Quantum Ground State Optimization Techniques

Symplectic Optimization on Gaussian States https://lnkd.in/eP8bKg69 Abstract Computing Gaussian ground states via variational optimization is challenging because the covariance matrices must satisfy the uncertainty principle, rendering constrained or Riemannian optimization costly, delicate, and thus difficult to scale, particularly in large and inhomogeneous systems. We introduce a symplectic optimization framework that addresses this challenge by parameterizing covariance matrices directly as positive-definite symplectic matrices using unit-triangular factorizations. This approach enforces all physical constraints exactly, yielding a globally unconstrained variational formulation of the bosonic ground-state problem. The unconstrained structure also naturally supports solution reuse across nearby Hamiltonians: warm-starting from previously optimized covariance matrices substantially reduces the number of optimization steps required for convergence in families of related configurations, as encountered in crystal lattices, molecular systems, and fluids. We demonstrate the method on weakly dipole-coupled lattices, recovering ground-state energies, covariance matrices, and spectral gaps accurately. The framework further provides a foundation for large-scale approximate treatments of weakly non-quadratic interactions and offers potential scaling advantages through tensor-network enhancements.

I’m excited to share this new work from our IBM Quantum team in collaboration with Oak Ridge National Laboratory. This is a major demonstration of what we mean by realizing useful Quantum-centric supercomputing. Building on the chemistry work developed with RIKEN (https://lnkd.in/eK8jW-Wp) last year, and the previous Krylov demonstration with University of Tokyo (https://lnkd.in/eae_8zGc), the IBM Quantum and ORNL teams developed a quantum algorithm for ground states with convergence guarantees similar to phase estimation, while retaining the error mitigation aspect of sample-based methods. Putting together sample-based approaches and Krylov methods, we call this sample-based Krylov quantum diagonalization (SKQD). The algorithm can be used to compute ground state energies of quantum systems for many lattice models relevant in materials science and high-energy physics. SKQD is demonstrated experimentally on 85 qubits and 6,000 two-qubit gates on IBM quantum processors, against the ground state of the Anderson impurity model, obtaining high accuracies for problem sizes beyond the reach of exact diagonalization. This marks one of the largest implementations of quantum diagonalization to date, and points at how quantum computing, combined with classical computation in quantum-centric supercomputing environments, will enable us to push beyond classical methods for interesting applications. These new results also show again how algorithmic discovery is essential, especially for quantum-centric supercomputing architectures. Classical algorithms for materials science have made an impressive progress in the last decades. However, by thinking of quantum-classical workflows where quantum can deliver a value that cannot be matched by classical, we will move closer to demonstrating quantum advantage. Congratulations again to the team on this achievement. Check out the paper here: https://lnkd.in/epwCrG5R.

⚛️ Hybrid Sequential Quantum Computing 📑 We introduce hybrid sequential quantum computing (HSQC), a paradigm for combinatorial optimization that systematically integrates classical and quantum methods within a structured, stagewise workflow. HSQC may involve an arbitrary sequence of classical and quantum processes, as long as the global result outperforms the standalone components. Our testbed begins with classical optimizers to explore the solution landscape, followed by quantum optimization to refine candidatesolutions, and concludes with classical solvers to recover nearby or exact-optimal states. We demonstrate two instantiations: (i) a pipeline combining simulated annealing (SA), bias-field digitized counterdiabatic quantum optimization (BF-DCQO), and memetic tabu search (MTS); and (ii) a variant combining SA, BF-DCQO, and a second round of SA. This workflow design is motivated by the complementary strengths of each component. Classical heuristics efficiently find low-energy configurations, but often get trapped in local minima. BF-DCQO exploits quantum resources to tunnel through these barriers and improve solution quality. Due to decoherence and approximations, BF-DCQO may not always yield optimal results. Thus, the best quantum-enhanced state is used to continue with a final classical refinement stage. Applied to challenging higher-order unconstrained binary optimization (HUBO) problems on a 156-qubit heavy-hexagonal superconducting quantum processor, we show that HSQC consistently recovers ground-state solutions in just a few seconds. Compared to standalone classical solvers, HSQC achieves a speedup of up to 700× over SA and up to 9× over MTS in estimated runtimes. These results demonstrate that HSQC provides a flexible and scalable framework capable of delivering up to two orders of magnitude improvement at runtime quantum-advantage level on advanced commercial quantum processors. ℹ️ Chandarana et al - 2025

AI Meets Quantum Physics: Neural Network Finds Ground State of Fractional Quantum Hall Liquids Introduction: Harnessing AI to Tackle Quantum Complexity The quantum world is notoriously difficult to simulate, especially when it comes to exotic states of matter like fractional quantum Hall (FQH) liquids. These states, arising in two-dimensional electron systems under extreme magnetic fields, host rich topological behaviors and fractionalized excitations. Now, researchers at MIT and the Cavendish Laboratory have made a breakthrough by using a fermionic neural network (FNN) to accurately find the ground state of these elusive quantum systems. Key Findings: AI Tackles Quantum Many-Body Challenges • The Quantum Problem: • FQH liquids are among the most intriguing quantum phases, but simulating their behavior is incredibly difficult due to quantum superposition across exponentially many states. • Determining the ground state (the lowest-energy configuration) is essential for understanding the system’s physics. • Fermionic Neural Network (FNN): • The team developed an attention-based FNN, specifically designed to obey the antisymmetry of fermionic wavefunctions—essential for simulating electrons. • Trained using machine learning, the FNN was able to accurately approximate the ground state energy of FQH liquids. • Results Published: • The work appears in Physical Review Letters and represents a pioneering fusion of artificial intelligence and quantum many-body physics. • Team Motivation: • “AI has transformed many areas of society and science, but we are yet to see an AI breakthrough in quantum physics,” said Liang Fu, co-author of the paper. • The research was inspired by the idea of using AI to “conquer the quantum world” by solving problems that defy classical computation. Why It Matters: Toward an AI-Powered Quantum Revolution • New Era in Quantum Simulation: • This is one of the first successful applications of AI to a high-complexity quantum system, signaling a new toolset for condensed matter physics. • Accelerating Discovery: • The FNN approach could help physicists simulate materials with topological properties, key for quantum computing, spintronics, and low-power electronics. • Scalability and Future Potential: • As AI models improve, they could tackle even larger and more entangled systems, providing solutions previously thought computationally intractable. By blending deep learning with deep physics, this research marks a major step forward in solving the “everything everywhere all at once” problem at the heart of quantum theory. Keith King https://lnkd.in/gHPvUttw