Correlated Atom Loss as a Resource for Quantum Error Correction

Abstract

Atom loss is a dominant error source in neutral-atom quantum processors, yet its correlated structure remains largely unexploited by existing quantum error correction decoders. We analyze the performance of the surface code equipped with teleportation-based loss-detection units for neutral-atom quantum processors subject to circuit-level, partially correlated atom loss and depolarizing noise. We introduce and implement a decoding strategy that exploits loss correlations, effectively converting the \textit{delayed} erasure channels stemming from atom loss to erasure channels. The decoder constructs a loss graph and dynamically updates loss probabilities, a procedure that is highly parallelizable and compatible with real-time operation. Compared to a decoder that assumes independent loss events, our approach achieves up to an order-of-magnitude reduction in logical error probability and increases the loss threshold from $3.2\%$ to $4\%$. Our approach extends to experimentally relevant regimes with partially correlated loss, demonstrating robust gains beyond the idealized fully correlated setting.

Figures (7)

• Figure 1: a) Sketch of the correlated atom loss mechanism: an atom lost during the Rydberg pulse (step 1.) causes the remaining atom to be projected to $\ket{1}$ and potentially re-excited (step 2.), where it either undergoes subsequent loss (step 3.a) or decays back to the computational subspace (step 3.b). b) Loss graph schematic: red/blue plaquettes denote $X/Z$ stabilizers; black/white dots are data/ancilla qubits; solid dots mark lost qubits (graph nodes). Edges connect simultaneously lost qubit pairs, with probabilities $p_i$ updated to $\tilde{p}_i$ by the fast correlated decoder based on the local neighborhood (see Eq. \ref{['eq:update_proba']}). c) Logical error probabilities per round at vanishing depolarizing noise, $p_d = 0$ and for a fully correlated loss model $p_c=1$, as a function of the atom loss probability $p_l$ for code distances $d = 3, 5, 7, 9$ obtained by employing the independent-loss decoder (semi-transparent dotted lines) and the fast correlated loss decoder (solid lines). The dashed red vertical lines indicate the independent-loss decoder and the correlated loss decoder thresholds respectively at $p_l = 3.2\%$ and $p_l=4\%$.
• Figure 2: A schematic representation of the loss graph. Red (resp. blue) semi-transparent plaquettes correspond to $X$ (resp. $Z$) stabilizers, which detect $Z$ (resp. $X$) errors. Black (resp. white) dots represent data (resp. ancilla) qubits. Semi-transparent dots indicate qubits that remain present during the error-correction cycle, while solid dots denote lost qubits and define the nodes of the loss graph. An edge is drawn between two lost qubits whenever a physical error mechanism that lost simultaneously both qubits exist. a): A connected component of the loss graph consisting of two lost qubits b): A connected component consisting of four lost qubits, for which two distinct pairing configurations are possible, shown in green and yellow. c): A connected component consisting of three lost qubits. In this case, the only possible matching requires the ancilla qubit to be matched twice. The figure illustrates a single time slice corresponding to one cycle of the quantum memory experiment. To fully capture all loss mechanisms, the model must be extended to the time domain, since losses induced by the LDU CZ gates can connect qubits across consecutive error-correction cycles.
• Figure 3: Distribution of the loss graph construction time and the a posteriori probability estimation time, normalized by the number of rounds $d = 9$. The a posteriori probability estimation time is further normalized by the number of edges in the loss graph, which varies fromshot to shot. Dashed lines indicate the mean of each distribution. These timing have been estimated for a surface code of distance $d=9$ with a partially correlated loss model ($p_l=0.01$, $p_c = 0.5$ ) at vanishing depolarizing noise $p_d=0$ over $10^5$ shots. The a posteriori probability estimation time also includes the time to load the various loss DEMS, reweight them by the estimated probability and combined them in a single file.
• Figure 4: Logical error probability normalized by the number of rounds at vanishing depolarizing noise, $p_d = 0$, as a function of the atom loss probability $p_l$ for code distances $d = 3, 5, 7, 9$ with $d$ cycles of stabilizer measurements obtained by employing the independent-loss decoder of perrin2025. Solid lines correspond to results obtained for a fully correlated loss model $p_c=1$, while dashed lines show the logical error probabilities in the independent-loss regime. The dashed red vertical line indicates the independent-loss decoder threshold at $p_l = 3.2\%$ for both loss models. At least $10^4$ shots were used to estimate the logical error probabilities, with up to $\sim10^6$ shots employed for the lowest error rates.
• Figure 5: Logical error probability normalized by the number of rounds at vanishing depolarizing noise, $p_d = 0$, as a function of the fully correlated loss probability $p_l$ ($p_c = 1$), for code distances $d = 3, 5, 7, 9$ with $d$ cycles of stabilizer measurements. Solid lines with circular markers correspond to results obtained using the fast decoder, while dashed lines show the logical error probabilities decoded with the accurate decoder. The dashed red vertical line indicates the fast decoder threshold at $p_l = 4\%$. Semi-transparent gray dash-dotted curves show fits of power-law $d$ with respect to the fast decoder data. At least $10^4$ shots were used to estimate the logical error probabilities, with up to $10^6$ shots employed for the lowest error rates.