Classically-Controlled Quantum Computation
<|reference_start|>Classically-Controlled Quantum Computation: Quantum computations usually take place under the control of the classical world. We introduce a Classically-controlled Quantum Turing Machine (CQTM) which is a Turing Machine (TM) with a quantum tape for acting on quantum data, and a classical transition function for a formalized classical control. In CQTM, unitary transformations and measurements are allowed. We show that any classical TM is simulated by a CQTM without loss of efficiency. The gap between classical and quantum computations, already pointed out in the framework of measurement-based quantum computation is confirmed. To appreciate the similarity of programming classical TM and CQTM, examples are given.<|reference_end|>
@article{perdrix2004classically-controlled,
    title={Classically-Controlled Quantum Computation},
    author={Simon Perdrix, Philippe Jorrand},
    journal={Math. Struct. in Comp. Science, 16:601-620, 2006},
    year={2004},
    doi={10.1017/S096012950600538X},
    archivePrefix={arXiv},
    eprint={quant-ph/0407008},
    primaryClass={quant-ph cs.CC}
}