Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Checking Equivalence of Quantum Circuits and States   Quantum computing promises exponential speed-ups for important simulation and
optimization problems. It also poses new CAD problems that are similar to, but
more challenging, than the related problems in classical (non-quantum) CAD,
such as determining if two states or circuits are functionally equivalent.
While differences in classical states are easy to detect, quantum states, which
are represented by complex-valued vectors, exhibit subtle differences leading
to several notions of equivalence. This provides flexibility in optimizing
quantum circuits, but leads to difficult new equivalence-checking issues for
simulation and synthesis. We identify several different equivalence-checking
problems and present algorithms for practical benchmarks, including quantum
communication and search circuits, which are shown to be very fast and robust
for hundreds of qubits.

18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
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The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
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The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph