1. From molecules to qubits

Electronic-structure problems are expressed in a basis, transformed to second-quantized Hamiltonians, and mapped to qubits using Jordan-Wigner, Bravyi-Kitaev, or related encodings. Basis and active-space choices dominate resource needs.

The quantum circuit is one stage in a larger chemistry pipeline.

2. State preparation and energy estimation

Approaches include adiabatic preparation, selected configuration interaction, coupled-cluster-inspired ansatzes, VQE, and phase estimation. Accuracy targets such as chemical accuracy determine depth and repetitions.

State overlap and precision strongly affect resource estimates.

3. Resource realism

Fault-tolerant estimates should include logical qubits, T gates, T-depth, magic-state factories, cycle time, error budget, and total wall-clock time. Compare against evolving classical chemistry.

A useful estimate converts an algorithm into hardware and time requirements.

4. Applied activity

Advanced exercise: derive or simulate one representative result from this module, document assumptions, and produce a one-page technical interpretation for a non-specialist decision maker.