Correction of chain losses in trapped ion quantum computers

TL;DR

The paper addresses the challenge of ion loss in long trapped-ion chains, which can destabilize an entire quantum register. It introduces a distributed quantum error correction framework that spreads data across multiple chains, uses beacon qubits for rapid loss detection, and employs a decoder capable of handling both circuit faults and erasures turning chain losses into more tractable erasure errors. The approach is instantiated with a modified $[[72,12,6]]$ BB code and a sparse cyclic layout, and validated through circuit-level simulations showing performance close to a no-loss baseline for favorable loss-exponent regimes, along with quantified thresholds and beacon timing benefits. The work demonstrates a viable path toward scalable, loss-robust trapped-ion quantum computers and highlights design considerations for fast, distributed loss detection and erasure-aware decoding.

Abstract

Neutral atom quantum computers and to a lesser extent trapped ions may suffer from atom loss. In this work, we investigate the impact of atom loss in long chains of trapped ions. Even though this is a relatively rare event, ion loss in long chains must be addressed because it destabilizes the entire chain resulting in the loss of all the qubits of the chain. We propose a solution to the chain loss problem based on (1) a quantum error correction code distributed over multiple long chains, (2) beacon qubits within each long chain to detect the loss of a chain, and (3) a decoder adapted to correct a combination of circuit faults and erasures after beacon qubits convert chain losses into erasures. We verify the chain loss correction capability of our scheme through circuit level simulations with a distributed $[[72,12,6]]$ BB code with beacon qubits.

Figures (5)

• Figure 1: Catastrophic chain loss: The loss of one module leads to the subsequent loss of all modules after several cyclic shift and merge operations. The top row (D0, D1, D2) contains fixed modules of data qubits, and the bottom row (A0, A1, A2) contains moving modules of ancilla qubits. A dashed rectangle indicates merged modules.
• Figure 2: Logical error rate as a function of $p$, with $p_{\text{loss}} = p^\alpha$ for $\alpha \in \{1.7, 1.9, 2.1\}$.
• Figure 3: Logical error rate as a function of $p$, with $p_{\text{loss}} = p^\alpha$ for $\alpha \in \{1.5, 1.7, 1.9, 2.1\}$. We plot dashed curves only for $\alpha \in \{1.5, 2.1\}$, as the 4 dashed curves are closely clustered.
• Figure 4: Effect of losing data module 0 at different time steps. The top plot shows results for the X-then-Z stabilizer measurement order, while the bottom plot uses the reverse Z-then-X order. Shaded areas (blue for X, red for Z) indicate stabilizer measurement steps, during which some modules are merged to execute 2-qubit gates. White areas represent ancilla reset/measurement steps, during which all modules are separate. Solid curves represent the $X$ logical error rate, and dashed curves represent the $Z$ logical error rate. $p$ in the legend denotes the physical 2-qubit gate error rate.
• Figure 5: Effect of a single random chain loss occurring at a random time step. Each of the three plots corresponds to a different 2-qubit gate error rate. The colored squares show the logical error rate for $600$ randomly sampled chain loss events, defined by the time step ($x$-axis) and the lost module index ($y$-axis). During merged steps (unshaded regions), an ancilla module cannot be lost independently; it is lost jointly with the data module it is merged with. For this reason, no independent loss events are sampled for ancilla modules (indices 24-35) in the unshaded regions. To aid interpretation, the plot uses nearest-neighbor interpolation for unsampled data module (indices 0-23) loss events. Therefore, for the data modules, the color map represents true simulated data only at the locations of the colored squares.