The simplified quantum circuits for implementing quantum teleportation

TL;DR

This work tackles the resource intensity of quantum teleportation circuits by developing simplified implementations across diverse entangled channels (GHZ, cluster states, Brown, Borras, and entanglement swapping). By applying circuit identities and absorbing certain operations, the authors achieve substantial reductions in gate-count, cost, and depth, while eliminating the need for feed-forward recover operations. The proposed schemes are validated experimentally on IBM’s quantum hardware, with quantum-state tomography showing fidelities above $0.9$ for the simplified circuits. The results offer practical improvements for scalable quantum communication and networked quantum information processing on near-term devices.

Abstract

It is crucial to design quantum circuits as small as possible and as shallow as possible for quantum information processing tasks. We design quantum circuits with simplified gate-count, cost, and depth for implementing quantum teleportation among various entangled channels. Here the gate-count/cost/depth of the Greenberger-Horne-Zeilinger-based quantum teleportation is reduced from 10/6/8 to 9/4/6, the two-qubit-cluster-based quantum teleportation is reduced from 9/4/5 to 6/3/5, the three-qubit-cluster-based quantum teleportation is reduced from 12/6/7 to 8/4/5, the Brown-based quantum teleportation is reduced from 25/15/17 to 18/8/7, the Borras-based quantum teleportation is reduced from 36/25/20 to 15/8/11, and the entanglement-swapping-based quantum teleportation is reduced from 13/8/8 to 10/5/5. Note that, no feed-forward recover operation is required in the simplified schemes. Moreover, the experimentally demonstrations on IBM quantum computer indicate that our simplified and compressed schemes can be realized with good fidelity.

Figures (20)

• Figure 1: Legend description.book
• Figure 2: The original GHZ-based quantum teleportation.old$|M \rangle =\alpha|0\rangle + \beta|1\rangle$, and it can be implemented by employing one fundamental single-qubit gate. Here $|a \rangle$, $|b\rangle$, and $|c\rangle$ refer to $|0\rangle$.
• Figure 3: The simplified GHZ-based quantum teleportation. The single-qubit message can be implemented by employing three single-qubit rotations. Therefore, the Hadamard gate $H$ in dashed box can be absorbed by the neighborhood $|M\rangle$. Here $|a \rangle$, $|b\rangle$, and $|c\rangle$ refer to $|0\rangle$.
• Figure 4: The original two-qubit-cluster-based quantum teleportation.old Here $|a\rangle$ and $|b\rangle$ refer to $|0\rangle$.
• Figure 5: The simplified two-qubit-cluster-based quantum teleportation. Here $|a\rangle$ and $|b\rangle$ refer to $|0\rangle$.