Quantum Query Complexity
Upper and lower bounds on the number of quantum queries needed against an oracle-based primitive.
| Status | Statement | Tags |
|---|---|---|
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Constant-round Luby–Rackoff, quantum Resolved for r=7. Carolan (Compressed Permutation Oracles, ePrint 2025/1734, STOC 2026) proves seven-round Luby-Rackoff with truly random round functions is indistinguishable from a random invertible permutation against Omega(N^{1/12}) bidirectional quantum queries (his Theorem 6.5), exactly this page’s conjecture with r=7 – and states, without full proof here, that the result lifts to pseudorandom round functions (the strong qPRP form) by a standard hybrid argument. The paper’s own abstract calls this ‘resolving an open question of (Zhandry, 2012).’ |
Feistel NetworksPseudorandom PermutationsQuantum Query Complexityotherequivalenceresearch-solved | |
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Quantum two-block MD collisions Open, in both directions and with no partial result: whether the best known quantum preprocessing attack, of advantage ST^2/N + T^3/N, is optimal for two-block Merkle-Damgård collisions. The source reports that no matching quantum bounds are known at any block length. 7 open |
Collision FindingCollision Resistant HashingQuantum Query ComplexityQuantum Random Oracle ModelTime Space Tradeoffsqromtight-bound | |
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Fully quantum time-lock puzzles Open in the fully quantum case. Settled by the source paper when the generator is classical and the solver quantum, and when the generator is quantum and the solver classical under perfect completeness; a classical-query attack on the remaining cell would prove a simulation conjecture. 5 open |
Quantum Query ComplexityQuantum Random Oracle ModelTime Lock Puzzlesqromimpossibility | |
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CAQB key agreement, imperfect completeness Open. Settled for perfect completeness by the source paper’s Theorem 3.1; the argument’s final step uses perfect completeness in a way that no known weakening survives, and the paper’s Simulation-Conjecture barrier does not cover this party structure. 5 open |
Quantum Key AgreementQuantum Query ComplexityQuantum Random Oracle Modelqromimpossibility | |
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Classical presampling, quantum queries Open, and provably hard to prove: the source’s Theorem 4 shows it implies a central open problem in quantum computing. No refutation has been attempted either, and the source takes no position on which way it goes – it states the conjecture in order to show that the classical technique cannot simply be transplanted. 6 open |
PresamplingQuantum Query ComplexityQuantum Random Oracle ModelRandom Oracle Modelqromlower-boundbarrier (ai) | |
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Double-sided zero search Resolved, unconditionally. Carolan (Compressed Permutation Oracles, ePrint 2025/1734, STOC 2026) proves this exact statement – his Problem 3, p. 72, naming it ‘the double-sided zero search problem, due to Unruh’ – as a corollary (Corollary 7.6) of a general predicate-search lower bound (Theorem 7.5) proved directly from his own compressed permutation oracle’s soundness (Theorem 5.19). Unlike Unruh’s own derivation, this proof does not route through Unruh’s CPO-soundness conjecture (c/0036) at all, so it holds regardless of that conjecture’s status. |
Compressed OracleQuantum Query Complexityotherlower-boundresearch-solved | |
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Compressed permutation oracle soundness Still open as formalized, but the underlying research question – can the compressed-oracle technique be extended to permutations at all – is now resolved in the affirmative by a different construction. Carolan (Compressed Permutation Oracles, ePrint 2025/1734, STOC 2026) proves his own compressed permutation oracle unconditionally sound. That oracle is, in his own words, ‘similar to that of Unruh [Unr23], though we explicitly and unitarily maintain injectivity of the database’ – a change that goes beyond resolving Unruh’s own left-open choice of how the flipping operator acts on non-injective inputs. Whether Unruh’s original construction (for an arbitrary such choice) is itself sound remains, on the reading defended here, unestablished. |
Compressed OraclePseudorandom PermutationsQuantum Query Complexityotherequivalence | |
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Polynomial Compatibility Conjecture Open in the inverse-polynomial regime. Proved for exponentially small influences by the paper that introduced it, and false for influences at or above 1/(2d); everything between is what the quantum separations depend on. 5 open |
Compressed OracleQuantum Query ComplexityQuantum Random Oracle Modelqromassumption |
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