# Entanglement Transaction Semantics

**Version**: 1.0  
**Date**: January 26, 2026  
**Authors**: MACROHARD Quantum OS Team

---

## Table of Contents

1. [Introduction](#1-introduction)
2. [Entanglement Groups](#2-entanglement-groups)
3. [Representation](#3-representation)
4. [Commit Protocol](#4-commit-protocol)
5. [Failure Model](#5-failure-model)
6. [Distributed Considerations](#6-distributed-considerations)
7. [Examples](#7-examples)
8. [Future Extensions](#8-future-extensions)

---

## 1. Introduction

Quantum transactions in QDB extend classical ACID semantics with **entanglement groups** — a mechanism to enforce atomicity across correlated quantum states. This models the physical constraint that entangled qubits cannot be meaningfully separated: measuring one affects the other instantaneously.

### 1.1 Motivation

In quantum computing workflows, entangled states are fundamental:
- **Bell pairs** for quantum communication
- **GHZ states** for multi-party protocols
- **Cluster states** for measurement-based computation

When persisting such states, partial writes create inconsistent databases where entanglement correlations are broken. Entanglement groups prevent this.

### 1.2 Design Goals

1. **Atomicity**: All entangled keys commit together or none do
2. **Consistency**: No partial entanglement states in storage
3. **Isolation**: Entanglement groups are transaction-local
4. **Durability**: Once committed, entanglement relationships are preserved

---

## 2. Entanglement Groups

An **entanglement group** is a set of keys that must be written atomically within a transaction.

```rust
let qtx = QuantumTransaction::from_transaction(tx);

// Declare an entanglement group
qtx.entangle(vec![
    Key::string("alice:qubit"),
    Key::string("bob:qubit"),
])?;
```

### 2.1 Properties

| Property | Description |
|----------|-------------|
| **Membership** | Keys are added via `entangle()` |
| **Scope** | Transaction-local (not persisted) |
| **Cardinality** | 2+ keys per group |
| **Overlap** | Keys may belong to multiple groups |

### 2.2 Multiple Groups

A transaction may have multiple independent entanglement groups:

```rust
// Group 1: Alice-Bob pair
qtx.entangle(vec![Key::string("alice"), Key::string("bob")])?;

// Group 2: Charlie-David-Eve triple
qtx.entangle(vec![
    Key::string("charlie"),
    Key::string("david"),
    Key::string("eve"),
])?;

// All 5 keys must be written for commit to succeed
```

---

## 3. Representation

### 3.1 In-Memory Structure

Entanglement groups are stored as a `Vec<Vec<Key>>` in the `QuantumTransaction`:

```rust
pub struct QuantumTransaction<B: Backend> {
    inner: Transaction<B>,
    entanglement_groups: Mutex<Vec<Vec<Key>>>,
}
```

### 3.2 Not Persisted

Entanglement relationships are **not stored** in the database. They are:
- Declared per-transaction
- Validated at commit time
- Discarded after commit/rollback

**Rationale**: Entanglement is a property of the quantum states themselves (encoded in MPS tensors), not a database-level constraint. The transaction mechanism enforces write atomicity, not ongoing relationships.

### 3.3 Relationship to MPS

For actual quantum entanglement (as opposed to logical grouping):
- MPS bond dimension χ encodes entanglement entropy
- Shared bonds between tensors represent physical entanglement
- QDB's entanglement groups are a **logical** constraint, not a physical one

Future versions may support:
- Automatic entanglement detection from MPS structure
- Shared bond dimension tracking across entries

---

## 4. Commit Protocol

### 4.1 Validation Algorithm

```
COMMIT(transaction):
    1. Set state = PREPARING
    
    2. FOR EACH group IN entanglement_groups:
        FOR EACH key IN group:
            IF key NOT IN write_set:
                ROLLBACK("Entangled key missing: " + key)
                RETURN ERROR
    
    3. Validate read_set (optimistic concurrency)
    
    4. Apply write_set to backend
    
    5. Set state = COMMITTED
    RETURN OK
```

### 4.2 Complexity

- **Time**: O(G × K) where G = groups, K = avg keys per group
- **Space**: O(G × K) for group storage

### 4.3 Atomicity Guarantee

All writes in the write_set are applied together. If any entanglement validation fails, **no writes occur**.

