Towards Distributed Quantum Computing by Qubit and Gate Graph Partitioning Techniques

Abstract: 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.

• The paper introduces qubit and gate partitioning techniques that minimize inter-QPU operations using METIS to optimize nonlocal CNOT execution.
• The methodology employs the SeQUeNCe simulator to evaluate runtime trade-offs, balancing e-bit usage and qubit operations in distributed circuits.
• Results indicate that gate partitioning reduces runtime in certain scenarios, while qubit partitioning remains effective for circuits with high nonlocal gate demands.

Distributed Quantum Computing by Qubit and Gate Graph Partitioning

Introduction

The concept of distributed quantum computing (DQC) emerges as a promising solution to the challenge of scaling up quantum computers, which currently face physical and technical limitations in integrating large numbers of qubits on a single chip. DQC involves partitioning a large quantum circuit and distributing the tasks to multiple smaller quantum computers, or quantum processing units (QPUs), networked through quantum communication channels enabled by entangled qubits (e-bits).

This paper explores two techniques for DQC: qubit partitioning and gate partitioning, providing a detailed analysis of their implementation and efficiency using the METIS graph partitioning algorithms and the SeQUeNCe quantum network simulator.

Methods and Techniques

Qubit Partitioning

In qubit partitioning, the goal is to minimize the number of CNOT gates that need to be executed nonlocally between different QPUs. The partitioning problem is represented as a graph where nodes are qubits, and edges represent CNOT operations. The METIS graph partitioning algorithm is applied to achieve balanced partitions that reduce inter-partition CNOT operations.

Figure 1: (a) and (b) depict examples of qubit partitioning and gate partitioning in a quantum circuit, respectively.

Gate Partitioning

Gate partitioning considers both quantum gate teleportation and state teleportation, allowing more flexibility. Here, nodes represent single-qubit operations or parts of CNOT operations, and edges capture logical qubit interactions chronologically. This approach aims to balance the workload across partitions while reducing e-bit usage by leveraging teleportations.

Figure 2: Comparison of simulated runtime for circuits under qubit partitioning (nonlocal CNOTs) and gate partitioning (qubit teleportations).

Evaluation with SeQUeNCe

The evaluation of the techniques was carried out using the SeQUeNCe quantum network simulator, which estimates runtime based on the required number of e-bits, fidelity targets, and available qubits. The simulations demonstrated that gate partitioning allowed for reduced runtime in scenarios where state teleportation was more beneficial, while qubit partitioning was optimal when nonlocal CNOTs were favorable.

This runtime analysis is pivotal in selecting between the partitioning strategies based on circuit characteristics, highlighting scenarios where particular strategies can provide computational advantages over single large QPU circuits.

Figure 3: Trade-off analysis between e-bit and qubit usage among different partitioning approaches.

Conclusion

The study illustrates that the choice between qubit and gate partitioning strategies significantly impacts the efficiency and resource allocation in distributed quantum computing systems. While gate partitioning is more flexible, qubit partitioning's simplicity can be advantageous for specific types of quantum circuits. Future work should focus on more complex quantum circuits and experimental validation on existing quantum network testbeds.

Overall, this research presents foundational techniques for partitioning quantum circuits that optimize distributed execution, paving the way for scalable quantum computing systems.