hamiltonian-simulation

Quantum time evolution under a Hamiltonian is simulated using product-formula methods like deterministic Trotter-Suzuki decomposition and randomized QDrift sampling to approximate e^{-iHt}. The Skill provides a modular API returning lazy-evaluated results for direct comparison against exact matrix exponentials.

Trotter-Suzuki provides deterministic Hamiltonian decomposition for structured systems, while QDrift uses randomized sampling to trade circuit depth for accuracy. The Skill supports both approaches to compute e^{-iHt}, allowing explicit error comparison against exact matrix exponentials.

Product-formula methods are applied to both spin-chain and molecular Hamiltonians in this Skill. It computes e^{-iHt} evolution using a unified API that returns lazy-evaluated results, tracking simulation error against exact matrix exponentials.

Comparing simulated quantum evolution against the exact matrix exponential is handled directly by the unified API, which returns lazy-evaluated results. This built-in comparison tracks the error of Trotter-Suzuki and QDrift approximations automatically.

Circuit depth and accuracy in quantum Hamiltonian simulation are traded off by switching between deterministic Trotter-Suzuki decomposition and randomized QDrift sampling. Both methods approximate e^{-iHt} and are benchmarked against exact matrix exponentials to measure error.

Demonstrating Hamiltonian simulation benchmarks is supported through educational examples using a minimal two-qubit Hamiltonian. The unified API computes e^{-iHt} via Trotter-Suzuki or QDrift and compares the results against exact matrix exponentials to visualize error.