Explicit reversible quantum oracles for bounded Diophantine systems achieve quadratic speedup with qubit count O((n + d²) log₂ N) and Toffoli depth O(q²).
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Clifford-deformed zero-rate LDPC codes achieve code-capacity thresholds approaching 50% under i.i.d. pure dephasing when the number of biased logical operators scales slower than distance or overlaps satisfy stated conditions, with new examples from tile codes.
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From Hilbert's Tenth Problem to Quantum Speedup: Explicit Oracles for Bounded Diophantine Systems
Explicit reversible quantum oracles for bounded Diophantine systems achieve quadratic speedup with qubit count O((n + d²) log₂ N) and Toffoli depth O(q²).
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Clifford-deformed zero-rate LDPC codes with 50% biased noise thresholds
Clifford-deformed zero-rate LDPC codes achieve code-capacity thresholds approaching 50% under i.i.d. pure dephasing when the number of biased logical operators scales slower than distance or overlaps satisfy stated conditions, with new examples from tile codes.