Many large-scale optimisation problems, such as those in power systems, finance and logistics can be potentially solved in the fundamentally new approach of quantum algorithms, namely Quantum Approximate Optimisation Algorithm (QAOA). In the context of fuzzy systems for instance, it is already shown that some of the intense computation associated with complex or higher-order fuzzy logic systems can be offloaded to such quantum algorithms. While the quantum computation hardware technology is still in its infancy, efficient simulations of the quantum algorithms play a crucial role in advancing quantum algorithms. The current CPU/GPU-based approaches suffer from high energy consumption and speed and scalability limitations. This paper presents the current position of our research to develop an efficient and scalable QAOA simulation based on a large network of Field-Programmable Gate Array (FPGA) modules, inspired by FPGA’s hardware-level parallelism. Although there exist a few attempts on using FPGA for general quantum circuits simulation, this project introduces a novel approach by employing a highly efficient recursive matrix decomposition algorithms specifically designed for QAOA. This work can pave the pathway a scalable and energy-efficient solution for cross-domain optimisation problems. The actual results and evaluations are to be reported in follow-up publications.
Many large-scale optimisation problems, such as those in power systems, finance and logistics can be potentially solved in the fundamentally new approach of quantum algorithms, namely Quantum Approximate Optimisation Algorithm (QAOA). In the context of fuzzy systems for instance, it is already shown that some of the intense computation associated with complex or higher-order fuzzy logic systems can be offloaded to such quantum algorithms. While the quantum computation hardware technology is still in its infancy, efficient simulations of the quantum algorithms play a crucial role in advancing quantum algorithms. The current CPU/GPU-based approaches suffer from high energy consumption and speed and scalability limitations. This paper presents the current position of our research to develop an efficient and scalable QAOA simulation based on a large network of Field-Programmable Gate Array (FPGA) modules, inspired by FPGA’s hardware-level parallelism. Although there exist a few attempts on using FPGA for general quantum circuits simulation, this project introduces a novel approach by employing a highly efficient recursive matrix decomposition algorithms specifically designed for QAOA. This work can pave the pathway a scalable and energy-efficient solution for cross-domain optimisation problems. The actual results and evaluations are to be reported in follow-up publications.
Quantum computing QC emulation is crucial for advancing QC applications, especially given the scalability constraints of current devices. FPGA-based designs offer an efficient and scalable alternative to traditional large-scale platforms, but most are tightly integrated with high-performance systems, limiting their use in mobile and edge environments. This study introduces a compact, standalone FPGA-based QC emulator designed for embedded systems, leveraging the Quantum Approximate Optimization Algorithm (QAOA) to solve the Weighted-MaxCut problem. By restructuring QAOA operations for hardware compatibility, the proposed design reduces time complexity from O(N^2) to O(N), where N equals 2^n for n qubits. This reduction, coupled with a pipeline architecture, significantly minimizes resource consumption, enabling support for up to nine qubits on mid-tier FPGAs, roughly three times more than comparable designs. Additionally, the emulator achieved energy savings ranging from 1.53 times for two-qubit configurations to up to 852 times for nine-qubit configurations, compared to software-based QAOA on embedded processors. These results highlight the practical scalability and resource efficiency of the proposed design, providing a robust foundation for QC emulation in resource-constrained edge devices.
The Quantum Approximate Optimization Algorithm (QAOA) is a prominent quantum algorithm designed to find approximate solutions to combinatorial optimization problems, which are challenging for classical computers. In the current era, where quantum hardware is constrained by noise and limited qubit availability, simulating the QAOA remains essential for research. However, existing state-of-the-art simulation frame-works suffer from long execution times or lack comprehensive functionality, usability, and versatility, often requiring users to implement essential features themselves. Additionally, these frameworks are primarily restricted to Python, limiting their use in safer and faster languages like Rust, which offer, e.g., advanced parallelization capabilities. In this paper, we develop a GPU accelerated QAOA simulation framework utilizing the NVIDIA CUDA toolkit. This framework offers a complete interface for QAOA simulations, enabling the calculation of (exact) expectation values, direct access to the statevector, fast sampling, and high-performance optimization methods using an advanced state-of-the-art gradient calculation technique. The framework is designed for use in Python and Rust, providing flexibility for integration into a wide range of applications, including those requiring fast algorithm implementations leveraging QAOA at its core. The new framework's performance is rigorously benchmarked on the MaxCut problem and compared against the current state-of-the-art general-purpose quantum circuit simulation frameworks Qiskit and Pennylane as well as the specialized QAOA simulation tool QOKit. Our evaluation shows that our approach outperforms the existing state-of-the-art solutions in terms of runtime up to multiple orders of magnitude. Our implementation is publicly available at https://github.com/JFLXB/cuaoa and Zenodo [1].
