rates from the utility experiment — now at 0.101% in simultaneous operation across the layout! Thanks to our collaborators at Algorithmiq, Simons Foundation Flatiron Institute. We shared these results in the new open community Quantum advantage tracker (https://lnkd.in/eG6Ue3sg), that includes the theoretical background for the experiment, classical simulation and experimental details, run-times, open-source code, etc. This tracks progress towards observable estimation with rigorous error bounds, ground state problems with variational solutions, and problems with efficient classical verification, and also invites proposals for new advantage candidates! Looking forward to sharing upcoming results from experiments and simulations, as they roll in, in this new open "lab notebook". I hope this accelerates the feedback loop between quantum experiments and classical simulation, without boundaries, and ultimately advances the pace of scientific discovery.

Wave-based inverse problems are prevalent in disciplines such as seismology, medical imaging, nondestructive testing and metamaterial research. However, these fields are fundamentally limited by the current state of conventional high-performance computing resources due to the excessive computational cost of the numerical wave simulation. Future quantum computers are expected to offer promising runtime improvements for numerous computational problems.   In this work, led by Cyrill Bösch, Malte Schade, Giacomo Aloisi and Scott Keating, we present a quantum algorithmic framework for simulating linear, anti-Hermitian (lossless) wave equations in heterogeneous, anisotropic media. It encompasses a broad class of wave equations, including the acoustic wave equation, Maxwell’s equations and the elastic wave equation. Our formulation is compatible with standard numerical discretization schemes and allows for the efficient implementation of multiple practically relevant time- and space-dependent sources. Furthermore, we demonstrate that subspace energies can be extracted and wave fields compared through an L2 loss function, achieving optimal precision scaling with the number of samples taken. Additionally, we introduce techniques for incorporating boundary conditions and linear constraints that preserve the anti-Hermitian nature of the equations.   Leveraging the Hamiltonian simulation algorithm, our framework achieves a quartic speedup over classical solvers in three-dimensional simulations, under conditions of sufficiently global measurements and compactly supported sources and initial conditions. This quartic speedup is optimal for time-domain solutions, as the Hamiltonian of the discretized wave equations has local couplings. In summary, our framework provides a versatile approach for simulating wave equations on quantum computers, offering substantial speedups over state-of-the-art classical methods. The open-access paper can be found here: https://lnkd.in/de9ubsyK This work would not have been possible without the help and advice of Marion Dugué, Patrick Marty, Ines Ulrich, Václav Hapla and several colleagues at Google Quantum AI (Ryan Babbush, Rolando Somma and many others). #quantumcomputing #highperformancecomputing #waves #physics #metamaterials #seismology #ndt #medicalimaging #science #research

⚛️ Comparing performance of variational quantum algorithm simulations on HPC systems 📑 Variational quantum algorithms are of special importance in the research on quantum computing applications because of their applicability to current Noisy Intermediate-Scale Quantum (NISQ) devices. The main building blocks of these algorithms (among them, the definition of the Hamiltonian and of the ansatz, the optimizer) define a relatively large parameter space, making the comparison of results and performance between different approaches and software simulators cumbersome and prone to errors. In this paper, we employ a generic description of the problem, in terms of both Hamiltonian and ansatz, to port a problem definition consistently among different simulators. Three use cases of relevance for current quantum hardware (ground state calculation for H2 molecule, MaxCut, Travelling Salesman Problem) have been run on a set of HPC systems and software simulators to study the dependence of performance on the runtime environment, the scalability of the simulation codes and the mutual agreement of the physical results, respectively. The results show that our toolchain can successfully translate a problem definition between different simulators. On the other hand, variational algorithms are limited in their scaling by the long runtimes with respect to their memory footprint, so they expose limited parallelism to computation. This shortcoming is partially mitigated by using techniques like job arrays. The potential of the parser tool for exploring HPC performance and comparisons of results of variational algorithm simulations is highlighted. ℹ️ De Pascale et al - 2025

I'm really happy with the rapid development of CUDA-Q QEC, our toolkit for quantum error correction. QEC is an incredibly rich and fast-moving field, and in CUDA-Q QEC we aim to provide a platform with a diverse set of accelerated decoders, AI infrastructure, tools to enable researchers to develop and test their own codes, decoders, and architectures, hopefully even better than our own! As we dig deeper into the problem of scalable QEC, the benefits of GPUs and AI have become much clearer. We started with research tools, for simulation and offline decoding, which is still an important capability. Now with the 0.5.0 release we also provide the infrastructure for real-time decoding, where syndrome processing occurs concurrently with quantum operations. This release also introduces GPU-accelerated algorithmic decoders like RelayBP, a promising approach developed in the past year that aims to overcome the convergence limitations of traditional belief propagation. For scenarios demanding maximum throughput, we have integrated a TensorRT-based inference engine that allows researchers to deploy custom AI decoders trained in frameworks like PyTorch and exported to ONNX directly into the quantum control loop. To address the complexities of continuous system operation, we added sliding window decoders that handle circuit-level noise across multiple rounds without assuming temporal periodicity. These tools are designed to be hardware-agnostic and scalable, supporting our partners across the ecosystem who are building the first generation of reliable logical qubits. Check out the full technical breakdown in our latest developer blog by Kevin Mato, Scott Thornton, Ph.D., Melody Ren, Ben Howe, and Tom L. https://lnkd.in/gvC__zRd

Can we find hidden tunnels using quantum computers? For our quantum computing final project, my team and I decided to find out. Detecting subsurface structures, such as tunnels, aquifers, or voids, is impossible using classical methods, as classical gravimeters are plagued by vibrations, tilt, and drift. That's where Akshat, Aakrisht, Sahana, Landon, and I's Physics 19N final project, GraviQ: Simulating Subsurface Mapping with a Qubit-Based Gravimeter, comes in. By simulating an "hourglass" configuration of two atom clouds, we can measure the vertical gravity gradient (Gzzs) while canceling out the environmental noise. We built our procedure in three steps: 1) We generated 2D density grids representing rock, ore, tunnels, and caves to create synthetic environments. 2) We used Qiskit, a quantum simulator to model a Ramsey interferometer. We mapped subsurface density to qubit phase shifts, simulating the behavior of a real quantum sensor (including decoherence and sampling noise). 3) We fed the resulting Gzz maps into a U-Net machine learning segmentation model. The tentative results are notable. Despite the simulated noise, our model achieved ~95% accuracy in detecting tunnel presence and a Dice score of up to 0.85 for localization. We believe if we can replicate this in real life, the applications are far-reaching in fields ranging from civil engineering and infrastructure, to mineral extraction, to even space exploration. Here are links to our code and slides: GitHub: https://lnkd.in/eRUYWvj6 Slides: https://lnkd.in/eeBv-F5h Huge thanks to my teammates Akshat Kannan, Aakrisht Mehra, Sahana, and Landon Moceri, and Professor Hari Manoharan for the guidance and discussions along the way. Happy to chat with anyone interested in or working on quantum sensing or related research!