Scalable Simulation of Quantum Many-Body Dynamics with Or-Represented Quantum Algebra

Abstract

High-performance numerical methods are essential not only for advancing quantum many-body physics but also for enabling integration with emerging quantum computing platforms. We present a scalable and general-purpose parallel algorithm for quantum simulations based on or-represented quantum algebra (ORQA). This framework applies to arbitrary spin systems and naturally integrates with quantum circuit simulation in the Heisenberg picture, particularly relevant to recent large-scale experiments on superconducting qubit processors [Kim et al., Nature 618, 500 (2023)]. As a benchmark, we simulate the kicked Ising model on a 127-qubit heavy-hexagon lattice, tracking the time evolution of local magnetization using up to one trillion Pauli strings. Executed on the supercomputer Fugaku, our simulations exhibit strong scaling up to $2^{17}$ parallel processes with near-linear communication overhead. These results establish ORQA as a practical and high-performance tool for quantum many-body dynamics, and highlight its potential for integration into hybrid quantum-classical computational frameworks, complementing recent advances in tensor-network and surrogate simulation techniques.

References in corpus (18)

• Quantum Computing in the NISQ era and beyond
• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Quantum Machine Learning
• The density-matrix renormalization group in the age of matrix product states
• Noisy intermediate-scale quantum (NISQ) algorithms
• Improved Simulation of Stabilizer Circuits
• Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
• Challenges and Opportunities in Quantum Machine Learning
• Quantum error correction below the surface code threshold
• Time-evolution methods for matrix-product states
• Tensor networks for complex quantum systems
• Complete universal quantum gate set approaching fault-tolerant thresholds with superconducting qubits
• Valence Bond Solids for Quantum Computation
• Efficient tensor network simulation of IBM's Eagle kicked Ising experiment
• Quantum-centric Supercomputing for Materials Science: A Perspective on Challenges and Future Directions
• Simulation of Qubit Quantum Circuits via Pauli Propagation
• Efficient tensor network simulation of IBM's largest quantum processors
• Real-time operator evolution in two and three dimensions via sparse Pauli dynamics