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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 (10[1])that, when applied to spaces of dimensions m and n, produces one of dimension m times n. These objects can be divided (-5[1])into covariant and contravariant components. A generalization of trace on these objects (-5[1])called “contraction” applies when an index appears as both a subscript and superscript in Einstein notation. (10[1])A product named for these objects is denoted by a times symbol inside a circle. For 10 points, name these objects that correspond to multilinear maps (-5[1])and whose rank-2 representations are matrices. (0[1])■END■ (10[2]0[1])

ANSWER: tensors [accept tensor products or tensor networks; prompt on multilinear maps until read]
<UNC A, Physics>
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