Fixed Depth Hamiltonian Simulation via Cartan Decomposition

Abstract

Simulating quantum dynamics on classical computers is challenging for large systems due to the significant memory requirements. Simulation on quantum computers is a promising alternative, but fully optimizing quantum circuits to minimize limited quantum resources remains an open problem. We tackle this problem presenting a constructive algorithm, based on Cartan decomposition of the Lie algebra generated by the Hamiltonian, that generates quantum circuits with time-independent depth. We highlight our algorithm for special classes of models, including Anderson localization in one dimensional transverse field XY model, where a O(n^2)-gate circuits naturally emerge. Compared to product formulas with significantly larger gate counts, our algorithm drastically improves simulation precision. In addition to providing exact circuits for a broad set of spin and fermionic models, our algorithm provides broad analytic and numerical insight into optimal Hamiltonian simulations.

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Cited by in corpus (33)

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• Quantum Computing for High-Energy Physics: State of the Art and Challenges. Summary of the QC4HEP Working Group
• A Lie Algebraic Theory of Barren Plateaus for Deep Parameterized Quantum Circuits
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• Algebraic Bethe Circuits
• State Preparation on Quantum Computers via Quantum Steering
• Dynamical simulation via quantum machine learning with provable generalization
• Optimizing quantum circuits with Riemannian gradient flow
• On the complexity of implementing Trotter steps
• Classification of dynamical Lie algebras for translation-invariant 2-local spin systems in one dimension
• Variational quantum simulation: a case study for understanding warm starts
• An Algebraic Quantum Circuit Compression Algorithm for Hamiltonian Simulation
• Generalization of Quantum Machine Learning Models Using Quantum Fisher Information Metric
• Efficient Hamiltonian Simulation for Solving Option Price Dynamics
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