Constructions for quantum computing with symmetrized gates (pp0411-0429)
          Gabor Ivanyos, Attila B. Nagy, and Lajos Ronyai 
          doi: https://doi.org/10.26421/QIC8.5-4
Abstracts: 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.
Key words: Symmetrized gate, quantum computing, commutator