Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Arbitrary Two-qubit Computation In 23 Elementary Gates   Quantum circuits currently constitute a dominant model for quantum
computation. Our work addresses the problem of constructing quantum circuits to
implement an arbitrary given quantum computation, in the special case of two
qubits. We pursue circuits without ancilla qubits and as small a number of
elementary quantum gates as possible. Our lower bound for worst-case optimal
two-qubit circuits calls for at least 17 gates: 15 one-qubit rotations and 2
CNOTs. To this end, we constructively prove a worst-case upper bound of 23
elementary gates, of which at most 4 (CNOT) entail multi-qubit interactions.
Our analysis shows that synthesis algorithms suggested in previous work,
although more general, entail much larger quantum circuits than ours in the
special case of two qubits. One such algorithm has a worst case of 61 gates of
which 18 may be CNOTs. Our techniques rely on the KAK decomposition from Lie
theory as well as the polar and spectral (symmetric Shur) matrix decompositions
from numerical analysis and operator theory. They are related to the canonical
decomposition of a two-qubit gate with respect to the ``magic basis'' of
phase-shifted Bell states, published previously. We further extend this
decomposition in terms of elementary gates for quantum computation.

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The categories of this paper are: hep-lat
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The categories of this paper are: gr-qc
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The categories of this paper are: stat
30
The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn
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The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: nlin
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The categories of this paper are: supr-con
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The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
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The categories of this paper are: econ
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The categories of this paper are: hep-ph
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The categories of this paper are: math-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys