Quantum and Circuits

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1 \begingroup\small
2 
3 \begin{longtable}{@{}L{.25\textwidth}L{.66\textwidth}@{}}
4 \toprule
5 Term & Meaning\\
6 \midrule
7 \endfirsthead
8 \toprule
9 Term & Meaning\\
10 \midrule
11 \endhead
12 Active packet & A symmetry sector or representation component reached by the input and gates.\\
13 Approximate packet & A subspace or representation that is not exactly invariant but has certified leakage.\\
14 Compressed packet & A packet whose states are represented by a compact classical data structure rather than explicit amplitudes.\\
15 Coherence block & $P_\alpha\rho P_\beta$ with possibly distinct left and right packet labels.\\
16 Equitable partition & A graph partition whose cells have uniform neighbor counts, yielding an invariant quotient subspace.\\
17 Global interference & Dependence of the output on coherent phase relations among many contributions or packets.\\
18 Invariant packet & A subspace mapped into itself by every gate in the declared circuit decomposition.\\
19 Leakage & Amplitude or probability transferred outside a proposed active representation.\\
20 Multiplicity space & Repeated-copy factor accompanying an irreducible representation in a group decomposition.\\
21 Orbit state & Normalized uniform superposition over one group orbit of basis states or graph vertices.\\
22 Packet transfer graph & Directed graph recording nonzero blocks $P_\alpha G P_\beta$.\\
23 Symmetry collapse & Exact or controlled replacement of a quantum evolution by a polynomial classical representation using symmetry or related compression.\\
24 Uniform circuit family & Circuits generated from the input by a deterministic polynomial-time procedure.\\
25 \bottomrule
26 \end{longtable}
27 \endgroup

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