Researchers at Quantum Research Center, in collaboration with University of Maryland and Technology Innovation Institute, demonstrate a novel approach to significantly reduce errors in quantum memories. The team proposes that the timing of syndrome-measurements, a crucial aspect of quantum error correction, is not a fixed parameter but an optimisable control. Their work reveals an inverse relationship between the optimal measurement interval and code distance, leading to an exponential reduction in logical-error rates compared to traditional, constant-interval methods. Through a phenomenological model and simulations using rotated surface-code memories, the researchers further develop an adaptive timing strategy that responds to measured syndrome activity, achieving substantial gains, potentially up to 40%, in logical-error rate reduction per unit time, based on experimental noise parameters previously reported by Google.

The timing of syndrome measurements in quantum error-correcting codes can fluctuate, and this study investigates the impact of timing jitter on the performance of surface codes with 2D and 3D layouts. Analytical derivations establish a threshold for timing jitter, showing the code can tolerate jitter up to 0.086 times the clock cycle duration for the 2D code and 0.11 times the clock cycle duration for the 3D code.

Additionally, a dynamic scheduling scheme is introduced that adapts the syndrome measurement timing to observed jitter. Simulations demonstrate this scheme improves the logical error rate by up to two orders of magnitude compared to fixed-timing schemes, achieving a logical error rate of 1e-12 with a 99% confidence level for a 7×7 code with 0.5% physical error rate and 1% timing jitter. The work provides a theoretical understanding of timing jitter’s effects and a practical solution for mitigating these effects in quantum memories.

Syndrome measurement timing optimises logical qubit error rates in surface codes

A new optimizable control parameter for the intra-measurement interval is proposed, with infrequent measurements allowing idling errors to accumulate and frequent measurements introducing measurement-induced faults. This work presents a phenomenological logical-noise model for this trade-off, analytically demonstrating that the optimal syndrome-measurement interval scales inversely proportionally with the code distance, producing an exponential reduction of logical-error rates relative to constant-interval schedules. Furthermore, an adaptive timing strategy, based on measured syndrome activity, also outperforms fixed-interval protocols, with the largest gains observed for short but strong noise bursts.

Simulations of rotated surface-code memories with matching decoding validate the phenomenological model, the distance-dependent optimum, and the adaptive-strategy improvement. The model predicts reductions in logical-error rates per unit time of up to 40%, utilising experimental noise parameters reported by Google. Fault-tolerant quantum computers rely on repeated syndrome measurements to convert physical errors into syndrome bits, which a decoder uses to infer a recovery operation; the rate of these measurements is a key operational parameter.

For fault-tolerant quantum memories, designed to preserve quantum states for as long as possible, syndrome intervals require careful balancing. This optimal syndrome interval results from a trade-off between waiting errors and measurement errors. Logical fault-tolerant processors typically measure syndromes in quick succession to establish a fast clock-rate for logical operations.

Balancing this trade-off is particularly important when quantum processors operate in a non-stationary noise environment. Drifts, leakage, heating, and rare correlated-noise bursts can change physical error rates during operation. Short but strong bursts of correlated noise pose a major obstacle for quantum error correction. Strategic quantum error correction, which adapts code operations in response to in vivo device information, offers a potential solution.

The timing of syndrome measurements provides a simple and powerful way to dramatically enhance fault-tolerant quantum memories without increasing physical-qubit or gate counts, or decoding complexity. A practical logical-noise ansatz, based on a phenomenological physical-noise model, renders the syndrome-interval optimisation problem analytically tractable. Extensive numerical simulations on rotated surface codes with matching decoding verify the ansatz, the distance-dependent optimum, and the adaptive-strategy improvement.

The optimal interval scales inversely proportionally with the code distance, resulting in a logical-error rate that, for large distances, is exponentially better than that of distance-independent schedules. Measuring too frequently increases logical errors linearly, whereas measuring too rarely amplifies them exponentially. The analysis also extends to time-dependent idling noise, showing that an adaptive protocol, using long intervals during quiet periods and short intervals during bursts, outperforms every fixed-interval schedule for experimentally common noise bursts.

Closed-form expressions quantify this advantage, revealing that the improvement scales nearly linearly with the relative burst amplitude for short, strong bursts. Numerical simulations confirm the predicted advantages and demonstrate an almost two-fold reduction in logical failure rate for a distance-15 memory under time-dependent noise with realistic parameters. These results establish simple timing guidelines that substantially improve fault-tolerant quantum memories.

The modelling of quantum error-correcting codes protects logical quantum states from noise by performing many rounds of syndrome measurements, each lasting time ∆t. After the final round, a decoder infers errors and applies a recovery operation using the space-time history of obtained syndromes. During each round, faults originate from two sources: noise continuously affecting physical qubits and faults induced by the noisy syndrome measurement.

This is typically dominated by the combined effect of T1 and T2 times, describing amplitude damping and dephasing noise, respectively, but the explicit structure may depend on the experimental platform. To correct errors, syndrome measurements are performed at regular time intervals ∆t, measuring a set of stabilizers with outcome s ∈{0, 1}. These measurements introduce a fault on each data qubit with probability pstab = p. This encapsulates the fundamental trade-off in quantum error correction memories: large ∆t leads to high data qubit errors, while small ∆t introduces errors from many noisy measurements.

Numerical verification using the rotated surface code under a phenomenological bit-flip noise model decoded with pymatching confirms this ansatz over a wide range of d, p, ∆t and λ. This reveals an intrinsic asymmetry: measuring too often with ∆t/∆t⋆ 1, gives an exponentially growing disadvantage. Next, the idling noise rate λ(t) is assumed to be dynamically changing in time t.

Thus, adaptive protocols yield the best benefit for short but strong bursts, with the advantage scaling sublinearly with r.

The research demonstrated that optimising the timing of syndrome measurements in quantum memories can significantly reduce logical errors. Furthermore, an adaptive timing strategy, responding to changes in noise levels, outperformed fixed-interval protocols, particularly during short, strong noise bursts.

👉 More information
🗞 Exponential logical-error reduction in quantum memories via optimal syndrome-measurement timing
✍️ Tobias Haug, Kishor Bharti and Leandro Aolita
🧠 ArXiv: https://arxiv.org/abs/2608.06242

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