arXiv subjects

Yuexin Su

Publications and source records attributed to Yuexin Su.

6 recordsLinked to original sources

arXiv2026

Quantum Algorithm for Elliptic Curve Discrete Logarithms with Space-Efficient Point Addition

The Elliptic Curve Discrete Logarithm Problem (ECDLP) is a fundamental problem in cryptography, and reducing the resource requirements of quantum algorithms for solving ECDLP is an important goal. In this work, we present a space-efficient quantum algorithm for solving the ECDLP over prime fields, achieving an implementation with only $3n+6\lfloor \log_2 n \rfloor+O(1)$ logical qubits and $1056n^3/\log_2 n+O(n^2)$ Toffoli gates, where $n$ is the bit-length of the prime. For a 256-bit prime-field curve, our construction requires only 835 logical qubits, reducing the previous best estimates of 1098 and 1175 logical qubits by Chevignard et al. [EUROCRYPT 2026] and Babbush et al. [ArXiv Preprint 2026], respectively. The key to our improvement is a new space-efficient reversible modular inversion circuit, which addresses the dominant space bottleneck in affine-coordinate point addition. Starting from the extended Euclidean algorithm (EEA), we refine the register-sharing technique of Proos and Zalka by introducing length registers and location-controlled arithmetic to compactly store and update intermediate variables. We further optimize the reversible update procedures and construct the corresponding controlled arithmetic circuits, resulting in a modular inversion circuit implemented by only $2n+6\lfloor \log_2 n \rfloor+O(1)$ logical qubits and $229n^2+O(n\log_2 n)$ Toffoli gates. This modular inversion circuit together with mid-circuit measurements and classical feed-forward operations provides a space-efficient controlled affine point-addition circuit and a complete implementation of Shor's algorithm for ECDLP.

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arXiv2026

Scalable First-Order Interior Point Trust Region Algorithms for Linearly Constrained Optimization

Computing approximate Karush--Kuhn--Tucker (KKT) points for constrained nonconvex programs is a fundamental problem in mathematical programming. Interior-point trust-region (IPTR) methods are particularly attractive for such problems because they maintain strictly feasible iterates throughout the iterative process and converge to a first-order and second-order KKT solution. Their scalability, however, is limited by the repeated computation of trust-region search directions. In this paper, we propose an approximate first-order IPTR framework that addresses this bottleneck by replacing exact trust-region subproblem solves with an approximate projector maintained through low-rank updates. The resulting method preserves feasibility and the global convergence guarantees of standard IPTR schemes while substantially reducing the per-iteration cost. We further extend the framework to obtain approximate second-order KKT points using only first-order information by integrating a gradient-based negative-curvature routine, thus avoiding explicit Hessian computations. We conduct numerical experiments to demonstrate the scalability of our approximate first-order IPTR framework in large-scale settings, where it achieves up to a $2.48\times$ speedup over the existing first-order IPTR algorithm.

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arXiv2026

Space-Efficient Quantum Algorithm for Elliptic Curve Discrete Logarithms with Resource Estimation

Solving the Elliptic Curve Discrete Logarithm Problem (ECDLP) is critical for evaluating the quantum security of widely deployed elliptic-curve cryptosystems. Consequently, minimizing the number of logical qubits required to execute this algorithm is a key object. In implementations of Shor's algorithm, the space complexity is largely dictated by the modular inversion operation during point addition. Starting from the extended Euclidean algorithm (EEA), we refine the register-sharing method of Proos and Zalka and propose a space-efficient reversible modular inversion algorithm. We use length registers together with location-controlled arithmetic to store the intermediate variables in a compact form throughout the computation. We then optimize the stepwise update rules and give concrete circuit constructions for the resulting controlled arithmetic components. This leads to a modular inversion circuit that uses $3n + 4\lfloor \log_2 n \rfloor + O(1)$ logical qubits and $204n^2\log_2 n + O(n^2)$ Toffoli gates. By inserting this modular inversion component into the controlled affine point-addition circuit, we obtain a space-efficient algorithm for the ECDLP with $5n + 4\lfloor \log_2 n \rfloor + O(1)$ qubits and $O(n^3)$ Toffoli gates. In particular, for a 256-bit prime-field curve, our estimate reduces the logical-qubit count to 1333, compared with 2124 in the previous low-width implementation of Häner et al.

