Current verdict
A complexity advantage is only the beginning
Where does quantum help, and where does it not?
Describe the problem, then audit the algorithm, data access, hardware, and overhead. The result is an educational estimate, not a benchmark or promise.
Browser-local scenario
Problem fit explorer
Change any assumption. The comparison updates immediately.
Medium confidence
Illustrative work units
Algorithmic work before hardware cost
Formula audit
Follow every multiplier
Decision checklist
Ask before saying “advantage”
Worked, not hand-waved
Five examples with different answers
Values are illustrative. Complexity is not elapsed time.
Hardware reality
The asymptote does not run the machine.
Practical advantage includes the entire workflow, not one favorable term.
State preparation and data loading
A fast quantum subroutine can lose its benefit if classical data takes too long to encode. An efficient oracle or native quantum state is an assumption to prove.
Error correction and logical qubits
Useful fault-tolerant algorithms operate on logical qubits. Each logical qubit can require many physical qubits plus continuous error correction; estimates depend on hardware and target error rates.
Sampling and readout
Quantum measurements return samples, not a full hidden state. Precision can require repeated circuit runs, and extracting a large classical answer can dominate the workflow.
Classical baselines keep improving
Compare against the best relevant classical method, including approximation, parallelism, specialized accelerators, preprocessing, and problem structure.
Claim check
Which statement survives scrutiny?
Choose one answer.