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.
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.
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.
Abstract It is crucial to design quantum circuits as small as possible and as shallow as possible for quantum information processing tasks. Quantum circuits are designed 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 the simplified and compressed schemes can be realized with good fidelity.
Quantum information processing has a wide range of uses, including the solution of complex algorithms, cryptography, dense coding, quantum computation, and quantum teleportation. Quantum entanglement, a phenomenon that is crucial to many different applications of quantum computation, is an essential resource for quantum computation, and the need for quantum circuits that generate entangled states is one of the ongoing needs for constructing quantum computers. In this study, we present a general approach to the design of quantum circuits that produce entangled states. The approach can be applied to the design of various entanglement circuits with any number of qubits (n-qubit systems), and it makes use of a set of CNOT and Hadamard gates, where the number of CNOT gates should always be (n-1) and each gate connects the two adjacent qubits. In this paper, a three-entangled teleportation scheme of a GHZ-like state (named after its inventor Greenberger-Horne-Zeilinger) through three particles as a quantum channel is presented. The probability of successful teleportation depends on the degree of entanglement of GHZ-like states. A 5-qubit quantum teleportation over a GHZ-like channel has also been used. And single-qubit gates are defined, which are Pauli gates. These gates are represented by arrays I, X, Y, and Z. The results in this paper are good and promising theoretical results in the field of quantum entanglement and quantum teleportation using the Mathematica program.
Abstract The limited qubit connectivity of quantum processors poses a significant challenge in deploying practical algorithms and logical gates, necessitating efficient qubit mapping and routing strategies. When implementing a gate that requires additional connectivity beyond the native connectivity, the qubit state must be moved to a nearby connected qubit to execute the desired gate locally. This is typically achieved using a series of SWAP gates creating a SWAP path. However, routing methods relying on SWAP gates often lead to increased circuit depth and gate count, motivating the need for alternative approaches. This work explores the potential of teleported gates to improve qubit routing efficiency, focusing on implementation within specific hardware topologies and benchmark quantum algorithms. We propose a routing method that is assisted by gate teleportation. It establishes additional connectivity using gate teleportation paths through available unused qubits, termed auxiliary qubits, within the topology. To optimize this approach, we have developed an algorithm to identify the best gate teleportation connections, considering their potential to reduce the depth of the circuit and address possible errors that may arise from the teleportation paths. Finally, we demonstrate depth reduction with gate teleportation-assisted routing in various benchmark algorithms, including case studies on the compilation of the Deutsch–Jozsa algorithm and the quantum approximation optimization algorithm for heavy-hexagon topology used in IBM 127-qubit Eagle r3 processors. Our benchmark results show a 10%–25% depth reduction in the routing of selected algorithms compared to regular routing without using teleported gates.
Quantum simulation traditionally relies on unitary dynamics, inherently imposing efficiency constraints on the generation of intricate entangled states. In principle, these limitations can be superseded by nonunitary, dynamic circuits. These circuits exploit measurements alongside conditional feed-forward operations, providing a promising approach for long-range entangling gates, higher effective connectivity of near-term hardware, and more efficient state preparations. Here, we explore the utility of shallow dynamic circuits for creating long-range entanglement on large-scale quantum devices. Specifically, we study two tasks: controlled- gate teleportation between up to 101 qubits by feeding forward 99 midcircuit measurement outcomes, and the preparation of Greenberger–Horne–Zeilinger states with genuine entanglement. In the former, we observe that dynamic circuits can outperform their unitary counterparts. In the latter, by tallying instructions of compiled quantum circuits, we provide an error budget detailing the obstacles that must be addressed to unlock the full potential of dynamic circuits. Looking forward, we expect dynamic circuits to be useful for generating long-range entanglement in the near term on large-scale quantum devices. Published by the American Physical Society 2024
In many domains, quantum computing has demonstrated its superiority over classical computing, and it continues to expand. It has demonstrated exponential speedups compared to the classic approach in certain problems. Nevertheless, scalability and noisy environments remain challenges for quantum hardware. In contrast to the unitary dynamics that characterise quantum circuits, recent research has introduced dynamic circuits with non-unitary dynamics. Dynamic circuits include mid-circuit measurement and conditional feed-forward operations. Our proposal involves using dynamic circuits to achieve reduced circuit depth, which in turn significantly decreases error rates by integrating error-correcting feed-forward operations within the circuit. Long-Range Teleportation enables the expansion of teleportation protocols to accommodate intricate quantum states spanning multiple qubits. We have employed Dynamic circuits to ensure an optimal circuit depth and showcase the efficacy of dynamic circuits in facilitating reliable teleportation with an increasing number of qubits. Our findings highlight the benefits of using dynamic circuits to optimize the compilation time of the multi qubit quantum teleportation protocol.