Fail Fast: Techniques Probe Rare Quantum Error Correction Events at 0.1×10⁻¹² Rates

Creating stable quantum computers demands exceptionally reliable qubits, capable of performing billions of operations without error, yet directly testing the performance of such advanced systems presents a significant challenge because failures become incredibly rare events. Michael Beverland, Malcolm Carroll, and Andrew Cross, alongside Theodore Yoder, all from IBM Quantum, address this problem by developing innovative techniques to probe these elusive errors in quantum error correction codes. Their work introduces three complementary methods to characterise the behaviour of these systems, even when failures are infrequent, allowing researchers to accurately predict performance at extremely low error rates. By applying these tools to advanced quantum codes, the team not only confirms the potential of recently proposed decoding strategies, but also identifies clear pathways towards building even more robust and reliable quantum computers.

Building on existing approaches to this problem, the team develops three complementary techniques to characterise the rare-event regime for general quantum low-density parity-check (qLDPC) codes under circuit noise.

Low Failure Rate Quantum Error Characterization

Scientists have developed three complementary techniques to accurately characterize quantum error correction systems, even when logical failure rates are extremely low, below 10 -12 , a regime inaccessible to standard simulation methods. This work addresses a critical challenge in building large-scale, fault-tolerant quantum computers where assessing the performance of highly accurate logical qubits is essential. The team focused on characterizing the failure spectrum, which details the fraction of fault sets of each size that lead to failure, and applied these techniques to distance-6, -12, and -18 bivariate bicycle codes under circuit noise. The research introduces a low-parameter ansatz, an educated guess, for the failure spectrum that empirically fits all quantum error correction systems studied, successfully predicting logical failure rates across all physical error rates.

This approach allows scientists to estimate performance without requiring an infeasibly large number of simulation runs, a common limitation of traditional Monte Carlo sampling. Furthermore, the team precisely computed the number of minimum-weight failing configurations by identifying min-weight logical operators within the syndrome measurement circuits. To improve convergence for systems with many inequivalent logical operators, scientists generalized the splitting method using multi-seeded Metropolis sampling. This technique estimates ratios of logical error rates across a sequence of physical error rates, providing a robust method for characterizing system performance. Experiments demonstrate strong low-error rate performance with the Relay decoder, while also revealing considerable scope for further improvement in decoding algorithms. The combination of these three techniques provides a comprehensive approach to characterizing quantum error correction systems and paves the way for building more reliable and scalable quantum computers.

Realistic Error Analysis of Quantum Codes

This research presents significant advances in characterizing the performance of quantum error correction codes, essential for building practical quantum computers. Scientists developed three complementary techniques to assess low-density parity-check codes under realistic circuit noise, focusing on the challenging rare-event regime where logical failures are infrequent. The team proposed a new approach to modelling the failure spectrum, accurately predicting logical error rates across various physical error rates and code distances. Furthermore, they precisely calculated the number of minimal-weight failing configurations, providing deeper insight into error behaviour.

To improve the convergence of simulations, the researchers generalized a splitting method, enabling more reliable analysis of systems with numerous logical operators. Applying these tools to bicycle codes of different distances, they demonstrated strong performance with the Relay decoder, while also identifying areas for further optimization. The study acknowledges limitations in the splitting method, specifically challenges in achieving adequate mixing between failing sectors in certain simulations, and suggests that modifying the transition function may improve convergence. Future work could focus on refining this transition function to reduce error bars and enhance the accuracy of simulations. These findings represent a crucial step towards validating and improving quantum error correction strategies, paving the way for more robust and scalable quantum computation.