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arXiv:2409.02509

Distributed Quantum Computation via Entanglement Forging and Teleportation

Tian‐Ren Jin, Kai Dong Xu, Heng Fan

Published Sep 4, 2024• 1 citation
arXivHTMLPDF

Abstract

Distributed quantum computation is a practical method for large-scale quantum computation on quantum processors with limited size. It can be realized by direct quantum channels in flying qubits. Moreover, the pre-established quantum entanglements can also play the role of quantum channels with local operations and classical channels. However, without quantum correlations like quantum channels and entanglements, the entanglement forging technique allows us to classically forge the entangled states with local operations and classical channels only. In this paper, we demonstrate the methods to implement a nonlocal quantum circuit on two quantum processors without any quantum correlations, which is based on the fact that teleportation with classically forged Bell states is equivalent to quantum state tomography. In compensation, the overhead of single-shot measurement will increase, and several auxiliary qubits are required. Our results extend the possibility of integrating quantum processors. We expect that our methods will complement the toolbox of distributed quantum computation, and facilitate the extension of the scale of quantum computations.

DOI
10.48550/arxiv.2409.02509

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Distributed quantum computation is a practical method for large-scale quantum computation on quantum processors with limited size. It can be realized by direct quantum channels in flying qubits. Moreover, the pre-established quantum entanglements can also play the role of quantum channels with local operations and classical channels. However, without quantum correlations like quantum channels and entanglements, the entanglement forging technique allows us to classically forge the entangled states with local operations and classical channels only. In this paper, we demonstrate the methods to implement a nonlocal quantum circuit on two quantum processors without any quantum correlations, which is based on the fact that teleportation with classically forged Bell states is equivalent to quantum state tomography. In compensation, the overhead of single-shot measurement will increase, and several auxiliary qubits are required. Our results extend the possibility of integrating quantum processors. We expect that our methods will complement the toolbox of distributed quantum computation, and facilitate the extension of the scale of quantum computations.
Distributed quantum computing combines the computational power of multiple devices to overcome the limitations of individual devices. Circuit cutting techniques enable the distribution of quantum computations through classical communication. These techniques involve partitioning a quantum circuit into smaller subcircuits, each containing fewer qubits. The original circuit's outcome can be replicated by executing these subcircuits on separate devices and combining their results. However, the number of shots required to achieve a fixed result accuracy with circuit cutting grows exponentially with the number of cuts, posing significant costs. In contrast, quantum teleportation allows the distribution of quantum computations without an exponential increase in shots. Nevertheless, each teleportation procedure requires a pre-shared pair of maximally entangled qubits for transmitting a quantum state, and non-maximally entangled qubits cannot be used for this purpose. To address this, we propose a novel circuit cutting technique that leverages non-maximally entangled qubit pairs, effectively reducing the cost associated with circuit cutting. By considering the degree of entanglement in the pre-shared qubit pairs, our technique provides a continuum between existing circuit cutting methods and quantum teleportation, adjusting the cost of circuit cutting accordingly.
In noisy intermediate-scale quantum computing, the limited scalability of a single quantum processing unit (QPU) can be extended through distributed quantum computing (DQC), in which one can implement global operations over two QPUs by entanglement-assisted local operations and classical communication. To facilitate this type of DQC in experiments, we need an entanglement-efficient protocol. To this end, we extend the protocol in [Eisert et. al., PRA, 62:052317(2000)] implementing each nonlocal controlled-unitary gate locally with one maximally entangled pair to a packing protocol, which can pack multiple nonlocal controlled-unitary gates locally using one maximally entangled pair. In particular, two types of packing processes are introduced as the building blocks, namely the distributing processes and embedding processes. Each distributing process distributes corresponding gates locally with one entangled pair. The efficiency of entanglement is then enhanced by embedding processes, which merge two non-sequential distributing processes and hence save the entanglement cost. We show that the structure of distributability and embeddability of a quantum circuit can be fully represented by the corresponding packing graphs and conflict graphs. Based on these graphs, we derive heuristic algorithms for finding an entanglement-efficient packing of distributing processes for a given quantum circuit to be implemented by two parties. These algorithms can determine the required number of local auxiliary qubits in the DQC. We apply these algorithms for bipartite DQC of unitary coupled-cluster circuits and find a significant reduction of entanglement cost through embeddings. This method can determine a constructive upper bound on the entanglement cost for the DQC of quantum circuits.
