Quantum Fourier transform of polarization photons mediated by weak cross-Kerr nonlinearity

Abstract

We present a scheme of two-photon quantum Fourier transform at first, where the controlled π∕2 phase gate and the Hadamard gates are applied. The indirect interaction between two photons can be realized through a coupling bus provided by a coherent state in Kerr media. Employing photon-number measurements and the corresponding classical feed-forward techniques, the task of low-error quantum Fourier transform can be fulfilled. With revision and modulation on the optical elements, controlled π∕2 n (n 2; 3; …) phase gates are constructed, and the multiphoton quantum Fourier transform can be achieved by integrating these controlled phase gates and Hadamard gates.

Photonic scheme of discrete quantum Fourier transform for quantum algorithms via quantum dots

“…Also, the affection of the inaccuracy influences the entire performance of quantum algorithms because QFT or DQFT is a main subroutine of quantum algorithms. Therefore, many researchers have proposed the QFT schemes via the nonlinearly optical devices, such as cross-Kerr nonlinearities (XKNLs) 17,25 , and optical cavities 15,27,31–33 . However, the experimental realization of strong XKNL is still a big challenge 75 .…”

“…However, the experimental realization of strong XKNL is still a big challenge 75 . And the decoherence effect, which can occurs the evolution of the mixed state after homodyne measurement, is also unavoidable when a coherent state is transmitted through a fiber in practice 17,25,36,69 . From this point of view, well-isolated qubits might not necessarily suffer from the same decoherence effects in Kerr medium.…”

“…Compared with the previous schemes 15,17,21,22,25,27,31–33 , our DQFT scheme consists of the QD-cavity systems (nonlinearly optical devices) to implement the CRk operations as the basic modules for the deterministic performance and simple expansion into multi-qubit DQFT. Moreover, in our scheme, the flying photons play the roles of qubits transferring quantum information, and QDs are the ancillary systems to efficiently perform the CRk operations for the applications of various quantum computations and algorithms.…”

“…In various quantum algorithms and quantum computations, such as quantum phase estimation algorithm 1–3 , the factoring problem 4–7 , the discrete logarithm problem 2,4,8,9 , and the hidden subgroup problem 10–12 , a discrete quantum Fourier transform (DQFT) 2,13–19 plays a critical role in accomplishing quantum information processing. Thus, for the experimental implementation of DQFT, a variety of physical resources have been used, including those based on linear optical systems 20–22 , nonlinear optical systems 17,23–25 , nuclear magnetic resonance or ion trap systems 26–29 , superconducting circuits 30 , and cavity-QED 15,31–33 .…”

Implementation of the quantum Fourier transform on a hybrid qubit–qutrit NMR quantum emulator

“…The quantum Fourier transform (QFT) needs to be specifically tailored for qudit computers as it plays a key role in several quantum algorithms such as factorization [27], quantum phase estimation [28] and the hidden subgroup problem [29]. An efficient decomposition of the QFT for qubits achieves an exponential speedup over the classical fast Fourier transform [30], and has been experimentally implemented by several groups on different physical systems [31][32][33][34][35]. Decompositions of the QFT for qudit systems have been worked out by several groups [36][37][38][39].…”