Quantum Circuits for Isometries

@article{Iten2016QuantumCF,
  title={Quantum Circuits for Isometries},
  author={R. Iten and R. Colbeck and I. Kukuljan and J. Home and M. Christandl},
  journal={Physical Review A},
  year={2016},
  volume={93},
  pages={032318}
}
We consider the decomposition of arbitrary isometries into a sequence of single-qubit and controlled-not (cnot) gates. In many experimental architectures, the cnot gate is relatively costly and hence we aim to keep the number of these as low as possible. We derive a theoretical lower bound on the number of cnot gates required to decompose an arbitrary isometry from $m$ to $n$ qubits and give three explicit gate decompositions that achieve this bound up to a factor of about 2 in the leading… Expand
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