An Evaluation of the Remote CX Protocol under Noise in Distributed Quantum Computing

TL;DR

This paper evaluates distributed quantum circuits that use the remote CX protocol under noise across different network configurations and QPU counts. It employs a high-level simulation to augment monolithic circuits with remote CX gates and compares naive versus graph-partitioning qubit scheduling while testing Grover, GHZ, VQC, and random circuits. Fidelity is used as the primary performance metric to quantify how well distributed executions approximate the ideal states, revealing that fidelity declines as the number of QPUs grows and that scheduling benefits are circuit-dependent. The study highlights the need for more realistic network models and topology-aware compilation to sustain fidelity in distributed quantum computing deployments, offering initial guidance for designing QPU networks and schedulers.

Abstract

Quantum computers connected through classical and quantum communication channels can be combined to function as a single unit to run large quantum circuits that each device is unable to execute on their own. The distributed quantum computing paradigm is therefore often seen as a potential pathway to scaling quantum computing to capacities necessary for practical and large-scale applications. Whether connecting multiple quantum processing units (QPUs) in clusters or over networks, quantum communication requires entanglement to be generated and distributed over distances. Using entanglement, the remote CX protocol can be performed, which allows the application of the CX gate involving qubits located in different QPUs. In this work, we use a specialized simulation framework for a high-level evaluation of the impact of the protocol when executed under noise in various network configurations using different number of QPUs. We compare naive and graph partitioning qubit assignment strategies and how they affect the fidelity in experiments run on Grover, GHZ, VQC, and random circuits. The results provide insights on how QPU and network configurations or naive scheduling can degrade performance.

Figures (6)

• Figure 1: The entanglement swapping (ES) protocol requires three parties and two Bell pairs, as well as classical communication (blue lines). A and C, and B and C each share a Bell pair. C applies a Bell state measurement and sends the results over a classical communication channel to A and B who each can then apply correcting gates. By applying this protocol, the entanglement can be transferred such that A and B become entangled.
• Figure 2: The teleportation protocol caleffi2024distributed. The state $\psi_0$ is transferred to qubit $\psi_1$, which results in its destruction at its original location. The protocol requires a third party and a Bell pair.
• Figure 3: The remote CX protocol ferrari2021compiler. The protocol requires a Bell pair between a communication qubit of each QPU.
• Figure 4: On the left, the circuit only with computational qubits, i.e, the architecture of the monolithic circuit is shown. Qubits marked blue are assigned to QPU 0 and red indicates QPU 1. On the right, the distributed version of the circuit is shown, including computational and communication qubits.
• Figure 5: The results of all experiments. Runs are compared in terms of fidelity. All experiments were run for five different seeds. Plots show mean fidelity with std.