arXiv subjects

Xiao-Hui Ni

Publications and source records attributed to Xiao-Hui Ni.

9 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.

quant-ph↗

arXiv2025

An Adaptive Mixer Allocation Algorithm for the Quantum Alternating Operator Ansatz

Recently, Hadfield et al. proposed the quantum alternating operator ansatz algorithm (QAOA+), an extension of the quantum approximate optimization algorithm (QAOA), to solve constrained combinatorial optimization problems (CCOPs). Compared with QAOA, QAOA+ enables the search for optimal solutions within a feasible solution space by encoding problem constraints into the mixer Hamiltonian, thereby reducing the search space and eliminating the possibility of yielding infeasible solutions. However, QAOA+ may incur high overall gate costs when the mixer is applied to all qubits in each layer, and each mixer is costly to implement. To address this challenge, an adaptive mixer allocation strategy is tailored for QAOA+. The resulting algorithm, which integrates this strategy into the original QAOA+ framework, is referred to as AMA-QAOA+. Unlike QAOA+, AMA-QAOA+ adaptively applies the mixer to a subset of qubits in each layer of the mixer unitary operator based on an evaluation function. The performance of AMA-QAOA+ is evaluated on the maximum independent set problem. Numerical simulation results show that, under the same number of optimization runs, AMA-QAOA+ achieves better solution quality than QAOA+, with the optimal approximation ratio improved by $5.30\%$ on ER random graphs and $5.41\%$ on 3-regular graphs. Moreover, AMA-QAOA+ significantly reduces the CNOT gate consumption, requiring only $15.30\%$ and $25.18\%$ of the CNOT gates used by QAOA+ on ER and 3-regular random graphs, respectively. These results demonstrate that AMA-QAOA+ enhances solution quality and computational efficiency, enabling the design of more compact and resource-efficient quantum circuits.

quant-ph↗

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.

quant-ph↗

arXiv2025

Progressive Quantum Algorithm for Maximum Independent Set with Quantum Alternating Operator Ansatz

Hadfield et al. proposed a novel Quantum Alternating Operator Ansatz algorithm (QAOA+), and this algorithm has wide applications in solving constrained combinatorial optimization problems (CCOPs) because of the advantages of QAOA+ ansatz in constructing a feasible solution space. In this paper, we propose a Progressive Quantum Algorithm (PQA) with QAOA+ ansatz to solve the Maximum Independent Set (MIS) problem using fewer qubits. The core idea of PQA is to construct a subgraph that is likely to contain the MIS solution of the target graph and then solve the MIS problem on this subgraph to obtain an approximate solution. To construct such a subgraph, PQA starts with a small-scale initial subgraph and progressively expands its graph size utilizing heuristic expansion strategies. After each expansion, PQA solves the MIS problem on the newly generated subgraph. In each run, PQA repeats the expansion and solving process until a predefined stopping condition is reached. Simulation results demonstrate that to achieve an approximation ratio of 0.95, PQA requires only $5.565\%$ ($2.170\%$) of the qubits and $17.59\%$ ($6.430\%$) of the runtime compared with directly solving the original problem using QAOA+ on Erdős-Rényi (3-regular) graphs, highlighting the efficiency of PQA.

quant-ph↗

arXiv2024

Multilevel leapfrogging initialization for quantum approximate optimization algorithm

Recently, Zhou et al. have proposed a novel Interpolation-based (INTERP) strategy to generate the initial parameters for the Parameterized Quantum Circuit (PQC) in Quantum Approximate Optimization Algorithm (QAOA). INTERP produces the guess of the initial parameters at level $i+1$ by applying linear interpolation to the optimized parameters at level $i$, achieving better performance than random initialization (RI). Nevertheless, INTERP consumes extensive running costs for deep QAOA because it necessitates optimization at each level of the PQC. To address this problem, a Multilevel Leapfrogging Interpolation (MLI) strategy is proposed. MLI can produce the guess of the initial parameters from level $i+1$ to $i+l$ ($l>1$) at level $i$, omitting the optimization rounds from level $i+1$ to $(i+l-1)$. The final result is that MLI executes optimization at few levels rather than each level, and this operation is referred to as Multilevel Leapfrogging optimization (M-Leap). The performance of MLI is investigated on the Maxcut problem. Compared with INTERP, MLI reduces most optimization rounds. Remarkably, the simulation results demonstrate that MLI can achieve the same quasi-optima as INTERP while consuming only 1/2 of the running costs required by INTERP. In addition, for MLI, where there is no RI except for level $1$, the greedy-MLI strategy is presented. The simulation results suggest that greedy-MLI has better stability (i.e., a higher average approximation ratio) than INTERP and MLI beyond obtaining the same quasi-optima as INTERP. According to the efficiency of finding the quasi-optima, the idea of M-Leap might be extended to other training tasks, especially those requiring numerous optimizations, such as training adaptive quantum circuits.

