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Quantum Fourier transform (QFT) is a key ingredient of many quantum algorithms where a considerable amount of ancilla qubits and gates are often needed to form a Hilbert space large enough for high-precision results. Qubit recycling reduces the number of ancilla qubits to one but imposes the requirement of repeated measurements and feedforward within the coherence time of the qubits. Moreover, recycling only applies to certain cases where QFT can be carried out in a semi-classical way. Here, we report a novel approach based on two harmonic resonators which form a high-dimensional Hilbert space for the realization of QFT. By employing the all-resonant and perfect state-transfer methods, we develop a protocol that transfers an unknown multi-qubit state to one resonator. QFT is performed by the free evolution of the two resonators with a cross-Kerr interaction. Then, the fully-quantum result can be localized in the second resonator by a projective measurement. Qualitative analysis shows that a 2^10-dimensional QFT can be realized in current superconducting quantum circuits which paves the way for implementing various quantum algorithms in the noisy intermediate-scale quantum (NISQ) era.
The Quantum Fourier Transformation ($QFT$) is a key building block for a whole wealth of quantum algorithms. Despite its proven efficiency, only a few proof-of-principle demonstrations have been reported. Here we utilize $QFT$ to enhance the perf
Fourier transform spectroscopy with classical interferometry corresponds to the measurement of a single-photon intensity spectrum from the viewpoint of the particle nature of light. In contrast, the Fourier transform of two-photon quantum interferenc
Quantum computers will allow calculations beyond existing classical computers. However, current technology is still too noisy and imperfect to construct a universal digital quantum computer with quantum error correction. Inspired by the evolution of
In this Letter, we present a physical scheme for implementing the discrete quantum Fourier transform in a coupled semiconductor double quantum dot system. The main controlled-R gate operation can be decomposed into many simple and feasible unitary tr
The self-learning Metropolis-Hastings algorithm is a powerful Monte Carlo method that, with the help of machine learning, adaptively generates an easy-to-sample probability distribution for approximating a given hard-to-sample distribution. This pape