Quantum Circuits Architecture

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This is the case of frequency standards (where one needs to estimate a phase-shift of a two-level oscillator), or of clock synchronization. The encoding information into parametrized unitary transformations is also exploited in quantum information tasks, e.g. in some quantum cryptographic protocols and quantum algorithms

Cited in the paper.

Here we consider only finite dimensions, and denote the linear space of operators on 𝖧 {\sf H} as 𝖫𝗂𝗇 ⁡ ( 𝖧 ) {\sf Lin(H)}

Cited in the paper.

The map 𝒞 {\mathscr{C}} has to preserve positivity of quantum states even when acting on a part of a compound system

Cited in the paper.

This can be proved within an axiomatic introduction of combs and supermaps, where a realization theorem holds stating that any CP supermap from combs to combs has a physical scheme corresponding to another comb

Cited in the paper.

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