Suzuki-Trotter Decompositions and other Methods for Quantum Time Evolution

arXiv:2609.19184 · quant-ph, cond-mat.stat-mech, cond-mat.str-el, hep-lat, physics.comp-ph · Submitted 2026-09-15 · Read on arXiv

quant-ph, cond-mat.stat-mech, cond-mat.str-el, hep-lat, physics.comp-ph

Submitted: 2026-09-15

Updated: 2026-09-15

Code: https://github.com/MarkoMalezic/qiskit-omelyan

Terminology

• Entanglement — 9× in this paper · explained in 4 episodes
• BQP — 6× in this paper · explained in 2 episodes
• Benchmark — 6× in this paper · explained in 2 episodes
• Accuracy — 5× in this paper · explained in 1 episode
• Hubbard Model — 5× in this paper · explained in 3 episodes
• Quantum Circuits — 5× in this paper · explained in 2 episodes
• SYK Model — 3× in this paper · explained in 2 episodes
• Block Encoding — 2× in this paper · explained in 4 episodes
• Chebyshev Polynomials — 2× in this paper · explained in 2 episodes
• Fidelity — 2× in this paper · explained in 2 episodes
• Robustness — 2× in this paper · explained in 5 episodes
• Sparsity — 2× in this paper · explained in 4 episodes
• Adaptive Sampling — 1× in this paper · explained in 1 episode
• Ancillary Qubits — 1× in this paper · explained in 1 episode
• Computational overhead — 1× in this paper · explained in 2 episodes
• Decoupling — 1× in this paper · explained in 2 episodes
• Effective Hamiltonian — 1× in this paper · explained in 2 episodes
• Entanglement Entropy — 1× in this paper · explained in 2 episodes
• Matrix Product States (MPS) — 1× in this paper · explained in 2 episodes
• Systematic Bias — 1× in this paper · explained in 3 episodes

Sources

• Optimised Trotter Decompositions for Classical and Quantum Computing
• Efficient Trotter-Suzuki Schemes for Long-time Quantum Dynamics
• Lecture Notes on Quantum Algorithms for Scientific Computation
• Splitting Methods for differential equations
• Time-evolution methods for matrix-product states
• Selection and improvement of product formulae for best performance of quantum simulation
• Reducing the Gate Count with Efficient Trotter-Suzuki Schemes
• Quantum computing with Qiskit
• Early fault-tolerant simulations of the Hubbard model
• Trotter error with commutator scaling for the Fermi-Hubbard model
• An Error-aware and Adaptive Method for the Estimation of Quantum Observables on Qudit-Based Quantum Computers
• An Analysis of Commutation-Based Trotter Ordering Strategies on Heisenberg-Style Hamiltonians
• Physics Guided Generative Optimization for Trotter Suzuki Decomposition
• Beyond Commutativity: Redesigning Trotter Decomposition via Local Symmetry
• A note on the Baker--Campbell--Hausdorff series in terms of right-nested commutators
• Finding Exponential Product Formulas of Higher Orders
• A Theory of Trotter Error
• Toward the first quantum simulation with quantum speedup
• Nearly optimal lattice simulation by product formulas
• Lindbladian Simulation with Commutator Bounds

Related papers

• Reconquering Bell sampling on qudits: stabilizer learning and testing, quantum pseudorandomness bounds, and more
• Encrypted clones can leak: Classification of informative subsets in Quantum Encrypted Cloning
• Polynomial-time classical and quantum simulation of quantum impurity models
• Theory of quantum-enhanced interferometry with general Markovian light sources
• A convergent hierarchy of spectral gap certificates for qubit Hamiltonians
• Universal Bound and Phase Transition in Many-Body Fermionic Non-Gaussianity