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Optics and Spectroscopy

Cubic Phase Gate Operation to Decrease the Error of Two-Mode Transformations

E. R. Zinatullin, S. B. Korolev, T. Yu. Golubeva

Published Mar 1, 2024• 0 citations
Publisher

Abstract

Abstract The paper considers a strategy to decrease the error of the two-mode entanglement transformation Controlled-Z by introducing non-Gaussian nodes in the cluster. Non-Gaussian nodes are obtained by using a cubic phase gate. We have shown that this strategy can significantly decrease the transformation error. The considered implementation of the Controlled-Z operation contains a teleportation scheme with the cubic phase gate. We have shown that the correct selection of phases during measurement allows for lower errors than in the initial teleportation protocol with the cubic phase gate and the original teleportation protocol.

DOI
10.1134/s0030400x24030196

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Abstract The paper considers a strategy to decrease the error of the two-mode entanglement transformation Controlled-Z by introducing non-Gaussian nodes in the cluster. Non-Gaussian nodes are obtained by using a cubic phase gate. We have shown that this strategy can significantly decrease the transformation error. The considered implementation of the Controlled-Z operation contains a teleportation scheme with the cubic phase gate. We have shown that the correct selection of phases during measurement allows for lower errors than in the initial teleportation protocol with the cubic phase gate and the original teleportation protocol.
In this paper we propose two strategies for decreasing the error of arbitrary single-mode Gaussian transformations implemented using one-way quantum computation on a four-node linear cluster state. We show that it is possible to minimize the error of the arbitrary single-mode Gaussian transformation by a proper choice of the weight coefficients of the cluster state. We modify the computation scheme by adding a non-Gaussian state obtained using a cubic phase gate as one of the nodes of the cluster. This further decreases the computation error. We evaluate the efficiencies of the proposed optimization schemes comparing the probabilities of the error correction of the quantum computations with and without optimizations. We show that for some transformations, the error probability can be reduced by up to 900 times.
Using the quantum teleportation in continuous variables as a test scheme, we compare two entangled transformations---mixing of signals on a beam splitter and by the controlled-ZZZ (cz) operation. We evaluate these transformations in terms of the errors added to teleported oscillators. We have shown that the cz operation leads to the lower error of teleportation. This error can be further reduced by choosing appropriate weight coefficients for the cz transforms. We have compared the errors of the theoretical cz scheme and its practical implementation in the optical design. Although the cz optical scheme adds intrinsic noise to the overall transformation, it is nevertheless possible to specify the parameters which provides a gain in comparison with the traditional teleportation protocol.
We experimentally demonstrate a controlled-phase gate for continuous variables using a cluster-state resource of four optical modes. The two independent input states of the gate are coupled with the cluster in a teleportation-based fashion. As a result, one of the entanglement links present in the initial cluster state appears in the two unmeasured output modes as the corresponding entangling gate acting on the input states. The genuine quantum character of this gate becomes manifest and is verified through the presence of entanglement at the output for a product two-mode coherent input state. By combining our gate with the recently reported module for single-mode Gaussian operations [R. Ukai et al., Phys. Rev. Lett. 106, 240504 (2011)], it is possible to implement any multimode Gaussian operation as a fully measurement-based one-way quantum computation.
We propose a modified quantum teleportation scheme to increase the teleportation accuracy by applying a cubic phase gate to the displaced squeezed state. We describe the proposed scheme in the Heisenberg picture, evaluating it from the point of view of adding an error in teleportation, and show that it allows achieving less error than the original scheme. Repeating the description in the Schr\"odinger picture, we find the range of the displacement values at which our conclusions are valid. Using the example of teleportation of the vacuum state and the squeezed states, we show that the scheme allows one to achieve high-fidelity values.
Abstract Quantum teleportation as the key strategy for quantum communication requires pure maximally shared entangled states among quantum nodes. In practice, quantum decoherence drastically degrades the shared entanglement during entanglement distribution, which is a serious challenge for the development of quantum networks. However, most of the decoherence control strategies proposed thus far are either resource-intensive or time-consuming. To overcome this obstacle, we enable noise-resistant teleportation through a noisy channel with a limited number of qubits and without applying time-consuming weak measurements. We apply a quantum gate control unit consisting of a controlled NOT gate and a rotation gate after the original teleportation protocol is accomplished. Furthermore, we demonstrate that a teleportation fidelity of unity is attainable when environment-assisted measurement is added to the proposed teleportation protocol via quantum gates. Moreover, we present an entanglement distribution process by employing the designed quantum gate control unit followed by the deterministic standard teleportation protocol to improve teleportation fidelity by establishing improved shared entanglement. Our performance analysis indicates that the proposed teleportation schemes offer a competitive fidelity and success probability compared with the conventional schemes and a recent weak measurement-based teleportation protocol.