A network that heals, not a pair that lives for ever.
A quantum network keeps a service alive by making fresh entanglement, spending it, retiring what decays, and protecting stored qubits with error correction. This page replays runs of the tested models: the pair ledger (qll/network/pair_ledger.py), the logical memory (qll/circuits/logical_memory.py), and the off-grid mesh (qll/link/mesh_messenger.py). SIMULATED everywhere: none of it is a measurement.
What physics allows. No finite noisy memory keeps one state for ever: a logical qubit that fails with probability pL per cycle survives N cycles with probability (1 − pL)N. A destroyed unknown state cannot be rebuilt from blank qubits, and a consumed pair never comes back. What can last is the service: new pairs replace spent ones, as long as usable pairs arrive faster than requests. And no amount of entanglement carries a message without a classical path.
Three nodes, one ledger: Alice · Relay · Charlie
This run
The ledger's rules
- A pair is pending until its herald, or the Bell-measurement outcome, has reached both ends at light speed.
- A swap consumes both inputs, whether it succeeds or not; a failure restores nothing.
- A success creates a new pair with a new identifier and fidelity F₁F₂ + (1 − F₁)(1 − F₂)/3: two 0.95 pairs give 0.9033.
- Stored pairs decay; below the floor they expire, and expired is final.
- Every run checks the conservation law: created = in use + consumed + expired.
A logical qubit with reused ancillas: distance 3, 5, 7
Below the threshold (about 0.6 % here) more distance means fewer logical errors; above it, more qubits make it worse. Rotated surface code, d rounds of syndrome extraction with every ancilla measured and reset each round, decoded by matching.
Messages with no internet: two valleys and a ridge
How long can one logical qubit last?
(1 − pL)N falls to zero for any pL > 0. The network's answer is replacement, not immortality.