Structure-Aware Variance Reduction for Unbiased Randomized Hamiltonian Simulation

arXiv:2606.23544 · quant-ph · Submitted 2026-06-22 · Read on arXiv

quant-ph

Submitted: 2026-06-22

Updated: 2026-09-17

Code: https://github.com/fredrikhassel/CTEPAI

Terminology

• Entanglement — 10× in this paper · explained in 3 episodes
• Accuracy — 7× in this paper · explained in 1 episode
• Core — 4× in this paper · explained in 2 episodes
• Systematic Bias — 4× in this paper · explained in 3 episodes
• Spectral Gap — 3× in this paper · explained in 5 episodes
• Trace — 3× in this paper · explained in 2 episodes
• Benchmark — 2× in this paper · explained in 2 episodes
• Adaptive Sampling — 1× in this paper · explained in 1 episode
• Aggregation — 1× in this paper · explained in 1 episode
• Ancilla Qubits — 1× in this paper · explained in 1 episode
• Benchmarking — 1× in this paper · explained in 3 episodes
• Conservation Laws — 1× in this paper · explained in 3 episodes
• Downstream Tasks — 1× in this paper · explained in 2 episodes
• Effective Hamiltonian — 1× in this paper · explained in 2 episodes
• Fidelity — 1× in this paper · explained in 2 episodes
• Graph Construction — 1× in this paper · explained in 3 episodes
• Hilbert Space — 1× in this paper · explained in 2 episodes
• Quantum Circuits — 1× in this paper · explained in 2 episodes
• Quantum Physics — 1× in this paper · explained in 10 episodes
• Sample Complexity — 1× in this paper · explained in 15 episodes
• Verification — 1× in this paper · explained in 2 episodes

Sources

• Importance sampling for stochastic quantum simulations
• STAR-Magic Mutation: Even More Efficient Analog Rotation Gates for Early Fault-Tolerant Quantum Computer
• Stratified Sampling for Quasi-Probability Decompositions
• MLMC-qDRIFT: Multilevel Variance Reduction for Randomized Quantum Hamiltonian Simulation
• Benchmarking Quantum Processor Performance at Scale
• Low-Resource Quantum Energy Gap Estimation via Randomization
• Correcting and extending Trotterized quantum many-body dynamics
• Explicit error bounds with commutator scaling for time-dependent product and multi-product formulas
• Characterization and Verification of Trotterized Digital Quantum Simulation via Hamiltonian and Liouvillian Learning
• Time-evolution methods for matrix-product states
• Proof of Aldous' spectral gap conjecture
• Operator scrambling and quantum chaos
• Quantum simulation of many-body dynamics with noise-robust Trotter decomposition based on symmetric structures
• Beyond Commutativity: Redesigning Trotter Decomposition via Local Symmetry
• More efficient Clifford+T synthesis for small-angle rotations and application to Trotterization

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• A convergent hierarchy of spectral gap certificates for qubit Hamiltonians
• Universal Bound and Phase Transition in Many-Body Fermionic Non-Gaussianity