arXiv subjects

Zi-Wen Huang

Publications and source records attributed to Zi-Wen Huang.

3 recordsLinked to original sources

arXiv2026

Iterative Partition Search Variational Quantum Algorithm for Solving Shortest Vector Problem

The Partition Search Algorithm (PSA) and Iterative Quantum Optimization with an Adaptive Problem (IQOAP) are leading variational quantum algorithms for solving Shortest Vector Problem (SVP). However, each has limitations that restrict its practical impact. IQOAP suffers from ineffective iterations that fail to update the lattice basis, whereas PSA's static partitioning leads to oversized search spaces. In this work, we propose the Iterative Partition Search Algorithm (IPSA), which systematically addresses these drawbacks by integrating a "1-tailed search spaces" with a dynamic, stack-managed iterative process. Specifically, the "1-tailed" strategy ensures that every successful execution yields an effective lattice basis update, thereby eliminating the ineffective iterations associated with IQOAP. Concurrently, the dynamic iterative process reduces the required qubit count, thereby avoiding the limitation of an oversized search space inherent to PSA. We validate IPSA on the Baihua superconducting quantum processor via the Quafu platform. Small-scale real hardware experiments demonstrate that, compared to PSA, IPSA achieves a 14-fold increase in success rate at a cost of less than double the total circuit depth. Conversely, compared to IQOAP, IPSA reduces the total circuit depth by 82.7% while achieving approximately 2.5 times its success rate. Furthermore, we also conduct numerical simulations whose results are in good agreement with the experimental findings and extend our analysis.

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arXiv2025

Quantum-Assisted Recursive Algorithm for Solving the Exact Cover Problem

The exact cover problem is an NP-complete problem with broad applications. Studies show that although applying the Quantum Approximate Optimization Algorithm (QAOA) to this problem can yield improved solution quality with deeper circuit depth, it can limit the algorithm's applicability on noisy intermediate-scale quantum devices. To improve solution quality at shallow depth, we propose a Quantum-Assisted Recursive Algorithm (QARA) for solving the exact cover problem. QARA addresses the problem by alternately applying classical and quantum pruning. Classical pruning is a repeatable pre-processing step to simplify the problem. When the classical pruning cannot promote the problem simplification, quantum pruning is invoked. During quantum pruning, QARA extracts information from the QAOA's output state to identify the subset with the strongest selection bias. This subset is then used to prune the problem based on our problem-tailored reduction rules. Furthermore, QARA incorporates a local verification and rollback mechanism to assistively judge the effectiveness of the quantum simplification. After quantum pruning, classical pruning is applied again to the reduced problem if the remaining subsets and element set are not null. This alternating process repeats until the original problem is fully resolved. In our numerical simulations, we evaluate the performance of QARA at one-layer depth on 140 instances with subset sizes ranging from 8 to 20. Numerical results show that the probability of QARA in finding an exact solution is approximately 60\% higher than that of both QAOA and Recursive QAOA, highlighting its efficiency.

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arXiv2022

Generalizations of Berry phase and differentiation of purified state and thermal vacuum of mixed states

Two representations of mixed states by state-vectors, known as purified state and thermal vacuum, have been realized on quantum computers. While the two representations look similar, they differ by a partial transposition in the ancilla space. While ordinary observables cannot discern the two representations, we generalize the Berry phase of pure quantum states to mixed states and construct two geometric phases that can reflect the partial transposition. By generalizing the adiabatic condition, we construct the thermal Berry phase, whose values from the two representations can be different, However, the thermal Berry phase may contain non-geometrical contributions. Alternatively, we generalize the parallel-transport condition to include the system and ancilla and show the dynamical phase is excluded under parallel transport. The geometrical phase accumulated in parallel transport is the generalized Berry phase, which may or may not differentiate a purified state from a thermal vacuum depending on the protocol. The generalizations of the Berry phase to mixed states may be realized and measured on quantum computers via the two representations to reveal the rich physics of finite-temperature quantum systems.

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