{-# LANGUAGE StrictData #-}

-- =====================================================================
-- IBM QUANTUM CHIP INTERFACE
-- Mock IBM Quantum API for Theorem 3 verification
-- Routes genus-0 proofs to quantum chip for witness generation
-- =====================================================================

module LiquidLean.Jacobian.QuantumChipInterface
  ( ibm_verify_genus_zero
  , ibm_estimate_circuit_depth
  , ibm_submit_job
  , IBM_JobStatus(..)
  ) where

import System.IO.Unsafe (unsafePerformIO)
import Control.Monad (when)
import Data.Time (getCurrentTime)

-- =====================================================================
-- IBM QUANTUM JOB TRACKING
-- =====================================================================

data IBM_JobStatus
  = JobPending
  | JobRunning
  | JobCompleted
  | JobFailed String
  deriving (Show, Eq)

-- =====================================================================
-- DETERMINISTIC IBM QUANTUM VERIFICATION
-- =====================================================================

{-|
Mock IBM Quantum verification: genus-0 witness generation.

For production:
  - Submits parameterized circuit to IBM Quantum backend
  - Circuit encodes genus-0 proof as density matrix eigenvalues
  - Returns True if quantum state matches genus-0 invariant

For testing (deterministic):
  - genus == 0 → True (proof verified)
  - genus > 0 → False (could be counterexample)
  - genus < 0 → error (invalid input)

Circuit depth:
  - Genus 0: ~10 qubits, ~50 gates (shallow)
  - Genus g: ~(2g+10) qubits (deeper for higher genus)
  - Timeout: 60 seconds (real quantum time)
-}
ibm_verify_genus_zero :: Int -> IO Bool
ibm_verify_genus_zero genus
  | genus < 0 = error ("ibm_verify_genus_zero: negative genus " ++ show genus)
  | genus == 0 = do
      -- Genus-0: quantum state verified as rational curve
      -- In mock: deterministic success
      return True
  | otherwise = do
      -- Higher genus: circuit would need deeper analysis
      -- In mock: reject (potential counterexample)
      return False

{-|
Estimate quantum circuit depth for genus verification.

Returns (depth, width) where:
  - depth = gate count (CNOT + single-qubit gates)
  - width = number of qubits needed

For genus 0:
  - width = 10 (Plücker coords + ancilla)
  - depth = 45-50 (shallow, <100ms on real hardware)

For genus g > 0:
  - width = 10 + 2*g
  - depth = 50 + 30*g (deeper, but polynomial)
-}
ibm_estimate_circuit_depth :: Int -> (Int, Int)
ibm_estimate_circuit_depth genus
  | genus < 0 = error "estimate_circuit_depth: negative genus"
  | genus == 0 = (50, 10)  -- Shallow circuit for genus-0
  | otherwise =
      let width = 10 + 2 * genus
          depth = 50 + 30 * genus
      in (depth, width)

{-|
Submit job to IBM Quantum.

Mock submission: returns job ID (hardcoded for testing).

Production path:
  1. Authenticate: IBM_Account.authenticate(api_key)
  2. Select backend: backend = provider.backend("ibmq_processor_2")
  3. Build circuit: qc = build_genus_circuit(genus_bound)
  4. Submit: job = execute(qc, backend, shots=1024)
  5. Poll: result = job.result()
  6. Extract: counts = result.get_counts()
  7. Verify: eigenvalues match genus-0 manifold

For mock: return fixed job ID
-}
ibm_submit_job :: Int -> IO String
ibm_submit_job genus = do
  now <- getCurrentTime
  let jobId = "job_theorem3_genus" ++ show genus ++ "_" ++ show (fromEnum now `mod` 10000)
  return jobId

{-|
Poll IBM Quantum job status.

Mock: always returns JobCompleted after 1 call.

Production: queries IBM API until terminal state (Completed or Failed).
-}
ibm_poll_job :: String -> IO IBM_JobStatus
ibm_poll_job _jobId = do
  -- Mock: deterministic completion
  return JobCompleted

-- =====================================================================
-- PLÜCKER FORMULA WITNESS GENERATION (Quantum Encoding)
-- =====================================================================

{-|
Encode genus-0 proof into quantum state.

The density matrix ρ encodes:
  - eigenvalue 1: genus = 0 (rational curve)
  - eigenvalue 0: genus > 0 (potential counterexample)
  - Other eigenvalues: Plücker coords {p_ij} for degree/singularity structure

For testing: mock returns deterministic state.

Production:
  - Uses parameterized circuit with Ry, Rz, CNOT gates
  - Runs with shot count = 1024
  - Extracts density matrix via tomography
-}
build_genus_witness :: Int -> String
build_genus_witness genus
  | genus == 0 = "ρ_genus0: diag(1, 0, 0, 0, 0, 0, 0, 0, 0, 0)"
  | otherwise = "ρ_genus" ++ show genus ++ ": mixed state"

-- =====================================================================
-- INTEGRATION WITH THEOREM 3 KERNEL
-- =====================================================================

{-|
Full verification pipeline:

  1. theorem3_kernel.forceGenusZero(poly) → Theorem3Evidence
  2. Extract genus_bound from evidence
  3. Estimate circuit depth via ibm_estimate_circuit_depth
  4. If circuit feasible: submit to quantum chip
  5. Poll until completion
  6. Extract density matrix eigenvalues
  7. Verify eigenvalue 1 present (genus = 0 verified)
  8. Return True if all checks pass

This module (QuantumChipInterface) handles steps 3-8.
QuantumFortranBridge (C FFI) handles step 1-2.
-}

-- Debug helper: print verification trace
debug_quantum_verification :: Int -> String
debug_quantum_verification genus =
  let (depth, width) = ibm_estimate_circuit_depth genus
      witness = build_genus_witness genus
  in unlines
    [ "=== IBM Quantum Verification Trace ==="
    , "Genus: " ++ show genus
    , "Circuit depth: " ++ show depth
    , "Qubits needed: " ++ show width
    , "Witness state: " ++ witness
    , "Status: " ++ if genus == 0 then "VERIFIED ✓" else "REJECTED ✗"
    ]