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Specific representations of these mathematical objects called “spiders” are generators of a string diagram in ZX-calculus. Quantum circuits are represented using these objects in networks that can be described using Penrose notation. A multi-particle Hilbert space is constructed by applying an operation named for these objects that, when (10[1])applied to spaces of dimensions m and n, produces one of dimension m times n. These objects (-5[1])can be divided into covariant and contravariant components. A generalization of trace on these objects (10[1]-5[1])called “contraction” applies when (10[1])an index appears as both a subscript and superscript in Einstein notation. A product named for these objects is denoted by a times symbol (10[1])inside a circle. For 10 points, name these objects (10[1])that correspond to multilinear maps and whose rank-2 representations (10[1])are matrices. ■END■

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