73,917 research outputs found
Quantum Circuits for Measuring Levin-Wen Operators
We construct quantum circuits for measuring the commuting set of vertex and
plaquette operators that appear in the Levin-Wen model for doubled Fibonacci
anyons. Such measurements can be viewed as syndrome measurements for the
quantum error-correcting code defined by the ground states of this model (the
Fibonacci code). We quantify the complexity of these circuits with gate counts
using different universal gate sets and find these measurements become
significantly easier to perform if n-qubit Toffoli gates with n = 3,4 and 5 can
be carried out directly. In addition to measurement circuits, we construct
simplified quantum circuits requiring only a few qubits that can be used to
verify that certain self-consistency conditions, including the pentagon
equation, are satisfied by the Fibonacci code.Comment: 12 pages, 13 figures; published versio
Short Cycle Covers of Cubic Graphs and Graphs with Minimum Degree Three
The Shortest Cycle Cover Conjecture of Alon and Tarsi asserts that the edges
of every bridgeless graph with edges can be covered by cycles of total
length at most . We show that every cubic bridgeless graph has a
cycle cover of total length at most and every bridgeless
graph with minimum degree three has a cycle cover of total length at most
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