Leveraging Qubit Loss Detection in Fault Tolerant Quantum Algorithms

TL;DR

This work tackles qubit loss as a dominant error source in fault-tolerant quantum computing and introduces a delayed-erasure decoder that leverages delayed loss-detection information to approximate optimal decoding across general codes and logical algorithms. It analyzes multiple syndrome-extraction strategies (conventional, teleportation-based, and mid-circuit erasure conversion) and demonstrates how algorithmic structure—particularly short lifecycles from gate teleportation—can mitigate loss with minimal overhead. A unified error-counting model links loss- and Pauli-errors to SE performance, revealing that loss fraction largely governs thresholds and effective distance, while hardware specifics determine the best SE approach. The results provide a practical, architecture-agnostic framework for integrating loss detection and decoding into large-scale fault-tolerant quantum computation, with strong relevance for neutral-atom and other platforms where loss and leakage are prevalent.

Abstract

Qubit loss errors constitute a dominant source of noise in many quantum hardware systems, particularly in neutral atom quantum computers. We develop a theoretical framework to effectively detect and correct loss errors in logical algorithms and leverage such loss information in decoding. Considering general quantum error correction codes and logical circuits, we introduce a delayed-erasure decoder for experimentally-motivated error models which leverages information from delayed loss detection to accurately correct loss errors, even when the precise moment of the error is unknown. Using this decoder, we identify strategies for detecting and correcting loss errors based on the logical circuit structure. For deep circuits prior to logical measurement, we explore methods to integrate loss detection into syndrome extraction with minimal overhead, identifying optimal strategies depending on the qubit loss fraction in the noise and hardware capabilities. In contrast, we find that many key algorithmic subroutines involve frequent gate teleportation, shortening the circuit depth before logical measurement and naturally replacing qubits with no additional experimental overhead. We simulate this setting using a toy model algorithm for small-angle synthesis, and find a significant performance improvement as the loss fraction increases. These results provide a path forward for advancing large-scale fault tolerant quantum computation in systems with loss error detection.

Figures (27)

• Figure 1: Loss errors in logical circuits. (a) Depiction of a logical algorithm with loss-detecting SE and gate teleportation. Physical qubit losses (red crosses) can generate correlated errors within and between logical qubits. (b) Space-time diagram of a logical circuit, focusing on a measure qubit lifecycle during syndrome extraction. Physical qubits progress through time, undergoing initialization, gate operations, idling, and measurement. A loss event causes future gates to be canceled, generating correlated errors between the qubits in the gate and flipping the corresponding stabilizers.
• Figure 2: Delayed-erasure decoder. (a) Illustration of a qubit lifecycle and its usage in the delayed-erasure decoder. From initialization to measurement, each physical qubit can be lost at multiple possible time points, each occurring with a potentially different probability and corresponding syndrome. Upon detection of a qubit loss, the decoder accounts for these possibilities in order to improve the accuracy of the assigned correction. (b) Logical error rate for a logical memory as a function of the number of conventional SE rounds before logical measurement, here with distance $d=5$ and loss errors with probability $p_{\text{loss}}=1\%$ per entangling gate. The delayed-erasure decoder (pink) substantially outperforms a decoder which does not account for loss information (black). Even without loss moment information, the delayed-erasure decoder achieves comparable performance to a decoder with perfect loss time-location (gray, dashed).
• Figure 3: Loss-detecting SE methods. (a) Modified SWAP SE: data and measure qubits are swapped each round to detect loss via SSR; the SWAP’s CNOT decomposition cancels with existing parity-extraction gates, with the remaining CNOT replaced by classical feedforward, so no additional entangling gates are required. (b) Teleportation-based SE: logical qubits are teleported to fresh blocks prepared in alternating bases, detecting loss via SSR and shortening lifecycles, at the cost of extra qubits. (c) Direct conversion SE: mid-circuit measurement and replacement convert loss to erasure using additional hardware wu2022erasure; detection/replacement frequency is varied in simulations. (d) Logical error rates vs. SE rounds ($d=7$, $p=1\%$) using the delayed-erasure decoder. Comparable performance is observed across SE methods in regimes with short lifecycles. (e) Error thresholds vs. loss fraction, showcasing the improvement with loss for all SE methods. (f) Effective distance vs. loss fraction ($d=7$), improving with loss for all SE methods. (g) Space-time overhead to reach $P_L=10^{-12}$ at $p=0.5\%$ vs. loss fraction. Legends for (d-g) appear in (e).
• Figure 4: Linking thresholds to key metrics. (a) Thresholds for different SE methods for different loss and Pauli error rates. The curves are linear fits to numerical finite-size data, with the region below each curve representing the correctable region. (b) Thresholds as a function of lifecycle length for various SE methods, in the loss error only limit.
• Figure 5: Deep logical circuits with qubit loss. (a) A deep Clifford logical algorithm consisting of random logical single-qubit and transversal $CX$ gate layers, with periodic SE rounds at varying frequencies. (b, c) Circuit-level simulation results showing the logical error rate as a function of the number of SE rounds per transversal gate layer, for different loss fractions. ($p=1\%$, $d=5$, 24 layers). The SWAP SE method (c) effectively mitigates loss errors, restoring the optimal SE frequency observed in Pauli-dominated scenarios. In contrast, conventional SE (b) exhibits varying error correction regimes, where loss can either improve or degrade performance depending on the lifecycle length.