### 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 language | English |
---|---|

Article number | 145302 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 44 |

Issue number | 14 |

DOIs | |

Publication status | Published - 2011 Apr 8 |

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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

*Journal of Physics A: Mathematical and Theoretical*,

*44*(14), [145302]. https://doi.org/10.1088/1751-8113/44/14/145302

**Time-optimal CNOT between indirectly coupled qubits in a linear Ising chain.** / Carlini, Alberto; Hosoya, Akio; Koike, Tatsuhiko; Okudaira, Yosuke.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and Theoretical*, vol. 44, no. 14, 145302. https://doi.org/10.1088/1751-8113/44/14/145302

}

TY - JOUR

T1 - Time-optimal CNOT between indirectly coupled qubits in a linear Ising chain

AU - Carlini, Alberto

AU - Hosoya, Akio

AU - Koike, Tatsuhiko

AU - Okudaira, Yosuke

PY - 2011/4/8

Y1 - 2011/4/8

N2 - 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

AB - 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

UR - http://www.scopus.com/inward/record.url?scp=79953699699&partnerID=8YFLogxK

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U2 - 10.1088/1751-8113/44/14/145302

DO - 10.1088/1751-8113/44/14/145302

M3 - Article

VL - 44

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 14

M1 - 145302

ER -