Distributed quantum computing offers a scalable route to quantum information processing by entangling spatially separated processors. Although gate teleportation enables universal computation across distributed nodes, it requires repeated consumption of high-fidelity Bell pairs, ancillary qubits, and real-time feedforward, which imposes significant overhead and reduces fidelity. However, many variational quantum algorithms do not demand full universality; rather, they rely on sufficient expressibility to explore solution spaces effectively. Building on this, we propose a distributed variational quantum computing protocol based on deterministic entanglement tuning. In contrast to probabilistic filtering, our approach deterministically modulates pre-shared entanglement using only local operations and classical communication. We validate the protocol through a proof-of-principle experiment by estimating ground-state energies of the He-H+^++ molecule and the Schwinger model, showing that diverse entanglement levels can be engineered to match problem-specific requirements. Our results suggest a practical alternative for near-term distributed quantum applications.
Abstract We present the first experimental demonstration of quantum circuit teleportation between heterogeneous quantum processors using Bell state topology as a hardware-agnostic encoding framework. A complete quantum circuit---comprising 4 gate instructions (H, CNOT, Z measurements)---was teleported from Rigetti Computing's Ankaa-3 superconducting QPU to IQM Quantum Computers' Garnet system, with successful reconstruction and execution. The protocol encodes circuit instructions as Bell state manifolds using a 3-qubit error correction code with majority voting, achieving complete circuit fidelity despite architectural differences in native gate sets and connectivity topologies. By treating quantum gates as equivalence classes under entanglement structure---mapping H→∣Φ+⟩H \to |\Phi^+\rangleH→∣Φ+⟩, CNOT→∣Ψ+⟩\mathrm{CNOT} \to |\Psi^+\rangleCNOT→∣Ψ+⟩, Z→∣Φ−⟩Z \to |\Phi^-\rangleZ→∣Φ−⟩, and M→∣Ψ−⟩M \to |\Psi^-\rangleM→∣Ψ−⟩---we establish a foundational equivalence between gate operations and Bell basis projections. Implementation utilizes the hyperelliptic lattice infrastructure developed previously, enabling topologically-aware routing of quantum programs. This work demonstrates that heterogeneous quantum networks can execute distributed quantum algorithms without dedicated quantum channels or pre-shared high-fidelity entanglement, using only classical database coordination. The 100\% circuit execution success rate combined with error-corrected Bell state decoding provides strong evidence that topology-mediated programming offers a practical pathway toward distributed quantum computing infrastructure. We present comprehensive experimental data, theoretical analysis connecting Bell topology to quantum circuit semantics, and a scalable framework for cross-architecture quantum software distribution.
Distributed quantum computing is motivated by the difficulty in building large-scale, individual quantum computers. To solve that problem, a large quantum circuit is partitioned and distributed to small quantum computers for execution. Partitions running on different quantum computers share quantum information using entangled Bell pairs. However, entanglement generation and purification introduces both a runtime and memory overhead on distributed quantum computing. In this paper we study that trade-off by proposing two techniques for partitioning large quantum circuits and for distribution to small quantum computers. Our techniques map a quantum circuit to a graph representation. We study two approaches: one that considers only gate teleportation, and another that considers both gate and state teleportation to achieve the distributed execution. Then we apply the METIS graph partitioning algorithm to obtain the partitions and the number of entanglement requests between them. We use the SeQUeNCe quantum communication simulator to measure the time required for generating all the entanglements required to execute the distributed circuit. We find that the best partitioning technique will depend on the specific circuit of interest.
This paper addresses the challenge of scaling quantum computing by employing distributed quantum algorithms across multiple processors. As quantum circuits grow in complexity, efficiently managing the entanglement resources required for communication between quantum processing units (QPUs) becomes increasingly critical. We propose novel methods to optimize entanglement consumption while accounting for network constraints. Our approach leverages graph partitioning techniques to optimize both qubit teleportation and gate teleportation, minimizing the number of Einstein-Podolsky-Rosen (EPR) pairs required to execute general quantum circuits. Additionally, we formulate an integer linear program (ILP) to further reduce entanglement requirements by mapping the logical resources of partitioned circuits to the physical constraints of the underlying quantum network. Finally, we analyze the entanglement cost for implementing the Quantum Fourier Transform (QFT) across multiple QPUs, employing an approach that exploits the circuit's structure to minimize total entanglement consumption. These contributions provide a pathway to scalable and resource-efficient distributed quantum computing.