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arXiv2025

Quantum Algorithms for Bandits with Knapsacks with Improved Regret and Time Complexities

Bandits with knapsacks (BwK) constitute a fundamental model that combines aspects of stochastic integer programming with online learning. Classical algorithms for BwK with a time horizon $T$ achieve a problem-independent regret bound of ${O}(\sqrt{T})$ and a problem-dependent bound of ${O}(\log T)$. In this paper, we initiate the study of the BwK model in the setting of quantum computing, where both reward and resource consumption can be accessed via quantum oracles. We establish both problem-independent and problem-dependent regret bounds for quantum BwK algorithms. For the problem-independent case, we demonstrate that a quantum approach can improve the classical regret bound by a factor of $(1+\sqrt{B/\mathrm{OPT}_\mathrm{LP}})$, where $B$ is budget constraint in BwK and $\mathrm{OPT}_{\mathrm{LP}}$ denotes the optimal value of a linear programming relaxation of the BwK problem. For the problem-dependent setting, we develop a quantum algorithm using an inexact quantum linear programming solver. This algorithm achieves a quadratic improvement in terms of the problem-dependent parameters, as well as a polynomial speedup of time complexity on problem's dimensions compared to classical counterparts. Compared to previous works on quantum algorithms for multi-armed bandits, our study is the first to consider bandit models with resource constraints and hence shed light on operations research.

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arXiv2025

Performance guarantees of light-cone variational quantum algorithms for the maximum cut problem

Variational quantum algorithms (VQAs) are promising to demonstrate the advantage of near-term quantum computing over classical computing in practical applications, such as the maximum cut (MaxCut) problem. However, current VQAs such as the quantum approximate optimization algorithm (QAOA) have lower performance guarantees compared to the best-known classical algorithm, and suffer from hard optimization processes due to the barren plateau problem. We propose a light-cone VQA by choosing an optimal gate sequence of the standard VQAs, which enables a significant improvement in solution accuracy while avoiding the barren plateau problem. Specifically, we prove that the light-cone VQA with one round achieves an approximation ratio of 0.7926 for the MaxCut problem in the worst case of $3$-regular graphs, which is higher than that of the 3-round QAOA, and can be further improved to 0.8333 by an angle-relaxation procedure. Finally, our numerical results indicate an exponential speed-up in finding the exact solution using the light-cone VQA compared with the classical algorithm. Using IBM's quantum devices, we demonstrate that the single-round light-cone VQA exceeds the known classical hardness threshold in both 72- and 148-qubit demonstrations, whereas $p$-round $\text{QAOA}$ with $p=1,2,3$ does not in the latter one. Our work highlights a promising route towards solving classically hard problems on practical quantum devices.

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arXiv2025

Quantum Approximate Optimization Algorithms for Maximum Cut on Low-Girth Graphs

Maximum cut (MaxCut) on graphs is a classic NP-hard problem. In quantum computing, Farhi, Gutmann, and Goldstone proposed the Quantum Approximate Optimization Algorithm (QAOA) for solving the MaxCut problem. Its guarantee on cut fraction (the fraction of edges in the output cut over all edges) was mainly studied for high-girth graphs, i.e., graphs with only long cycles. On the other hand, low-girth graphs are ubiquitous in theoretical computer science, including expander graphs being outstanding examples with wide applications in theory and beyond. In this paper, we apply QAOA to MaxCut on a set of expander graphs proposed by Mohanty and O'Donnell known as additive product graphs. Additionally, we apply multi-angle QAOA (ma-QAOA) to better utilize the graph structure of additive product graphs in ansatz design. In theory, we derive an iterative formula to calculate the expected cut fraction of such graphs. This formula also extends to the quantum MaxCut problem. On the other hand, we conduct numerical experiments to compare between best-known classical local algorithms and QAOA with constant depth. Our results demonstrate that QAOA outperforms the best-known classical algorithms by 0.3% to 5.2% on several additive product graphs, while ma-QAOA further enhances this advantage by an additional 0.6% to 2.5%. In particular, we observe cases that ma-QAOA exhibits superiority over best-known classical algorithms but QAOA does not. Furthermore, we extend our experiments to planar graphs such as tiling grid graphs, where QAOA also demonstrates an advantage.

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