Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics

@article{Gilyn2018QuantumSV,
  title={Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics},
  author={Andr{\'a}s Gily{\'e}n and Yuan Su and Guang Hao Low and Nathan Wiebe},
  journal={CoRR},
  year={2018},
  volume={abs/1806.01838}
}
Quantum computing is powerful because unitary operators describing the time-evolution of a quantum system have exponential size in terms of the number of qubits present in the system. We develop a new “Singular value transformation” algorithm capable of harnessing this exponential advantage, that can apply polynomial transformations to the singular values of a block of a unitary, generalizing the optimal Hamiltonian simulation results of Low and Chuang [LC17a]. The proposed quantum circuits… CONTINUE READING
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