The continuous growth in computational demands has led to the exploration of innovative technologies for enhancing circuit efficiency. Quantum-inspired algorithms have garnered attention due to their potential to improve optimization, processing, and energy consumption in conventional circuit technologies. Traditional circuit designs, primarily based on classical computation, face limitations in handling large-scale problems due to inefficient algorithms and hardware constraints. These challenges prompt the need for alternative solutions capable of providing scalable, high-performance computation in complex environments. This research proposes integrating quantum- inspired algorithms into circuit technologies to address these challenges. Quantum algorithms, such as the Quantum Approximate Optimization Algorithm (QAOA) and quantum annealing, offer substantial benefits over classical counterparts, especially in solving NP-hard problems, simulating quantum systems, and optimizing complex functions. The integration of such algorithms into circuit design can potentially reduce computational complexity, improve data throughput, and optimize energy efficiency, offering a more sustainable approach in circuit development. The study investigates the adaptation of quantum-inspired algorithms into field-effect transistors (FETs) and other circuit components, focusing on optimizing power consumption and operational speed. A hybrid approach combining classical circuit elements with quantum-inspired strategies is implemented to evaluate its impact on both performance and scalability. The results show a notable reduction in energy consumption and improvement in processing speed, validating the promise of quantum-inspired solutions in enhancing computational efficiency.
Quantum computing holds great potential to accelerate the process of solving complex combinatorial optimization problems. The Distributed Quantum Approximate Optimization Algorithm (DQAOA) addresses high-dimensional, dense problems using current quantum computing techniques and high-performance computing (HPC) systems. In this work, we improve the scalability and efficiency of DQAOA through advanced problem decomposition and parallel execution using message passing on the Frontier CPU/GPU supercomputer. Our approach ensures efficient quantum-classical workload management by distributing large problem instances across classical and quantum resources. Experimental results demonstrate that enhanced decomposition strategies and GPU-accelerated quantum simulations significantly improve DQAOA's performance, achieving up to 10x speedup over CPU-based simulations. This advancement enables better scalability for large problem instances, supporting the practical deployment of GPU systems for hybrid quantum-classical applications. We also highlight ongoing integration efforts using the Quantum Framework (QFw) to support future HPC-quantum computing systems.
Quantum computing promises solutions to classically difficult and new-found problems through controlling the subtleties of quantum computing. The Quantum Approximate Optimisation Algorithm (QAOA) is a recently proposed quantum algorithm designed to tackle difficult combinatorial optimisation problems utilising both quantum and classical computation. The hybrid nature, generality and typically low gate-depth make it a strong candidate for near-term implementation in quantum computing. Finding the practical limits of the algorithm is currently an open problem. Until now, no tools to facilitate the design and validation of probabilistic quantum optimisation algorithms such as the QAOA on a non-trivial scale exist. Graph similarity is a long standing classically difficult problem withstanding decades of research from academia and industry. Determining the maximal edge overlap between all possible node label permutations is an NP-Complete task and provides an apt measure of graph similarity. We introduce a novel quantum optimisation simulation package facilitating investigation of all constituent components of the QAOA from desktop to cluster scale using graph similarity as an example. Our simulation provides flexibility and performance. We investigate eight classical optimisation methods each at six levels of decomposition. Moreover an encoding for permutation based problems such as graph similarity through edge overlap to the QAOA allows for significant quantum memory savings at the cost of additional operations. This compromise extends into the classical portion of the algorithm as the inclusion of infeasible solutions creates a challenging cost-function landscape. We present performance analysis of our simulation and of the QAOA setting a precedent for investigating and validating numerous other difficult problems to the QAOA as we move towards realising practical quantum computation.
A quantum computing simulation provides the opportunity to explore the behaviors of quantum circuits, study the properties of quantum gates, and develop quantum computing algorithms. Simulating quantum circuits requires geometric time and space complexities, impacting the size of the quantum circuit that can be simulated as well as the respective time required to simulate a particular circuit. Applying the parallelism inherent in the simulation and crafting custom architectures, larger quantum circuits can be simulated. A scalable accelerator architecture is proposed to provide a high performance, highly parallel, accelerator. Among the challenges of creating a scalable architecture is managing parallelism, efficiently routing quantum state components for gate evaluation, and measurement. An example is demonstrated on an Intel Agilex field programmable gate array (FPGA).