Juan Gonzalez De Mendoza

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

A gauge-invariant theory of small Markovian errors in quantum gate sets

Noisy logic operations on a quantum computational register -- e.g., one or more qubits -- can be described by transfer matrices (a.k.a. CPTP maps or superoperators) that act linearly on the density matrix representing the register's quantum state. Collectively, these operations form a gate set. Gate sets have a gauge freedom; many gate sets that appear different actually predict the same experimental outcomes. A property of a gate set can be observable (and thus physically relevant) only if it is gauge-invariant. Unfortunately, no good gauge-invariant parameterizations of gate sets are known. We introduce the next best thing, a perturbative gauge-invariant parameterization of small Markovian errors in gate sets. We construct vector spaces of properties that are first-order gauge-invariant (FOGI). We show how to construct and understand FOGI properties, how to use them as coordinates to parameterize gate sets without gauge freedom, and how to extract approximately gauge-invariant error metrics.

quant-ph↗