DLA-Protected Scar Memory

The scar-memory prototype uses the DLA parity theorem and the fixed-parity repetition-code memory sector from qec.dla_protected_subspace. It prepares a logical cat state across two synchronised repetition-code words inside one DLA parity sector and evolves it under a diagonal finite-dimensional Hamiltonian whose scar energies are commensurate.

The result is a falsifiable memory primitive:

• the state leaves and returns to the initial scar packet over one revival period;
• the probability distribution stays inside the protected repetition-code sector at every sampled time;
• opposite-parity leakage remains directly measurable;
• Rust PyO3 trajectory metrics score protected, code, parity, and total weights over the full trajectory when scpn_quantum_engine is available.

Public API

from scpn_quantum_control.qec import (
    DLAProtectedScarSpec,
    build_dla_protected_scar_prototype,
    simulate_dla_protected_scar_memory,
)

spec = DLAProtectedScarSpec()
prototype = build_dla_protected_scar_prototype(spec)
result = simulate_dla_protected_scar_memory(prototype)

print(result.final_revival_fidelity)
print(result.min_protected_weight)
print(result.max_parity_leakage)

The default prototype uses four logical oscillators with distance-three repetition blocks, giving twelve physical qubits. The default protected scar words are the all-zero and all-one logical synchronisation memories, which both live in the even DLA parity sector for an even number of logical oscillators.

Certificate

build_dla_protected_scar_prototype() carries the same analytic certificate as certify_dla_protected_subspace():

• odd repetition distance;
• fixed global DLA parity;
• protected logical dimension matching the target sector;
• synchronised scar words contained in the protected sector;
• heterogeneous XY DLA dimension $2^{2N-1} - 2 = \mathfrak{su}(2^{N-1}) \oplus \mathfrak{su}(2^{N-1})$.

Revival Model

For scar basis states $|s_k\rangle$, the prototype prepares

$$|\psi_0\rangle = \frac{1}{\sqrt m}\sum_{k=0}^{m-1}|s_k\rangle$$

and assigns commensurate energies

$$E_k = k\,\frac{2\pi}{T}.$$

For the default two-state memory, the survival probability is

$$|\langle\psi_0|\psi(t)\rangle|^2 = \cos^2\!\left(\frac{\pi t}{T}\right).$$

The final sample at $t=T$ must revive to the configured fidelity threshold, while the protected and parity weights are evaluated over the whole trajectory.

Count Snapshots

evaluate_dla_protected_scar_counts() accepts measured count dictionaries at sampled times. Counts cannot recover the phase-sensitive survival amplitude, so the count path treats scar support as the observable memory survival proxy and still enforces protected-sector and parity-leakage criteria.

Failure Criteria

The typed result fails when any configured criterion is violated:

• revival_fidelity_below_threshold;
• protected_weight_below_threshold;
• parity_leakage_above_threshold;
• scar_support_below_threshold;
• protection_certificate_failed.

These criteria make the prototype usable as a pre-hardware witness: a statevector simulation can validate phase revival, while measured counts can validate protected memory support and DLA parity leakage.