arXiv subjects

Jalan A. Ziyad

Publications and source records attributed to Jalan A. Ziyad.

3 recordsLinked to original sources

arXiv2026

Logical gate set tomography

Quantum error correction (QEC) can strongly suppress noise, but predicting whether a computation succeeds requires understanding not only how much effective noise persists after QEC, but what form that noise takes. To thoroughly characterize this noise, we introduce logical gate set tomography (``logical GST''). Logical GST produces detailed representations of noisy logical operations that can be used to derive higher-level metrics, such as gate fidelity and diamond distance, and to test for non-Markovian and coherent logical errors. We use logical GST to obtain the first full, self-consistent characterization of a universal single-qubit logical gate set, implemented in the seven-qubit Steane code using Quantinuum System Model H1, a 20-qubit trapped-ion quantum processor. In the experimental data from H1, logical GST identified predominantly logical Pauli-stochastic errors, found no evidence of logical non-Markovianity, and detected weak potential signatures of coherent logical error. By contrast, higher-shot datasets generated with Quantinuum's detailed system emulator, identify mechanisms for weak but statistically significant logical non-Markovianity and strong evidence of coherent logical error. Finally, we use logical GST to perform error attribution with the system emulator, revealing how specific physical error sources shape logical error mechanisms.

quant-ph↗

arXiv2026

Emergent Non-Markovianity in Logical Qubit Dynamics

Logical qubits encoded in quantum error correcting codes can exhibit non-Markovian dynamical evolution, even when the underlying physical noise is Markovian. To understand this emergent non-Markovianity, we define a Markovianity condition appropriate to logical gate operations, and study it by relating logical operations to their physical implementation (operations on the data qubits into which the logical qubit is encoded). We apply our analysis to small quantum codes, and show that they exhibit non-Markovian dynamics even for very simple physical noise models. We show that non-Markovianity can emerge from Markovian physical operations if (and only if) the physical qubits are not necessarily returned to the code subspace after every round of QEC. In this situation, the syndrome qubits can act as a memory, mediating time correlations and enabling violation of the Markov condition. We quantify the emergent non-Markovianity in simple examples, and propose sufficient conditions for reliable use of gate-based characterization techniques like gate set tomography in early fault-tolerant quantum devices.

quant-ph↗

arXiv2025

Constructing an approximate logical Markovian model of consecutive QEC cycles of a stabilizer code

As quantum error correction (QEC) experiments continue to make rapid progress, there is increased interest in designing experiments with guarantees of logical performance. At present, one difficulty is the lack of a clear connection between logical performance and the low-level error models. In this work, we take an important step toward addressing this issue by proving that consecutive QEC cycles of a stabilizer code with Pauli stochastic noise and with a single-cycle infidelity $ε_1 \leq 1/64$ admit an approximate logical Markovian model, meaning that consecutive noisy QEC cycles can be modeled by a memoryless error process acting only on the logical subsystem. The approximate logical Markovian model can be computed from the low-level error model, and the deviations from the true behavior are exponentially suppressed in the number of QEC cycles. Consequently, we expect that the approximate logical Markovian model will be both a useful tool for logical characterization and an aid for designing stabilizer-code implementations with guarantees of logical performance.

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