Noise-Aware Distributed Quantum Approximate Optimization Algorithm on Near-term Quantum Hardware

TL;DR

The paper proposes a noise-aware distributed QAOA framework designed for near-term quantum hardware, addressing NISQ limitations by decomposing large QAOA problems into subproblems executed across multiple QPUs and incorporating error mitigation. It introduces a three-step noise-aware compilation workflow (threshold filtering, symmetrical sampling, and compilation) guided by hardware calibration data to select high-fidelity qubits and gates, paired with qiskit-based optimizations. Evaluation using the HamilToniQ benchmarking toolkit demonstrates improved sampling speed and fidelity across distributed QPUs, including demonstrations of linear speedups and resource-aware scheduling via Balanced MinCut. The work advances practical quantum optimization on NISQ devices and suggests integration with other error-mitigation strategies to move toward quantum advantage in real-world problems.

Abstract

This paper introduces a noise-aware distributed Quantum Approximate Optimization Algorithm (QAOA) tailored for execution on near-term quantum hardware. Leveraging a distributed framework, we address the limitations of current Noisy Intermediate-Scale Quantum (NISQ) devices, which are hindered by limited qubit counts and high error rates. Our approach decomposes large QAOA problems into smaller subproblems, distributing them across multiple Quantum Processing Units (QPUs) to enhance scalability and performance. The noise-aware strategy incorporates error mitigation techniques to optimize qubit fidelity and gate operations, ensuring reliable quantum computations. We evaluate the efficacy of our framework using the HamilToniQ Benchmarking Toolkit, which quantifies the performance across various quantum hardware configurations. The results demonstrate that our distributed QAOA framework achieves significant improvements in computational speed and accuracy, showcasing its potential to solve complex optimization problems efficiently in the NISQ era. This work sets the stage for advanced algorithmic strategies and practical quantum system enhancements, contributing to the broader goal of achieving quantum advantage.

Figures (5)

• Figure 1: Visualization of 6-Qubit Distributed QAOA Sampling Process. The diagram depicts three overlapping sampling regions within a 6-qubit network, illustrating the execution of QAOA circuits. Highlighted is a pair of qubits experiencing elevated noise, potentially affecting algorithmic fidelity. The color-coded error metrics denote readout assignment and entanglement crosstalk errors (ECR), with values ranging from the minimum observed error to the maximum for each qubit connection.
• Figure 2: Integrated Workflow for Noise-Aware Distributed QAOA Execution Across Diverse QPUs. Panel (a) depicts the noise-aware QAOA process on a single-node QPU, utilizing multiple sampling techniques to address and mitigate noise-induced errors. Panel (b) expands the scenario to a distributed quantum computing system, where noise-aware QAOA is applied in conjunction with a balanced MinCut algorithm g2021efficient for efficient task distribution across the network. Panel (c) presents a hierarchical approach to solving a MaxCut problem that exceeds qubit capacity; the problem is partitioned by balanced MinCut and progressively reduced and reconstituted into smaller MaxCut instances, aligning with the available qubit resources. The process iterates between multi-node, number of QPU $QPU_n > 1$, execution as in (b) and single-node operation as in (a), depending on the computational structure and resources at each stage of the problem-solving hierarchy. $N$ represents the number of qubits required for a complete QAOA problem, while $N_i$ denotes the number of qubits for the $i$-th partitioned QAOA subproblem. Additionally, $n$ signifies the total number of qubits in a QPU, and $n_i$ corresponds to the number of qubits in the $i$-th QPU within a distributed quantum system.
• Figure 3: This flow chart illustrates the standard benchmarking procedures of a QPU (or Distributed QPUs) using HamilToniQ benchmarking toolkit.
• Figure 4: Benchmarking H-Score by the HamilToniQ Toolkit across various quantum devices with different topologies. The devices include IBM Lagos, IBM Cairo, IBM Perth, IBM Auckland (T-shape), and IBM Guadalupe (Heavy-Hex), contrasted with distributed-QAOA (5 nodes). The H-Score, indicative of quantum fidelity, is plotted against the number of layers within the quantum circuit. The graph illustrates the relative performance of each device topology, with distributed-QAOA showcasing enhanced sampling efficiency in the distributed quantum system.
• Figure 5: Validation and comparison of H-scores for best, worst, and random QPU selection across layers in a distributed QAOA benchmarking.