Journal
PHYSICAL REVIEW B
Volume 86, Issue 16, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevB.86.165113
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Funding
- US DOE [DE-FG02-97ER45639]
- Alexander von Humboldt foundation
- U.S. Department of Energy (DOE) [DE-FG02-97ER45639] Funding Source: U.S. Department of Energy (DOE)
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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.
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