Time-optimal unitary operations in Ising chains: Unequal couplings and fixed fidelity

Alberto Carlini, Tatsuhiko Koike

Research output: Contribution to journalArticlepeer-review

21 Citations (Scopus)


We analytically determine the minimal time and the optimal control laws required for the realization, up to an assigned fidelity and with a fixed energy available, of entangling quantum gates (CNOT) between indirectly coupled qubits of a trilinear Ising chain. The control is coherent and open loop, and it is represented by a local and continuous magnetic field acting on the intermediate qubit. The time cost of this local quantum operation is not restricted to be zero. When the matching with the target gate is perfect (fidelity equal to 1), we provide exact solutions for the case of equal Ising coupling. For the more general case when some error is tolerated (fidelity smaller than 1), we give perturbative solutions for unequal couplings. Comparison with previous numerical solutions for the minimal time to generate the same gates with the same Ising Hamiltonian but with instantaneous local controls shows that the latter are not time optimal.

Original languageEnglish
Article number045307
JournalJournal of Physics A: Mathematical and Theoretical
Issue number4
Publication statusPublished - 2013 Feb 1

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modelling and Simulation
  • Mathematical Physics
  • General Physics and Astronomy


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