Distributed Quantum Approximate Optimization Algorithm on a Quantum-Centric Supercomputing Architecture

TL;DR

A distributed QAOA (DQAOA), which leverages distributed computing strategies to decompose a large computational workload into smaller tasks that require fewer qubits and shallower circuits than necessitated to solve the original problem and can handle considerably large-scale optimization problems.

Abstract

Quantum approximate optimization algorithm (QAOA) has shown promise in solving combinatorial optimization problems by providing quantum speedup on near-term gate-based quantum computing systems. However, QAOA faces challenges for high-dimensional problems due to the large number of qubits required and the complexity of deep circuits, limiting its scalability for real-world applications. In this study, we present a distributed QAOA (DQAOA), which leverages distributed computing strategies to decompose a large computational workload into smaller tasks that require fewer qubits and shallower circuits than necessitated to solve the original problem. These sub-problems are processed using a combination of high-performance and quantum computing resources. The global solution is iteratively updated by aggregating sub-solutions, allowing convergence toward the optimal solution. We demonstrate that DQAOA can handle considerably large-scale optimization problems (e.g., 1,000-bit problem) achieving a high approximation ratio ($\sim$99%) and short time-to-solution ($\sim$276 s), outperforming existing strategies. Furthermore, we realize DQAOA on a quantum-centric supercomputing architecture, paving the way for practical applications of gate-based quantum computers in real-world optimization tasks. To extend DQAOA's applicability to materials science, we further develop an active learning algorithm integrated with our DQAOA (AL-DQAOA), which involves machine learning, DQAOA, and active data production in an iterative loop. We successfully optimize photonic structures using AL-DQAOA, indicating that solving real-world optimization problems using gate-based quantum computing is feasible. We expect the proposed DQAOA to be applicable to a wide range of optimization problems and AL-DQAOA to find broader applications in material design.

Figures (16)

• Figure 1: Workflow of DQAOA leveraging a quantum-centric supercomputing architecture.a, The schematic of a QAOA circuit, illustrating the iterative process to update variational parameters in both classical and quantum components. b, The number of single-qubit and two-qubit gates as a function of QUBO problem size, indicating that circuit depth grows significantly for larger problems, reflecting the increased complexity of solving large-scale optimization tasks. c, Time-to-solution of QAOA for QUBO problems on quantum hardware (IBM-Strasbourg), an emulator (IBM-FakeBrisbane), and a simulator (Qiskit-Aer). The dotted lines indicate the expected time-to-solution for solving large QUBOs (n$>$ 22). d, The schematic of DQAOA to solve large-scale optimization problems through distributed computing. A large QUBO is decomposed into p sub-QUBOs, which are solved by the quantum-centric supercomputing architecture.
• Figure 2: Performance analysis of dq-QAOA. Approximation ratio and time-to-solution for a 30-bit problem as a function of (a) the number of iterations, and (b) the sub-QUBO size. The number of iterations is set to 300 and sub-QUBO size to 4 for further studies, as approximation ratio nearly converges but time-to-solution continues to increase. (c) Approximation ratio and (d) time-to-solution of QAOA and dq-QAOA as a function of the problem size. Approximation ratio and time-to-solution of dq-QAOA for a problem size of (e) 100 and (f) 150 with the different number of iterations and sub-QUBO sizes. A: 300 iterations with the sub-QUBO size of 4. B: 3,000 iterations with the sub-QUBO size of 4. C: 300 iterations with the sub-QUBO size of 8. D: 1,000 iterations with the sub-QUBO size of 8.
• Figure 3: Performance analysis of DQAOA. Approximation ratio and time-to-solution for a 150-bit problem as a function of (a) the number of iterations, and (b) the number of cores used. (c) Approximation ratio and (d) time-to-solution of dq-QAOA and DQAOA as a function of the problem size (n). Note that the number of iterations, sub-QUBO size, and the number of cores used for DQAOA are set to 30, 4, and n, respectively.
• Figure 4: Performance analysis of dq-QAOA and DQAOA, and hardware implementation. Comparison of (a) approximation ratio and (b) time-to-solution between QAOA, DC-QAOA, dq-QAOA, and DQAOA, with DQAOA serving as the baseline for time-to-solution. c, Schematic representation of the implementation of dq-QAOA and DQAOA on the QCSC architecture. For a QUBO with n = 22, (d) approximation ratio and (e) time-to-solution of QAOA, dq-QAOA, and DQAOA on quantum devices (orange bar; IBM-Strasbourg and IBM-Kyiv) and emulators (grey bar; FakeBrisbane and FakeKyiv). f, For a QUBO with n = 100, approximation ratio of DQAOA (solid lines) and dq-QAOA (dotted lines) on quantum devices (orange; IBM-Strasbourg and IBM-Kyiv) and emulators (grey; FakeBrisbane and FakeKyiv).
• Figure 5: The AL-DQAOA algorithm for solving large-scale optimization problems in material science, exemplified by spectral filters with 12, 30, 50, and 100-bit systems.a, The schematic of AL-DQAOA integrating machine learning, DQAOA, and performance evaluation in an iterative loop. b, The schematic of a spectral filter for TRC windows, where the planar multilayered structure (PML) is subject to optimization. c, Solar spectral irradiance (yellow shade, air mass 1.5 global) and transmitted irradiance through the ideal spectral filter (red shade). The ideal spectral filter transmits the solar spectrum only in the visible range. d, The evolution of FOM as a function of optimization cycles for different problem sizes. e, Time required for an optimization cycle of AL-DQAOA for different problem sizes. f, Calculated optical properties of the spectral filter optimized by AL-DQAOA. The yellow shade presents solar spectral irradiance. g, Energy-saving potential when using the optimized spectral filter as TRC windows in cities around the world, compared to a conventional window.