Quantum approximate optimization algorithm (QAOA) is one of the popular quantum algorithms that are used to solve combinatorial optimization problems via approximations. QAOA is able to be evaluated on both physical and virtual quantum computers simulated by classical computers, with virtual ones being favored for their noise-free feature and availability. Nevertheless, performing QAOA on virtual quantum computers suffers from a slow simulation speed for solving combinatorial optimization problems which require large-scale quantum circuit simulation (QCS). In this paper, we propose techniques to accelerate QCS for QAOA using mathematical optimizations to compress quantum operations, incorporating efficient bitwise operations to further lower the computational complexity, and leveraging different levels of parallelisms from modern multi-core processors, with a study case to show the effectiveness on solving max-cut problems. The experimental results reveal substantial performance improvements, surpassing a state-of-the-art simulator, QuEST, by a factor of 17 on a virtual quantum computer running on a 16-core, 32-thread AMD Ryzen 9 5950X processor. We believe that this work opens up new possibilities for accelerating various QAOA applications.
Quantum approximate optimization algorithm (QAOA) is one of the popular quantum algorithms that are used to solve combinatorial optimization problems via approximations. QAOA is able to be evaluated on both physical and virtual quantum computers simulated by classical computers, with virtual ones being favored for their noise-free feature and availability. Nevertheless, performing QAOA on virtual quantum computers suffers from a slow simulation speed for solving combinatorial optimization problems which require large-scale quantum circuit simulation (QCS). In this paper, we propose techniques to accelerate QCS for QAOA using mathematical optimizations to compress quantum operations, incorporating efficient bitwise operations to further lower the computational complexity, and leveraging different levels of parallelisms from modern multi-core processors, with a study case to show the effectiveness on solving max-cut problems. The experimental results reveal substantial performance improvements, surpassing a state-of-the-art simulator, QuEST, by a factor of 17 on a virtual quantum computer running on a 16-core, 32-thread AMD Ryzen 9 5950X processor. We believe that this work opens up new possibilities for accelerating various QAOA applications.
The Quantum Approximate Optimization Algorithm (QAOA), which is a variational quantum algorithm, aims to give sub-optimal solutions of combinatorial optimization problems. It is widely believed that QAOA has the potential to demonstrate application-level quantum advantages in the noisy intermediate-scale quantum(NISQ) processors with shallow circuit depth. Since the core of QAOA is the computation of expectation values of the problem Hamiltonian, an important practical question is whether we can find an efficient classical algorithm to solve quantum mean value in the case of general shallow quantum circuits. Here, we present a novel graph decomposition based classical algorithm that scales linearly with the number of qubits for the shallow QAOA circuits in most optimization problems except for complete graph case. Numerical tests in Max-cut, graph coloring and Sherrington-Kirkpatrick model problems, compared to the state-of-the-art method, shows orders of magnitude performance improvement. Our results are not only important for the exploration of quantum advantages with QAOA, but also useful for the benchmarking of NISQ processors.
Maximum cut (Max-Cut) problem is one of the most important combinatorial optimization problems because of its various applications in real life, and recently Quantum Approximate Optimization Algorithm (QAOA) has been widely employed to solve it. However, as the size of the problem increases, the number of qubits required will become larger. With the aim of saving qubits, we propose a coupling framework for designing QAOA circuits to solve larger-scale Max-Cut problem. This framework relies on a classical algorithm that approximately solves a certain variant of Max-Cut, and we derive an approximation guarantee theoretically, assuming the approximation ratio of the classical algorithm and QAOA. Furthermore we design a heuristic approach that fits in our framework and perform sufficient numerical experiments, where we solve Max-Cut on various 24-vertex Erdős-Rényi graphs. Our framework only consumes 18 qubits and achieves 0.9950 approximation ratio on average, which outperforms the previous methods showing 0.9778 (quantum algorithm using the same number of qubits) and 0.9643 (classical algorithm). The experimental results indicate our well-designed quantum-classical coupling framework gives satisfactory approximation ratio while reduces the qubit cost, which sheds light on more potential computing power of NISQ devices.
