Implementing the Quantum Approximate Optimization Algorithms for QUBO problems Across Quantum Hardware Platforms: Performance Analysis, Challenges, and Strategies

TL;DR

This work compares standard QAOA and ADAPT‑QAOA for solving feature‑selection ($QUBO$) problems encoded as Ising Hamiltonians, accounting for practical hardware considerations. It shows ADAPT‑QAOA offers superior approximation ratios on harder instances (e.g., with $\alpha=0.6$) but incurs additional time per layer due to mixer selection, while standard QAOA is more efficient on easier problems. Through hardware‑aware scaling analyses using calibration data from IBM and Quantinuum devices, the study demonstrates topology and gate durations substantially influence time‑to‑solution and error rates, with all‑to‑all connectivity generally performing best in the estimates, though lower‑noise trapped‑ion devices can yield lower errors. A classical QUBO solver provides faster time‑to‑solution on these instances, highlighting the need for problem reformulations and hardware/software strategies to render quantum approaches competitive for near‑term optimization tasks in finance.

Abstract

Quantum computers are expected to offer significant advantages in solving complex optimization problems that are challenging for classical computers. Quadratic Unconstrained Binary Optimization (QUBO) problems represent an important class of problems with relevance in finance and logistics. The Quantum Approximate Optimization Algorithm (QAOA) is a prominent candidate for solving QUBO problems on near-term quantum devices. In this paper, we investigate the performance of both the standard QAOA and the adaptive derivative assembled problem tailored QAOA (ADAPT-QAOA) to solve QUBO problems of varying sizes and hardnesses with a focus on its practical applications in financial feature selection problems. Our main observation is that ADAPT-QAOA significantly outperforms QAOA with hard problems (trade-off parameter α = 0.6) when comparing approximation ratio and time-to-solution. However, the standard QAOA remains efficient for simpler problems. Additionally, we investigate the practical feasibility and limitations of QAOA by scaling analysis based on the real-device calibration data for various hardware platforms. Our estimates indicate that standard QAOA implemented on superconducting quantum computers provides a shorter time-to-solution compared to trapped-ion devices. However, trapped-ion devices are expected to yield more favorable error rates. Our findings provide a comprehensive overview of the challenges, trade-offs, and strategies for deploying QAOA-based methods on near-term quantum hardware.

Figures (7)

• Figure 1: The standard QAOA can be divided into three parts, initialization (colored green), the application of QAOA layers (colored orange and blue), and optimization (colored red). In the initialization step, every qubit is initialized to an equal superposition state by applying a Hadamard gates ($H$). After the initialization, cost and mixer layers are applied to the circuit. In the optimization step, a classical optimization method is used to update the variational parameters so that the expectation value of the cost Hamiltonian with respect to the variational state is minimized. In this work, we apply the layers iteratively, optimizing all variational parameters after each addition.
• Figure 2: Mean approximation ratio $r_k$ (a-b) and time-to-solution (c-d) with respect to the number of features $n$ using $30$ layers of standard QAOA and ADAPT-QAOA to solve feature selection problems with trade-off parameter set to $\alpha=0.2$ (a), (c) and $0.6$ (b), (d). Time-to-solution is given also for $1$ layer of standard QAOA and ADAPT-QAOA, for comparison. All results are averaged over $10$ problem instances obtained using $10$ different seeds to generate data for the problems. The vertical bars represent the minimum and maximum values obtained in each case.
• Figure 3: Mean approximation ratio $r_k$ (a-b) and time-to-solution (c-d) with respect to the number of layers $k$ when solving feature selection problems with $14$ features using standard QAOA and ADAPT-QAOA with trade-off parameter set to $\alpha=0.2$ (a), (c) and $0.6$ (b), (d). All results are averaged over $10$ problem instances obtained using $10$ different seeds to generate data for the problems. The caps connected with dotted lines represent the minimum and maximum values obtained in each case.
• Figure 4: Mean approximation ratio $r_k$ (a-b) and time-to-solution (c-d) with respect to the number of features $n$ using $30$ layers of standard QAOA and $15$ layers of ADAPT-QAOA to solve feature selection problems with trade-off parameter set to $\alpha=0.2$ (a), (c) and $0.6$ (b), (d). All results are averaged over $10$ problem instances obtained using $10$ different seeds to generate data for the problems. The vertical bars represent the minimum and maximum values obtained in each case.
• Figure 5: Visualization of (a) heavy-hex and (b) square lattice topologies. Purple nodes represent qubits.