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ANU Quantum Entropy + Destructive Interference
Quantum-inspired path validation using phase masks:
Valid paths → e^{i0} = +1 (constructive interference)
Invalid paths → e^{i*pi} = -1 (destructive interference)
Pipeline:
1. Quantum seed (entropy source)
2. Superpositioned candidates (multi-path)
3. Oracle validation (Z3/SPARK/Lean)
4. Phase mask application
5. Resolved state (only valid paths survive)
Key math:
Phase mask: valid → e^{i0}=1, invalid → e^{i*pi}=-1
Quantum perturbation: val *= 1.0 + strength * (seed_byte/255 - 0.5) * 2
Cancellation: invalid candidates get negative weight → not selected
Pipeline soundness: only states with oracle=True returned
Contact: jessica@collectivekitty.com
"""
import torch
import torch.nn as nn
import torch.nn.functional as F
import math
import asyncio
from typing import Optional, Tuple, Dict, List, Protocol
from dataclasses import dataclass, field
@dataclass
class QuantumIntegratedConfig:
"""Configuration for quantum-integrated system."""
d_model: int = 768
quantum_seed_dim: int = 32
perturbation_strength: float = 0.01
entropy_pool_size: int = 1024
oracle_type: str = "composite" # z3, spark, lean, composite, mock
num_candidates: int = 4
collapse_temperature: float = 1.0
class InvariantOracleInterface(Protocol):
"""Interface for invariant checking oracles."""
async def check(self, states: torch.Tensor) -> torch.Tensor:
"""Check validity of states. Returns bool mask."""
...
class MockOracle:
"""Mock oracle for testing (validates based on norm bound)."""
def __init__(self, threshold: float = 2.0):
self.threshold = threshold
async def check(self, states: torch.Tensor) -> torch.Tensor:
"""States with norm < threshold are valid."""
norms = states.norm(dim=-1)
return norms < self.threshold
class Z3OracleWrapper:
"""Z3 SMT solver wrapper for invariant checking."""
async def check(self, states: torch.Tensor) -> torch.Tensor:
"""Check states against Z3 constraints (placeholder)."""
# In production: encode states as Z3 bitvectors, check SAT
return torch.ones(states.shape[0], dtype=torch.bool, device=states.device)
class CompositeOracleWrapper:
"""Composite oracle: checks multiple backends, requires majority agreement."""
def __init__(self, oracles: List = None):
self.oracles = oracles or [MockOracle()]
async def check(self, states: torch.Tensor) -> torch.Tensor:
"""Majority vote across oracles."""
votes = []
for oracle in self.oracles:
result = await oracle.check(states)
votes.append(result)
# Majority vote
vote_stack = torch.stack(votes).float()
return vote_stack.mean(dim=0) > 0.5
class QuantumEntropyInterface:
"""Interface to quantum entropy source (ANU QRNG or fallback)."""
def __init__(self, pool_size: int = 1024):
self.pool_size = pool_size
# Fallback: use torch random (CSPRNG in production)
self._pool = torch.randint(0, 256, (pool_size,), dtype=torch.uint8)
self._idx = 0
async def get_seed(self, n_bytes: int) -> torch.Tensor:
"""Get n_bytes of quantum entropy."""
if self._idx + n_bytes > self.pool_size:
# Refresh pool
self._pool = torch.randint(0, 256, (self.pool_size,), dtype=torch.uint8)
self._idx = 0
seed = self._pool[self._idx:self._idx + n_bytes].float() / 255.0
self._idx += n_bytes
return seed
class QuantumInterferenceResolver:
"""
Resolves superpositioned candidates via phase mask interference.
Valid candidates: phase = +1 (constructive, e^{i0} = 1)
Invalid candidates: phase = -1 (destructive, e^{i*pi} = -1)
The invalid paths destructively interfere and cancel out,
leaving only valid paths in the final superposition.
"""
def __init__(self, config: QuantumIntegratedConfig):
self.config = config
self.entropy = QuantumEntropyInterface(config.entropy_pool_size)
async def resolve(
self,
candidates: torch.Tensor,
oracle: InvariantOracleInterface
) -> Tuple[Optional[torch.Tensor], Dict]:
"""
Resolve candidates via quantum interference.
