{% macro errorgenformula() %} {% if errorgen_type == "logTiG" %} G = G_0 e^{\mathbb{L}} {% elif errorgen_type == "logGTi" %} G = e^{\mathbb{L}} G_0 {% elif errorgen_type == "logG-logT" %} G = e^{\mathbb{L} + \log G_0} {% else %} ??? {% endif %} {% endmacro %}

Gate Error Generators

This tab presents the error generators for each of the estimated gates. Although these are not especially well-known in the literature, they are (in the pyGSTi authors' opinion) the most useful detailed diagnostic for gate errors. The error generator \mathbb{L} for a noisy gate G with ideal target G_0 is defined by writing {{ errorgenformula() }}. It can be thought of, more or less, as a Lindbladian superoperator that generates the error in the gate — with two caveats. First, it is not necessarily of strict Lindblad form, because the GST-estimated gates may not be CP, and because even if they are, not every CP map is "divisible" (and nondivisible maps are not generated by Lindblad evolution). Second, the generator reported here is a {% if errorgen_type == "logTiG" %} pre-gate generator, so it answers the question "If all the noise occurred before the ideal gate, what Lindbladian would generate it?" {% elif errorgen_type == "logGTi" %} post-gate generator, so it answers the question "If all the noise occurred after the ideal gate, what Lindbladian would generate it?" {% elif errorgen_type == "logG-logT" %} during-gate generator, so it answers the question "What Lindblad-type generate would produce this noise if it acted continuously during the gate?" Note that this does not necessarily give insight into physics producing the noise. {% else %} ??? {% endif %} Finally: the error generators are very definitely gauge-dependent, so caveat emptor (cross-validating any inferences drawn from these generators with some sort of gauge-invariant diagnostic is highly recommended).

Logic gate error generators The first column displays a heat map of the estimated error generator for each gate. This is (more or less) the Lindbladian \mathbb{L} that describes how the gate is failing to match the target. This error generator is defined by the equation {{ errorgenformula() }}. If it is zero, the estimated gate matches the corresponding ideal target gate. Note that the range of the color scale is dynamically adjusted. Subsequent columns show the result of projecting each generator onto some subspaces of the error generator space. Each corresponds to a different classes of well-known errors: Hamiltonian (coherent) errors, Pauli-stochastic errors, and affine (aka non-unital) errors. The Hamiltonian generators act by commutation with each Pauli basis element B_i, that is \rho \rightarrow -i[B_i, \rho]. Stochastic generators act by conjugation with each basis element, \rho \rightarrow B_i \rho B_i^\dagger. Affine generators act by projecting everything onto a particular basis element, \rho \rightarrow \mathrm{Tr}(\rho) B_i. Roughly speaking, the Hamiltonian projection corresponds precisely to the Hamiltonian that would produce the coherent part of the error, while the Pauli-stochastic generators correspond to the rates of all the Pauli errors (e.g., X errors, Z errors, their 2-qubit counterparts, or whatever is appropriate for the system being analyzed).
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