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Universal quantum computation and leakage reduction in the 3-qubit decoherence free subsystem. (English) Zbl 1238.81072

Summary: We describe exchange-only universal quantum computation and leakage reduction in the 3-qubit decoherence free subsystem (DFS). We discuss the angular momentum structure of the DFS, the proper forms for the DFS CNOT and leakage reduction operators in the total angular momentum basis, and new exchange-only pulse sequences for the CNOT and leakage reduction operators. Our new DFS CNOT sequence requires 22 pulses in 13 time steps. The DFS leakage reduction sequence, the first explicit leakage reduction sequence of its kind, requires 30 pulses in 20 time steps. Although the search for sequences was performed numerically using a genetic algorithm, the solutions presented here are exact, with closed-form expressions.

MSC:

81P68 Quantum computation
81V22 Unified quantum theories
81Q37 Quantum dots, waveguides, ratchets, etc.
81V65 Quantum dots as quasi particles
03C05 Equational classes, universal algebra in model theory
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