Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hamiltonian singular value transformation and inverse block encoding   The quantum singular value transformation is a powerful quantum algorithm
that allows one to apply a polynomial transformation to the singular values of
a matrix that is embedded as a block of a unitary transformation. This paper
shows how to perform the quantum singular value transformation for a matrix
that can be embedded as a block of a Hamiltonian. The transformation can be
implemented in a purely Hamiltonian context by the alternating application of
Hamiltonians for chosen intervals: it is an example of the Quantum Alternating
Operator Ansatz (generalized QAOA). We also show how to use the Hamiltonian
quantum singular value transformation to perform inverse block encoding to
implement a unitary of which a given Hamiltonian is a block. Inverse block
encoding leads to novel procedures for matrix multiplication and for solving
differential equations on quantum information processors in a purely
Hamiltonian fashion.

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The categories of this paper are: math-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
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The categories of this paper are: stat
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
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The categories of this paper are: solv-int
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The categories of this paper are: econ
27
The categories of this paper are: comp-gas