Time-optimal CNOT between indirectly coupled qubits in a linear Ising chain

Alberto Carlini, Akio Hosoya, Tatsuhiko Koike, Yosuke Okudaira

Research output: Contribution to journalArticlepeer-review

25 Citations (Scopus)


We give analytical solutions for the time-optimal synthesis of entangling gates between indirectly coupled qubits 1 and 3 in a linear spin chain of three qubits subject to an Ising Hamiltonian interaction with a symmetric coupling J plus a local magnetic field acting on the intermediate qubit. The energy available is fixed, but we relax the standard assumption of instantaneous unitary operations acting on single qubits. The time required for performing an entangling gate which is equivalent, modulo local unitary operations, to the CNOT(1, 3) between the indirectly coupled qubits 1 and 3 is , i.e. faster than a previous estimate based on a similar Hamiltonian and the assumption of local unitaries with zero time cost. Furthermore, performing a simple Walsh-Hadamard rotation in the Hilbert space of qubit 3 shows that the time-optimal synthesis of the CNOT(1, 3) (which acts as the identity when the control qubit 1 is in the state |0〉, while if the control qubit is in the state |1〉, the target qubit 3 is flipped as | 〉 → |∓〉) also requires the same time T.

Original languageEnglish
Article number145302
JournalJournal of Physics A: Mathematical and Theoretical
Issue number14
Publication statusPublished - 2011 Apr 8

ASJC Scopus subject areas

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


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