351 research outputs found
A sufficient condition for a balanced bipartite digraph to be hamiltonian
We describe a new type of sufficient condition for a balanced bipartite
digraph to be hamiltonian. Let be a balanced bipartite digraph and be
distinct vertices in . dominates a vertex if
and ; in this case, we call the pair dominating. In
this paper, we prove that a strong balanced bipartite digraph on
vertices contains a hamiltonian cycle if, for every dominating pair of vertices
, either and or and
. The lower bound in the result is sharp.Comment: 12 pages, 3 figure
Independent sets and non-augmentable paths in arc-locally in-semicomplete digraphs and quasi-arc-transitive digraphs
AbstractA digraph is arc-locally in-semicomplete if for any pair of adjacent vertices x,y, every in-neighbor of x and every in-neighbor of y either are adjacent or are the same vertex. A digraph is quasi-arc-transitive if for any arc xy, every in-neighbor of x and every out-neighbor of y either are adjacent or are the same vertex. Laborde, Payan and Xuong proposed the following conjecture: Every digraph has an independent set intersecting every non-augmentable path (in particular, every longest path). In this paper, we shall prove that this conjecture is true for arc-locally in-semicomplete digraphs and quasi-arc-transitive digraphs
Universality of universal single-qubit-gate decomposition with coherent errors
To generate arbitrary one- and two-qubit gates, the universal decompositions
are usually used in quantum computing, and the universality of these
decompositions has been demonstrated. However, in realistic experiments, gate
errors may affect the universality of the universal decompositions. Here, we
focus on the single-qubit-gate decomposition scheme and study the
coherent-error effects on universality. We prove that, in the parameter space
which we studied, some kinds of coherent errors will not affect the original
universality, but some others will destroy it. We provide the definition and
analytical solutions for universality with coherent errors and propose methods
to resume the accuracy of the operations with coherent errors based on our
analysis. We also give the analytical results for three kinds of fidelities,
which provide another metric for universality and comprehensively depict the
resilience of the decomposition scheme with various kinds of coherent errors.
Our work introduces a different way of thinking for quantum compilation than
existing methods
trans-Bis(4-methoxyÂthioÂphenolato-ÎșS)bisÂ(trimethylÂphosphine-ÎșP)nickel(II)
The title compound, [Ni(C7H7OS)2(C3H9P)2], was obtained as a product of the reaction of [NiMe2(PMe3)3] with two molar equivalents of 4-methoxyÂthioÂphenol in diethyl ether. The compound is stable in the air for several hours, but rapidly decomposes at room temperature in solution. The Ni atom displays a square-planar coordination with two P-donor atoms lying in trans positions. The benzene rings of the thioÂphenolate ligands are almost perpendicular to the square coordination plane, making dihedral angles of 80.43â
(4) and 72.60â
(4)°
Extremal digraphs on Meyniel-type condition for hamiltonian cycles in balanced bipartite digraphs
Let be a strong balanced digraph on vertices. Adamus et al. have
proved that is hamiltonian if whenever
and . The lower bound is tight. In this paper, we shall
show that the extremal digraph on this condition is two classes of digraphs
that can be clearly characterized. Moreover, we also show that if
whenever and , then is
traceable. The lower bound is tight.Comment: 16 page
Control and mitigation of microwave crosstalk effect with superconducting qubits
Improving gate performance is vital for scalable quantum computing. The
universal quantum computing also requires the gate fidelity to reach a high
level. For superconducting quantum processor, which operates in the microwave
band, the single-qubit gates are usually realized with microwave driving. The
crosstalk between microwave pulses is a non-negligible error source. In this
article, we propose an error mitigation scheme to address this crosstalk issue
for single-qubit gates. There are three steps in our method. First, by
controlling the detuning between qubits, the microwave induced classical
crosstalk error can be constrained within the computational subspace. Second,
by applying the general decomposition procedure, arbitrary single-qubit gate
can be decomposed as a sequence of and virtual Z gates. Finally, by
optimizing the parameters in virtual Z gates, the error constrained in the
computational space can be corrected. Using our method, no additional
compensation signals are needed, arbitrary single-qubit gate time will not be
prolonged, and the circuit depth containing simultaneous single-qubit gates
will also not increase. The simulation results show that, in specific regime of
qubit-qubit detuning, the infidelities of simultaneous single-qubit gates can
be as low as which without microwave crosstalk
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