Computational model exploiting quantum superposition, entanglement, and interference to solve problems with provable asymptotic advantages over the best known classical algorithms. Foundational algorithms: Deutsch 1985 / Deutsch-Jozsa…
quantum-computing
Deutsch-Jozsa 1992 oracle problem: constant vs balanced with 1 quantum query
Deutsch 1985 (Proc. R. Soc. A 400:97) introduced the single-bit precursor; Deutsch-Jozsa 1992 (Proc. R. Soc. A 439:553) extended it to n…
Grover 1996 unstructured-search with O(√N) queries
Grover 1996 (Proc. STOC 212) gave a quantum algorithm for unstructured search with quadratic speedup: given an oracle U_f marking M out of…
Bernstein-Vazirani 1993 hidden-string in 1 quantum query vs n classical
Bernstein-Vazirani 1993 (STOC 1993, refined paper SIAM J. Comput. 26:1411) refined the Deutsch-Jozsa problem to a learning task. Promise:…
Deutsch-Jozsa quantum/classical query complexity exponential separation
Exact closed-form query-complexity comparison. Quantum: Deutsch-Jozsa solves the constant-vs-balanced promise problem with exactly 1…
Grover iteration R=1 gives P=1 for N=4, M=1 (perfect 4-item search)
Textbook special case: Grover search over N=4 items with M=1 marked item gives certainty after a single Grover iteration. The rotation…
Bernstein-Vazirani quantum speedup = n (linear in problem size)
Exact query-complexity result. Quantum: 1 oracle query recovers the n-bit hidden string s exactly. Classical lower bound: any classical…