In this video, Ben introduces Grover’s algorithm, which searches through bit strings to find one which is different from the others. This different element (often called ‘the marked state’) is labelled by an oracle or black-box function. This prevents us from evaluating the number of quantum gates required, as the circuit decomposition for such an oracle is, in general, unknown. Instead, we use the number of oracle queries, or uses, as a stand-in. This number of queries scales as √N in contrast to the N queries which are required classically. This makes Grover’s algorithm interesting, though less of a ‘killer app’ than quantum phase estimation or factoring.

Main takeaways

• Not all quantum algorithms are necessarily exponentially faster than classical algorithms. Grover’s algorithm, for example, is only quadraticallyfaster than the classical brute-force method.
• Some quantum algorithms use oracles, which are black-box unitary operators whose circuit decompositions are not known. The number of times the oracle is used (the number of queries) is used as a surrogate for complexity.