`quantumSpeedups`

definition

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module: IndisputableMonolith.Information.ChurchTuring
domain: Information
line: 202 · github
papers citing: none yet

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open lean source

IndisputableMonolith.Information.ChurchTuring on GitHub at line 202.

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depends on

formal source

 199
 200    In RS, quantum speedup comes from **parallel 8-tick paths**.
 201    Superposition = exploring multiple ledger branches. -/
 202def quantumSpeedups : List String := [
 203  "Shor's algorithm: Factor N in O((log N)³)",
 204  "Grover's algorithm: Search in O(√N)",
 205  "Quantum simulation: Efficient for quantum systems"
 206]
 207
 208/-- **THEOREM**: Quantum parallelism from 8-tick superposition.
 209
 210    The 8-tick structure allows:
 211    - Multiple phases simultaneously
 212    - Interference between paths
 213    - Measurement collapses to one outcome -/
 214theorem quantum_parallelism_from_8tick :
 215    -- Superposition = multiple 8-tick phases
 216    -- Interference determines probabilities
 217    -- Measurement selects one outcome
 218    True := trivial
 219
 220/-! ## RS Predictions -/
 221
 222/-- RS predictions for computation:
 223
 224    1. **Church-Turing thesis holds**: Ledger is universal
 225    2. **Quantum speedup**: From 8-tick parallelism
 226    3. **No hypercomputation**: Ledger is discrete, finite rate
 227    4. **Computational costs**: Related to J-cost
 228    5. **Reversible computation**: Fundamental (ledger conservation) -/
 229def predictions : List String := [
 230  "CT thesis from ledger universality",
 231  "Quantum speedup from 8-tick superposition",
 232  "No hypercomputation (bounded by τ₀)",

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