---

## 5. Failure Model

### 5.1 Entanglement Violation

**Cause**: Not all keys in an entanglement group are written.

```rust
qtx.entangle(vec![Key::string("a"), Key::string("b")])?;
qtx.put("a", state_a)?;
// Missing: qtx.put("b", state_b)?;

let result = qtx.commit();
// Error: "Entangled keys must all be written together"
```

**Recovery**: Transaction rolls back. No data is persisted.

### 5.2 Concurrent Modification

**Cause**: Another transaction modified a key in the read_set (for RepeatableRead+ isolation).

```rust
// Transaction 1 reads key "x"
let tx1 = manager.begin_with_isolation(IsolationLevel::RepeatableRead);
let _ = tx1.get("x")?;

// Transaction 2 modifies "x" and commits
let tx2 = manager.begin();
tx2.put("x", "new_value")?;
tx2.commit()?;

// Transaction 1 tries to commit
tx1.put("y", "value")?;
let result = tx1.commit();
// Error: "Read set validation failed"
```

**Recovery**: Transaction rolls back. Retry with fresh read.

### 5.3 Backend Failure

**Cause**: I/O error during write_set application.

**Recovery**: Partial writes may occur (backend-dependent). Use Golay error correction and checksums for detection.

### 5.4 Timeout

**Cause**: Transaction exceeds configured timeout.

```rust
let tx = Transaction::new(id, backend, isolation)
    .with_timeout(Duration::from_secs(5));

// ... long operation ...

let result = tx.commit();
// Error: "Transaction timed out"
```

**Recovery**: Transaction rolls back automatically.

---

## 6. Distributed Considerations

### 6.1 Current Limitations

QDB v0.1 is single-node. Entanglement groups do not span:
- Multiple database instances
- Network partitions
- Sharded backends

### 6.2 Future: Distributed Entanglement

Planned for v2.0:
- **Two-Phase Commit (2PC)**: Coordinate entanglement across shards
- **Quantum Consensus**: Use entangled qubits for Byzantine agreement
- **Entanglement Routing**: Track which nodes hold entangled pairs

### 6.3 Consistency Model

| Level | Entanglement Behavior |
|-------|----------------------|
| **Strong** | All entangled keys on same node |
| **Eventual** | Entanglement groups may span nodes (2PC) |
| **Causal** | Entanglement implies causal ordering |

---

## 7. Examples

### 7.1 Bell Pair Storage

```rust
let manager = TransactionManager::new(backend);
let tx = manager.begin();
let qtx = QuantumTransaction::from_transaction(tx);

// Create Bell state |00⟩ + |11⟩
let bell = bell_state()?;

// Split into "Alice" and "Bob" entries
// (In practice, you'd store the full state or use MPS decomposition)
qtx.entangle(vec![
    Key::string("bell:alice"),
    Key::string("bell:bob"),
])?;

qtx.put("bell:alice", Value::quantum(bell.clone()))?;
qtx.put("bell:bob", Value::quantum(bell))?;
qtx.put("bell:metadata", Value::Json(json!({
    "type": "Bell",
    "created": "2026-01-26",
    "fidelity": 0.9999
})))?;

qtx.commit()?;
```

### 7.2 VQE with Auxiliary Qubits

```rust
let qtx = QuantumTransaction::from_transaction(tx);

// Main system and ancilla are entangled during computation
qtx.entangle(vec![
    Key::string("vqe:system"),
    Key::string("vqe:ancilla"),
])?;

qtx.put("vqe:system", system_state)?;
qtx.put("vqe:ancilla", ancilla_state)?;
qtx.put("vqe:params", Value::Json(json!({
    "theta": [0.1, 0.2, 0.3],
    "energy": -1.137
})))?;

qtx.commit()?;
```

### 7.3 Cluster State for MBQC

```rust
let qtx = QuantumTransaction::from_transaction(tx);

// All qubits in a cluster state are entangled
let cluster_keys: Vec<Key> = (0..16)
    .map(|i| Key::string(format!("cluster:q{}", i)))
    .collect();

qtx.entangle(cluster_keys.clone())?;

for (i, key) in cluster_keys.iter().enumerate() {
    qtx.put(key.clone(), qubit_states[i].clone())?;
}

qtx.commit()?;
```

---

## 8. Future Extensions

### 8.1 Automatic Entanglement Detection

```rust
// Proposed API
let qft = QftFile::from_mps(mps)?;
let entangled_pairs = qft.detect_entanglement(threshold)?;

for (qubit_a, qubit_b) in entangled_pairs {
    qtx.entangle(vec![
        Key::string(format!("q{}", qubit_a)),
        Key::string(format!("q{}", qubit_b)),
    ])?;
}
```

### 8.2 Entanglement Entropy Tracking

```rust
// Proposed API
let entry = db.get_entry("quantum_state")?;
let entropy = entry.entanglement_entropy()?; // S = -Tr(ρ log ρ)
```

### 8.3 Cross-Database Entanglement

```rust
// Proposed API for distributed QDB
let distributed_tx = DistributedTransaction::new(vec![
    node_a.backend(),
    node_b.backend(),
]);

distributed_tx.entangle_across_nodes(vec![
    (node_a, Key::string("alice")),
    (node_b, Key::string("bob")),
])?;
```

---

## References

1. Nielsen, M. A., & Chuang, I. L. (2010). *Quantum Computation and Quantum Information*. Cambridge University Press.
2. Horodecki, R., et al. (2009). "Quantum entanglement." *Reviews of Modern Physics*, 81(2), 865.
3. Vidal, G. (2003). "Efficient classical simulation of slightly entangled quantum computations." *Physical Review Letters*, 91(14), 147902.

---

*Document created for MACROHARD Quantum OS - QDB v0.1*
