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A Classical Verifier Reaches Beyond the Polynomial Hierarchy
Relative to a classical oracle, a public-coin protocol verifies an exactly quantum-decidable language outside the polynomial hierarchy with perfect completeness.
Summary
Relative to a classical oracle, a public-coin protocol verifies an exactly quantum-decidable language outside the polynomial hierarchy with perfect completeness.
Whether a classical polynomial-time verifier can efficiently check arbitrary quantum computation without computational assumptions remains open. This paper proves an oracle-relative result for a language outside the polynomial hierarchy but exactly decidable in quantum polynomial time. Its public-coin protocol has perfect completeness and soundness error at most one quarter, using recursively addressed code and data tables. The author also proves a switching theorem for the correlated restrictions that defeat standard tools. Because the construction is relative to a chosen oracle, it does not resolve unrelativized verification of arbitrary real quantum computations.
Why it matters
Relative to a classical oracle, a public-coin protocol verifies an exactly quantum-decidable language outside the polynomial hierarchy with perfect completeness.
Limits and context
- Because the construction is relative to a chosen oracle, it does not resolve unrelativized verification of arbitrary real quantum computations.
Key claims
Relative to a classical oracle, a public-coin protocol verifies an exactly quantum-decidable language outside the polynomial hierarchy with perfect completeness.
Qualification: Because the construction is relative to a chosen oracle, it does not resolve unrelativized verification of arbitrary real quantum computations.
Evidence: source-2026-10-29-013
Sources
- arXiv preprint 2610.37635, original v1arXiv · primary research
Corrections
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