Quantum Circuits for Measuring Levin-Wen Operators

Abstract

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.

12 pages, 13 figures; published version

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• Quantum and classical spin network algorithms for $q$-deformed Kogut-Susskind gauge theories
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• Universal logical gates with constant overhead: instantaneous Dehn twists for hyperbolic quantum codes
• Thermalization, Error-Correction, and Memory Lifetime for Ising Anyon Systems
• Quantum Origami: Transversal Gates for Quantum Computation and Measurement of Topological Order
• Analytic asymptotic performance of topological codes
• Classical Simulation of Quantum Error Correction in a Fibonacci Anyon Code
• Simulating the Transverse Ising Model on a Quantum Computer: Error Correction with the Surface Code
• Simulating topological tensor networks with Majorana qubits
• Instantaneous braids and Dehn twists in topologically ordered states
• Quasi-exact quantum computation
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• Universal Logical Gates on Topologically Encoded Qubits via Constant-Depth Unitary Circuits
• Systematically generated two-qubit anyon braids
• Theory of quasi-exact fault-tolerant quantum computing and valence-bond-solid codes
• Effective models of doped quantum ladders of non-Abelian anyons
• Methodology for bus layout for topological quantum error correcting codes
• Optimized Topological Quantum Compilation of Three-Qubit Controlled Gates in the Fibonacci Anyon Model: A Controlled-Injection Approach
• Hardness of decoding quantum stabilizer codes
• Universal fault tolerant quantum computation in 2D without getting tied in knots