Args:
candidates: [K, d] candidate states
oracle: validity checker
Returns:
resolved: [d] best valid state (or None if all invalid)
aux: dict with phase_mask, validity, cancellation_rate
"""
K = candidates.shape[0]
# Get quantum seed for perturbation
seed = await self.entropy.get_seed(K * self.config.quantum_seed_dim)
seed = seed.view(K, -1)
# Apply quantum perturbation to candidates
perturbed = candidates.clone()
for k in range(K):
perturbation = self.config.perturbation_strength * (seed[k].mean() - 0.5) * 2
perturbed[k] = candidates[k] * (1.0 + perturbation)
# Oracle check
validity = await oracle.check(perturbed) # [K] bool
# Apply phase mask
# Valid: +1 (constructive), Invalid: -1 (destructive)
phase_mask = torch.where(validity, torch.ones(K), -torch.ones(K))
# Weight candidates by phase
weighted = perturbed * phase_mask.unsqueeze(-1)
# Sum (destructive interference cancels invalid)
superposed = weighted.sum(dim=0)
# Normalize by number of valid paths
n_valid = validity.sum().item()
cancellation_rate = 1.0 - (n_valid / K)
aux = {
"phase_mask": phase_mask,
"validity": validity,
"cancellation_rate": cancellation_rate,
"n_valid": n_valid,
}
if n_valid == 0:
return None, aux
# Return normalized result (only valid contribute positively)
resolved = superposed / max(n_valid, 1)
return resolved, aux
class QuantumIntegratedSystem(nn.Module):
"""
Full quantum-integrated BURT-IMMA system.
Pipeline:
1. Quantum seed (entropy)
2. Superpositioned candidates (from induction heads)
3. Oracle validation
4. Phase mask (constructive/destructive)
5. Resolved state
6. Memory update
7. Output
"""
def __init__(self, config: Optional[QuantumIntegratedConfig] = None):
super().__init__()
self.config = config or QuantumIntegratedConfig()
self.resolver = QuantumInterferenceResolver(self.config)
# Candidate generator
self.candidate_proj = nn.Linear(
self.config.d_model,
self.config.d_model * self.config.num_candidates
)
self.output_proj = nn.Linear(self.config.d_model, self.config.d_model)
def generate_candidates(self, state: torch.Tensor) -> torch.Tensor:
"""Generate K candidate states from input."""
K = self.config.num_candidates
d = self.config.d_model
expanded = self.candidate_proj(state) # [batch, K*d]
return expanded.view(-1, K, d) # [batch, K, d]
async def forward_async(
self,
state: torch.Tensor,
oracle: Optional[InvariantOracleInterface] = None
) -> Tuple[torch.Tensor, Dict]:
"""
Async forward with quantum interference resolution.
Args:
state: [batch, d]
oracle: validity checker (default: MockOracle)
Returns:
output: [batch, d]
aux: dict with resolution info
"""
if oracle is None:
oracle = MockOracle()
batch = state.shape[0]
outputs = []
all_aux = []
for b in range(batch):
candidates = self.generate_candidates(state[b:b+1]).squeeze(0)
resolved, aux = await self.resolver.resolve(candidates, oracle)
if resolved is not None:
outputs.append(resolved)
else:
outputs.append(state[b]) # fallback to input
all_aux.append(aux)
output = torch.stack(outputs)
output = self.output_proj(output)
combined_aux = {
"cancellation_rate": sum(a["cancellation_rate"] for a in all_aux) / batch,
"avg_valid": sum(a["n_valid"] for a in all_aux) / batch,
}
return output, combined_aux
def forward(self, state: torch.Tensor) -> torch.Tensor:
"""Synchronous forward (uses mock oracle)."""
candidates = self.generate_candidates(state) # [batch, K, d]
# Simple validity: norm-based (no async oracle)
norms = candidates.norm(dim=-1) # [batch, K]
valid = norms < 2.0
phase_mask = torch.where(valid, torch.ones_like(norms), -torch.ones_like(norms))
weighted = candidates * phase_mask.unsqueeze(-1)
superposed = weighted.sum(dim=1) # [batch, d]
n_valid = valid.sum(dim=1, keepdim=True).clamp(min=1).float()
resolved = superposed / n_valid
return self.output_proj(resolved)
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