arXiv subjects

Xin Wei Lee

Publications and source records attributed to Xin Wei Lee.

3 recordsLinked to original sources

arXiv2026

CVaR-Assisted Custom Penalty Function for Constrained Optimization

We propose a slack-free penalty formulation for constrained binary optimization that eliminates auxiliary slack variables and preserves the feasibility structure of the original problem. The proposed approach introduces a nonlinear custom penalty function to enforce inequality constraints directly in the objective function. To address the computational challenges associated with evaluating nonlinear penalties in variational quantum algorithms, we employ the finite-sampling method that avoids the exponential complexity required by exact expectation computation. Furthermore, we integrate the Conditional Value-at-Risk (CVaR) objective to improve optimization robustness and guide the search toward high-quality solutions. The proposed framework is evaluated on instances of the multi-dimensional knapsack problem, a classical benchmark in combinatorial optimization. We showcase that the proposed custom-penalty formulation combined with CVaR sampling achieves improved optimality gaps and more consistent performance compared with conventional slack-based QUBO formulations. We also tested our method on the Quantinuum H2 quantum hardware, demonstrating the possibilities of training small-sized VQE on noisy trapped-ion quantum computers. The results suggest that careful penalty design can play a critical role in enabling quantum and hybrid quantum-classical algorithms for constrained optimization problems that arise in operations research.

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arXiv2025

Solving Constrained Combinatorial Optimization Problems with Variational Quantum Imaginary Time Evolution

Solving combinatorial optimization problems using variational quantum algorithms (VQAs) has emerged as a promising research direction. Since the introduction of the Quantum Approximate Optimization Algorithm (QAOA), numerous variants have been proposed to enhance its performance. QAOA was later extended to the Quantum Alternating Operator Ansatz (QAOA+), which generalizes the initial state, phase-separation operator, and mixer to address constrained problems without relying on the standard Quadratic Unconstrained Binary Optimization (QUBO) formulation. However, QAOA+ often requires additional ancilla qubits and a large number of multi-controlled Toffoli gates to prepare the superposition of feasible states, resulting in deep circuits that are challenging for near-term quantum devices. Furthermore, VQAs are generally hindered by issues such as barren plateaus and suboptimal local minima. Recently, Quantum Imaginary Time Evolution (QITE), a ground-state preparation algorithm, has been explored as an alternative to QAOA and its variants. QITE has demonstrated improved performance in quantum chemistry problems and has been applied to unconstrained combinatorial problems such as Max-Cut. In this work, we apply the variational form of QITE (VarQITE) to solve the Multiple Knapsack Problem (MKP), a constrained problem, using a Max-Cut-tailored ansatz. To the best of our knowledge, this is the first attempt to address constrained optimization using VarQITE. We show that VarQITE achieves significantly lower mean optimality gaps compared to QAOA and other conventional methods. Moreover, we demonstrate that scaling the Hamiltonian coefficients can further reduce optimization costs and accelerate convergence.

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arXiv2025

Implementing Slack-Free Custom Penalty Function for QUBO on Gate-Based Quantum Computers

Solving NP-hard constrained combinatorial optimization problems using quantum algorithms remains a challenging yet promising avenue toward quantum advantage. Variational Quantum Algorithms (VQAs), such as the Variational Quantum Eigensolver (VQE), typically require constrained problems to be reformulated as unconstrained ones using penalty methods.A common approach introduces slack variables and quadratic penalties in the QUBO formulation to handle inequality constraints. However, this leads to increased qubit requirements and often distorts the optimization landscape, making it harder to find high-quality feasible solutions. To address these issues, we explore a slack-free formulation that directly encodes inequality constraints using custom penalty functions, specifically the exponential function and the Heaviside step function. These step-like penalties suppress infeasible solutions without introducing additional qubits or requiring finely tuned weights. Inspired by recent developments in quantum annealing and threshold-based constraint handling in gate-based algorithms, we implement and evaluate our approach on the Multiple Knapsack Problem (MKP). Experimental results show that the step-based formulation significantly improves feasibility and optimality rates compared to unbalanced penalization, while reducing overall qubit overhead.

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