### Abstract

We investigate constructions for simulating quantum computers with a polynomial slowdown on ensembles composed of qubits on which symmetrized versions of one- and two-qubit gates can be performed. The simulation is based on taking Lie commutators of symmetrized Hamiltonians to extract Hamiltonians at desired local positions. During the simulation, only a part of the qubits can be used for storing information, the others are left unchanged by the commutators. We propose constructions for various symmetry groups where a pretty large fraction of the qubits can be used. As a few of the other qubits need to be set to one, our construction requires individual initialization of some of the qubits.

Original language | English |
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Pages (from-to) | 411-429 |

Number of pages | 19 |

Journal | Quantum Information and Computation |

Volume | 8 |

Issue number | 5 |

Publication status | Published - May 1 2008 |

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### Keywords

- Commutator
- Quantum computing
- Symmetrized gate

### ASJC Scopus subject areas

- Theoretical Computer Science
- Statistical and Nonlinear Physics
- Nuclear and High Energy Physics
- Mathematical Physics
- Physics and Astronomy(all)
- Computational Theory and Mathematics

### Cite this

*Quantum Information and Computation*,

*8*(5), 411-429.