Time-optimal unitary operations in Ising chains

Unequal couplings and fixed fidelity

Alberto Carlini, Tatsuhiko Koike

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

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
Volume46
Issue number4
DOIs
Publication statusPublished - 2013 Feb 1

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Unequal
Ising
Fidelity
Qubit
Hamiltonians
optimal control
Magnetic fields
Instantaneous
Optimal Control
Exact Solution
Magnetic Field
Numerical Solution
costs
Target
Costs
Zero
Energy
magnetic fields
energy

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics
  • Modelling and Simulation
  • Statistics and Probability

Cite this

Time-optimal unitary operations in Ising chains : Unequal couplings and fixed fidelity. / Carlini, Alberto; Koike, Tatsuhiko.

In: Journal of Physics A: Mathematical and Theoretical, Vol. 46, No. 4, 045307, 01.02.2013.

Research output: Contribution to journalArticle

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