In recent years, there have been significant advancements in various aspects of quantum computing. However, despite this substantial progress, the availability of fault-tolerant quantum computers is still out of reach and may remain so for decades. Therefore, a key challenge is to leverage current NISQ devices to achieve a quantum advantage effectively. In this context, the Quantum Approximate Optimization Algorithm (QAOA) was proposed to potentially demonstrate computational advantages in combinatorial optimization problems using NISQ computers. Meanwhile, quantum error mitigation (QEM) techniques have been developed to address errors, with their effectiveness validated in practical problems involving more than 100 qubits. Therefore, in this paper, we optimize QAOA circuits and apply various error mitigation methods, such as dynamic decoupling and Pauli-twirling, to scale problem sizes on IBM quantum processors. Additionally, we discuss optimal implementation strategies for scalable QAOA. We test our implementations on Max-Cut problems and compare our results with previous works.
The Quantum Approximate Optimization Algorithm (QAOA) is a promising approach for programming a near-term gate-based hybrid quantum computer to find good approximate solutions of hard combinatorial problems. However, little is currently know about the capabilities of QAOA, or of the difficulty of the requisite parameters optimization. Here, we study the performance of QAOA on the MaxCut combinatorial optimization problem, optimizing the quantum circuits on a classical computer using automatic differentiation and stochastic gradient descent, using QuantumFlow, a quantum circuit simulator implemented with TensorFlow. We find that we can amortize the training cost by optimizing on batches of problems instances; that QAOA can exceed the performance of the classical polynomial time Goemans-Williamson algorithm with modest circuit depth, and that performance with fixed circuit depth is insensitive to problem size. Moreover, MaxCut QAOA can be efficiently implemented on a gate-based quantum computer with limited qubit connectivity, using a qubit swap network. These observations support the prospects that QAOA will be an effective method for solving interesting problems on near-term quantum computers.
The max-cut problem (MCP) is a classic problem in the field of combinatorial optimization and has important applications in various fields, including statistical physics and image processing. However, except for some special cases, the MCP still encounters a non-deterministic polynomial complete problem (an NP-complete problem), and there is currently no known efficient classical algorithm that can solve it in polynomial time. The quantum approximate optimization algorithm (QAOA), as a pivotal algorithm in the noisy intermediate-scale quantum (NISQ) computing era, has shown significant potential for solving the MCP. However, due to the lack of quantum error correction, the reliability of computations in NISQ systems sharply declines as the circuit depth of the algorithm increases. Therefore, designing an efficient, shallow-depth, and low-complexity QAOA for the MCP is a critical challenge in demonstrating the advantages of quantum computing in the NISQ era.In this paper, according to the standard QAOA algorithm, we introduce Pauli Y rotation gates into the target Hamiltonian circuit for the MCP. By enhancing the flexibility of quantum trial functions and improving the efficiency of Hilbert space exploration within a single iteration, we significantly improve the performance of QAOA on the MCP.We conduct extensive numerical simulations using the MindSpore quantum platform, and compare the proposed RY-layer-assisted QAOA with standard QAOA and its existing variants, including MA-QAOA and QAOA+. The experiments are performed on various graph types, including complete graphs, 3-regular graphs, 4-regular graphs, and random graphs with edge probabilities between 0.3 and 0.5. Our results show that the RY-layer-assisted QAOA achieves higher approximation ratios in all graph types, particularly in regular and random graphs, where traditional QAOA variants are difficult to implement. Moreover, the proposed method exhibits strong robustness as the graph size increases, and can maintain high performance even for larger graphs. Importantly, the RY-layer-assisted QAOA requires fewer CNOT gates and has a lower circuit depth than the standard QAOA and its variants, making it more suitable for NISQ devices with limited coherence times and high error rates.In conclusion, the RY-layer-assisted QAOA provides a promising approach for solving MCP in the NISQ era. By improving the approximation ratio while reducing circuit complexity, this method demonstrates significant potential for practical quantum computing applications, thus paving the way for developing more efficient and reliable quantum optimization algorithms.
Quantum computing has emerged as a promising paradigm to tackle computationally intensive problems that classical computers struggle with. In this study, we explore the application of the Edge-based quantum approximate optimization algorithm (QAOA) to the MAX-CUT problem, a well-known combinatorial optimization challenge. MAX-CUT aims to partition the vertices of a graph into two subsets such that the number of edges between the subsets is maximized. We define the edge-based MAX-CUT problem and propose a method for applying QAOA specifically tailored to this formulation. We conduct simulations using IBM’s Qiskit framework, examining both vertex-based and edge-based QAOA implementations across various graph structures. Our results highlight the comparative performance of these approaches in terms of solution quality and computational efficiency. Specifically, we analyze the impact of different graph sizes and edge densities on the complexity and CNOT gate counts of the proposed algorithms. This analysis provides insights into leveraging quantum computing for combinatorial optimization tasks, particularly focusing on the implications for practical applications and future research directions.