quant-ph↗

arXiv2009

Scaling and memory in the non-poisson process of limit order cancelation

The order submission and cancelation processes are two crucial aspects in the price formation of stocks traded in order-driven markets. We investigate the dynamics of order cancelation by studying the statistical properties of inter-cancelation durations defined as the waiting times between consecutive order cancelations of 22 liquid stocks traded on the Shenzhen Stock Exchange of China in year 2003. Three types of cancelations are considered including cancelation of any limit orders, of buy limit orders and of sell limit orders. We find that the distributions of the inter-cancelation durations of individual stocks can be well modeled by Weibulls for each type of cancelation and the distributions of rescaled durations of each type of cancelations exhibit a scaling behavior for different stocks. Complex intraday patterns are also unveiled in the inter-cancelation durations. The detrended fluctuation analysis (DFA) and the multifractal DFA show that the inter-cancelation durations possess long-term memory and multifractal nature, which are not influenced by the intraday patterns. No clear crossover phenomenon is observed in the detrended fluctuation functions with respect to the time scale. These findings indicate that the cancelation of limit orders is a non-Poisson process, which has potential worth in the construction of order-driven market models.

q-fin.TR↗

arXiv2009

Degree distribution of the visibility graphs mapped from fractional Brownian motions and multifractal random walks

The dynamics of a complex system is usually recorded in the form of time series, which can be studied through its visibility graph from a complex network perspective. We investigate the visibility graphs extracted from fractional Brownian motions and multifractal random walks, and find that the degree distributions exhibit power-law behaviors, in which the power-law exponent $α$ is a linear function of the Hurst index $H$ of the time series. We also find that the degree distribution of the visibility graph is mainly determined by the temporal correlation of the original time series with minor influence from the possible multifractal nature. As an example, we study the visibility graphs constructed from two Chinese stock market indexes and unveil that the degree distributions have power-law tails, where the tail exponents of the visibility graphs and the Hurst indexes of the indexes are close to the $α\sim H$ linear relationship.

physics.soc-ph↗

arXiv2009

Empirical regularities of opening call auction in Chinese stock market

We study the statistical regularities of opening call auction using the ultra-high-frequency data of 22 liquid stocks traded on the Shenzhen Stock Exchange in 2003. The distribution of the relative price, defined as the relative difference between the order price in opening call auction and the closing price of last trading day, is asymmetric and that the distribution displays a sharp peak at zero relative price and a relatively wide peak at negative relative price. The detrended fluctuation analysis (DFA) method is adopted to investigate the long-term memory of relative order prices. We further study the statistical regularities of order sizes in opening call auction, and observe a phenomenon of number preference, known as order size clustering. The probability density function (PDF) of order sizes could be well fitted by a $q$-Gamma function, and the long-term memory also exists in order sizes. In addition, both the average volume and the average number of orders decrease exponentially with the price level away from the best bid or ask price level in the limit-order book (LOB) established immediately after the opening call auction, and a price clustering phenomenon is observed.

q-fin.ST↗

arXiv2007

Intraday pattern in bid-ask spreads and its power-law relaxation for Chinese A-share stocks

We use high-frequency data of 1364 Chinese A-share stocks traded on the Shanghai Stock Exchange and Shenzhen Stock Exchange to investigate the intraday patterns in the bid-ask spreads. The daily periodicity in the spread time series is confirmed by Lomb analysis and the intraday bid-ask spreads are found to exhibit $L$-shaped pattern with idiosyncratic fine structure. The intraday spread of individual stocks relaxes as a power law within the first hour of the continuous double auction from 9:30AM to 10:30AM with exponents $β_{\rm{SHSE}}=0.19\pm0.069$ for the Shanghai market and $β_{\rm{SZSE}}=0.18\pm0.067$ for the Shenzhen market. The power-law relaxation exponent $β$ of individual stocks is roughly normally distributed. There is evidence showing that the accumulation of information widening the spread is an endogenous process.

q-fin.ST↗