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

Alberto Carlini, Akio Hosoya, Tatsuhiko Koike, Yosuke Okudaira

Research output: Contribution to journalArticle

19 Citations (Scopus)

Abstract

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

Original languageEnglish
Article number145302
JournalJournal of Physics A: Mathematical and Theoretical
Volume44
Issue number14
DOIs
Publication statusPublished - 2011 Apr 8

Fingerprint

Hamiltonians
Qubit
Ising
Hilbert spaces
Magnetic fields
synthesis
Hilbert space
Costs
costs
Synthesis
estimates
Spin Chains
magnetic fields
Local Field
Instantaneous
Modulo
Analytical Solution
interactions
Magnetic Field
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 CNOT between indirectly coupled qubits in a linear Ising chain. / Carlini, Alberto; Hosoya, Akio; Koike, Tatsuhiko; Okudaira, Yosuke.

In: Journal of Physics A: Mathematical and Theoretical, Vol. 44, No. 14, 145302, 08.04.2011.

Research output: Contribution to journalArticle

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