Wildcard Superposition

A database query like 1*0* matches four records. Prepare a register that holds every matching bitstring in equal superposition, and nothing else.

Objective

prepare_uniform_state(pattern) receives a string of '0', '1' and '*' (rightmost character = qubit 0) and returns a len(pattern)-qubit circuit whose state is the uniform superposition over all bitstrings matching the pattern.

Constraints

• No initialize / state_preparation shortcuts.

Entry Point

Checks

• Exports prepare_uniform_state(pattern).
• Patterns such as "1*0*" and "*1*1*" give the right superposition.