Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Efficient quantum tensor product expanders and unitary t-designs via the
  zigzag product   A classical t-tensor product expander is a natural way of formalising
correlated walks of t particles on a regular expander graph. A quantum t-tensor
product expander is a completely positive trace preserving map that is a
straightforward analogue of a classical t-tensor product expander. Interest in
these maps arises from the fact that iterating a quantum t-tensor product
expander gives us a unitary t-design, which has many applications to quantum
computation and information. We show that the zigzag product of a high
dimensional quantum expander (i.e. t = 1) of moderate degree with a moderate
dimensional quantum t-tensor product expander of low degree gives us a high
dimensional quantum t-tensor product expander of low degree. Previously such a
result was known only for quantum expanders i.e. t = 1.
  Using the zigzag product we give efficient constructions of quantum t-tensor
product expanders in dimension D where t = polylog(D). We then show how
replacing the zigzag product by the generalised zigzag product leads to
almost-Ramanujan quantum tensor product expanders i.e. having near-optimal
almost quadratic tradeoff between the degree and the second largest singular
value. Both the products give better tradeoffs between the degree and second
largest singular value than what was previously known for efficient
constructions.

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The categories of this paper are: eess
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The categories of this paper are: atom-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: bayes-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: math
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The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: nlin
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-th
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The categories of this paper are: math-ph