# Convex optimization of programmable quantum computers

@article{Banchi2020ConvexOO, title={Convex optimization of programmable quantum computers}, author={Leonardo Banchi and Jason L. Pereira and Seth Lloyd and Stefano Pirandola}, journal={npj Quantum Information}, year={2020}, volume={6}, pages={1-10} }

A fundamental model of quantum computation is the programmable quantum gate array. This is a quantum processor that is fed by a program state that induces a corresponding quantum operation on input states. While being programmable, any finite-dimensional design of this model is known to be nonuniversal, meaning that the processor cannot perfectly simulate an arbitrary quantum channel over the input. Characterizing how close the simulation is and finding the optimal program state have been open…

## 25 Citations

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- Computer ScienceQuantum
- 2021

By leveraging the representation theory of the symmetry group action, it is shown how to remove redundancy in the program and proved that the resulting program register has minimum Hilbert space dimension.

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This work establishes universal limitations on the processing of both quantum states and channels, expressed in the form of no-go theorems and quantitative bounds for the manipulation of general quantum channel resources under the most general transformation protocols.

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An overview of quantum machine learning in the light of classical approaches is presented, discussing various technical contributions, strengths and similarities of the research work in this domain and elaborate upon the recent progress of different quantum machinelearning approaches, their complexity, and applications in various fields such as physics, chemistry and natural language processing.

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Comprehensive lower bounds for the overhead of any physical distillation protocol in terms of required channel uses are introduced, imposing strong limitations on the practical efficiency and cost of channel manipulation protocols.

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