Quantum Error Correction resilient against Atom Loss

TL;DR

This work demonstrates that neutral-atom quantum processors can achieve fault-tolerant storage and computation by augmenting the surface code with loss-detection units. It introduces a loss-aware MWPM decoder that leverages loss-location information to convert atom-loss events into an erasure-like correction, yielding up to nearly three orders of magnitude improvement in logical error rates for code distance $d=11$ under realistic loss and depolarizing-noise conditions. The comparison of standard versus teleportation-based LDUs shows that the teleportation-based approach generally achieves lower logical error probabilities due to fewer CZ gates and no active feedback, at the cost of slightly higher atom consumption in some regimes. Thresholds scale linearly with both $p_l$ and $p_d$, with a zero-noise loss threshold around $2.6\%$ and a revised loss model yielding $\sim2.1\%$, indicating practical resilience with current experimental parameters and suggesting a viable route to scalable fault-tolerant neutral-atom quantum computing.

Abstract

We investigate quantum error correction protocols for neutral atoms quantum processors in the presence of atom loss. We complement the surface code with loss detection units (LDU) and analyze its performances by means of circuit-level simulations for two distinct protocols -- the standard LDU and a teleportation-based LDU --, focussing on the impact of both atom loss and depolarizing noise on the logical error probability. We introduce and employ a new adaptive decoding procedure that leverages the knowledge of loss locations provided by the LDUs, improving logical error probabilities by nearly three orders of magnitude compared to a naive decoder. For the considered error models, our results demonstrate the existence of an error threshold line that depends linearly on the probabilities of atom loss and of depolarizing errors. For zero depolarizing noise, the atom loss threshold is about $2.6\%$.

Figures (17)

• Figure 1: Left circuit shows the typical operations seen by a bulk data qubit during a round. The red cross indicates loss of the data qubit between the first Hadamard gate and the third CZ gate. To simulate the loss, subsequent operations involving the lost atom are removed as shown in the right ("Effective") circuit.
• Figure 2: Top: Circuit representations of the two LDU protocols where ${\bf a)}$ shows the standard LDU and ${\bf b)}$ the teleportation LDU. In each cycle, data qubits are coupled to ancilla qubits using one of these protocols. Red circles indicate the potential locations where atoms might be lost in the LDU. The loss of the ancilla qubit in the standard LDU can always be detected using the measurement scheme, allowing for another LDU to be reapplied if necessary. This effectively prevents any loss on them. Bottom: The logical error probability normalized by the number of rounds for a surface code of distance $d=11$ and $d$ rounds of stabilizer measurements as a function of the loss probability $p_l$ and the depolarizing error probability $p_d$. The initial state is prepared in $\ket{0}_L$. ${\bf c)}$ corresponds to the standard LDU protocol, and ${\bf d)}$ represents the teleportation-based LDU protocol. Each logical error probability was evaluated with $10^5$ shots, except for regions with $p_l<4. 10^{-3}$ and $p_d<2. 10^{-3}$, where $10^6$ shots were employed. The solid red line marks the error threshold while the solid black lines show curves of constant logical error probability. The horizontal and vertical dashed red lines indicate the threshold at vanishing depolarizing noise and loss probability, respectively. For comparison, the threshold of the standard surface code is shown by a black dashed line. In $\bf d)$, the blank region indicates no errors were found. The dashed orange line indicates the current best CZ gate fidelity achieved in neutral atom systems, corresponding to a depolarizing error probability of $p_d=0.003$. A plot of the slice is shown in Fig \ref{['fig:depo_0.003']}.
• Figure 3: A schematic representation of the "loss-aware" DEM. Orange (respectively blue) semi-transparent plaquettes correspond to $Z$ (resp. $X$) stabilizers, which detect $X$ (resp. $Z$) errors. Black semi-transparent dots represent data qubits. Overlaid on the surface code is the DEM, consisting of orange (resp. blue) edges connecting neighboring ancilla qubits, representing $X$ (resp. $Z$) errors occurring on the intermediate data qubit, typically due to depolarizing noise. The edge thickness reflects their weights. In the case of data qubit loss (denoted by a red $L$) detected by its LDU, the weights of edges connecting neighboring stabilizers are reduced, as detailed in the main text. The figure illustrates a single time slice corresponding to one cycle of quantum memory operation. To fully capture the error dynamics, the model must be extended to the time domain to include errors on ancilla qubits.
• Figure 4: Logical error probability normalized by the number of rounds at vanishing depolarizing noise as a function of the loss probability for code distance $d=3,5,7,9,11$ and $d$ cycles of stabilizer measurements for ${\bf a)}$ the standard LDU protocol and ${\bf b)}$ the teleportation LDU protocol. The dashed red vertical line indicates the threshold at $2.6\%$ for both protocols. Other colored dashed lines represent fits of power laws $d$ for each curve respectively. $10^5$ shots were used to estimate the logical error probability.
• Figure 5: The logical error probability, normalized by the number of rounds at vanishing loss probability, is shown as a function of depolarizing noise error probability $p_d$ for code distances $d=3, 5, 7, 9, 11$ and $d$ cycles of stabilizer measurements. The plot includes results for ${\bf a)}$ the standard LDU protocol and ${\bf b)}$ the teleportation LDU protocol. The red dashed vertical line marks the threshold at $1.2\%$ for the standard LDU protocol and $1.4\%$ for the teleportation LDU protocol. For comparison, semi-transparent dashed-dotted lines represent the logical error probability per round for the standard surface code (i.e. without LDU), with its threshold indicated by a black dashed line. The logical error probability is estimated using $10^5$ shots.