# Methodology for quantum logic gate construction

@article{Zhou2000MethodologyFQ, title={Methodology for quantum logic gate construction}, author={Xinlan Zhou and Debbie W. Leung and Isaac L. Chuang Stanford University and Ibm Almaden Research Center}, journal={Physical Review A}, year={2000}, volume={62}, pages={052316} }

We present a general method to construct fault-tolerant quantum logic gates with a simple primitive, which is an analog of quantum teleportation. The technique extends previous results based on traditional quantum teleportation @Gottesman and Chuang, Nature ~London! 402, 390 ~1999!# and leads to straightforward and systematic construction of many fault-tolerant encoded operations, including the p/8 and Toffoli gates. The technique can also be applied to the construction of remote quantum…

## 91 Citations

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The gate synthesis algorithm introduced in this work, based on Dijkstra's algorithm, generates cost-optimal sequences for single-qubit target gates and supports arbitrary universal sets of single- qubit base gates with individually assigned cost values.

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It is proved that no universal set of transversal logic gates exists for GF(4)-additive quantum codes, and this result strongly supports the idea that additional quantum techniques are necessary to achieve universal fault-tolerant quantum computation on additive codes.

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This work provides general circuits that can be used to implement general circuits relevant to quantum error correction, measurement-based quantum computation and Bell state discrimination across a quantum network involving multiple parties.

### Fault-tolerant circuit synthesis for universal fault-tolerant quantum computing

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A quantum circuit synthesis algorithm for implementing universal fault-tolerant quantum computing based on concatenated codes and needs to recall faultTolerant protocols such as syndrome measure and encoder implicitly include classical control processing conditioned on the measurement outcomes.

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