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

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

PlayerTeamOpponentPositionValue
Peter BallasMichigan DCarnegie Mellon A61-5
Calvin BostlemanOhio State AKenyon7010
Leo TaoMichigan CMichigan State72-5
Mitchell IndekMichigan BOhio State B74-5
Yashwanth BajjiMichigan ACase Western B10610
Jayden KuCarnegie Mellon BCase Western A125-5
David NiemanCarnegie Mellon AMichigan D12810
Aditya PatnaikOhio State BMichigan B12810

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TournamentEditionTUHConv. %Neg %Average Buzz
California2025-02-013100%33%88.33
Florida2025-02-012100%0%80.00
Great Lakes2025-02-01667%67%108.00
Lower Mid-Atlantic2025-02-01667%50%99.00
Midwest2025-02-016100%33%92.83
North2025-02-013100%0%74.67
Northeast2025-02-01580%0%78.50
Overflow2025-02-01560%40%94.67
South Central2025-02-012100%0%78.50
Southeast2025-02-013100%0%64.67
UK2025-02-011090%40%109.22
Upper Mid-Atlantic2025-02-01786%14%89.33
Upstate NY2025-02-01367%0%84.00