### 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 language | English |
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Article number | 045307 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 46 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2013 Feb 1 |

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### 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.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and Theoretical*, vol. 46, no. 4, 045307. https://doi.org/10.1088/1751-8113/46/4/045307

}

TY - JOUR

T1 - Time-optimal unitary operations in Ising chains

T2 - Unequal couplings and fixed fidelity

AU - Carlini, Alberto

AU - Koike, Tatsuhiko

PY - 2013/2/1

Y1 - 2013/2/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84872714347&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84872714347&partnerID=8YFLogxK

U2 - 10.1088/1751-8113/46/4/045307

DO - 10.1088/1751-8113/46/4/045307

M3 - Article

AN - SCOPUS:84872714347

VL - 46

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 4

M1 - 045307

ER -