Quantum Algorithms, Complexity, and Fault Tolerance
summary
Theory reports that hardware now reaches 1,000-plus qubits but qubit error rates force focus on fault tolerance as the next milestone. Recent constructions give quantum LDPC codes with optimal parameters yet there are no efficient decoders yet and methods to compute on encoded data remain impractical, so full fault-tolerant protocols are still far off. Complexity results drive proofs of quantumness, the quantum PCP conjecture stays open, and cryptography demands post‑quantum protocols.
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