Quantum Fourier Transform in Oscillating Modes

  1. Qi-Ming Chen,
  2. Frank Deppe,
  3. Re-Bing Wu,
  4. Luyan Sun,
  5. Yu-xi Liu,
  6. Yuki Nojiri,
  7. Stefan Pogorzalek,
  8. Michael Renger,
  9. Matti Partanen,
  10. Kirill G. Fedorov,
  11. Achim Marx,
  12. and Rudolf Gross
Quantum Fourier transform (QFT) is a key ingredient of many quantum algorithms. In typical applications such as phase estimation, a considerable number of ancilla qubits and gates are used to form a Hilbert space large enough for high-precision results. Qubit recycling reduces the number of ancilla qubits to one, but it is only applicable to semi-classical QFT and requires repeated measurements and feedforward within the coherence time of the qubits. In this work, we explore a novel approach based on resonators that forms a high-dimensional Hilbert space for the realization of QFT. By employing the perfect state-transfer method, we map an unknown multi-qubit state to a single resonator, and obtain the QFT state in the second oscillator through cross-Kerr interaction and projective measurement. A quantitive analysis shows that our method allows for high-dimensional and fully-quantum QFT employing the state-of-the-art superconducting quantum circuits. This paves the way for implementing various QFT related quantum algorithms.
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