Ultrametric Quantum Computation Benchmark

From Shor's Dead End to the p-Adic Frontier

v0.1 Phase 5

The Challenge

Compute p-adic modular exponentiation — $c = a^b \bmod p$ for a 256-bit prime (secp256k1 modulus) — using only branch-respecting quantum operations on a hierarchical tree structure.

This is the ultrametric analog of the elliptic curve point addition targeted by the ecdsa.fail challenge.

Scoring

Score = BranchOps × TreeDepth

Gate Type	Base Cost	Cross-Branch Penalty
Single-qubit (within branch)	1	×1
Two-qubit (same branch)	2	×1
Two-qubit (cross-branch, distance k)	2	×(1 + 0.5k)
Multi-qubit (n branches)	n²	×max(penalty)

Reference Verifier

git clone [repo-url]
cd uqc-benchmark/src
python verifier.py --test
python verifier.py --submission submission.json

7 tests pass 16 vectors

Submission Format

{
  "benchmark": "uqc-v0.1",
  "target": "p-adic modexp",
  "params": {"a": ..., "b": ..., "p": "secp256k1"},
  "circuit": {
    "tree_depth": 64,
    "gates": [{"type": "cnot", "targets": [0], "controls": [1]}]
  }
}