arXiv subjects

Wenxuan Tao

Publications and source records attributed to Wenxuan Tao.

8 recordsLinked to original sources

arXiv2026

Deterministic Preparation of Arbitrary Spin Eigenfunctions

Quantum states with conserved total spins, or spin eigenfunctions, are important for studying quantum chemistry and quantum manybody physics problems. A typical class of spin eigenfunctions are Dicke states, which attain maximal spins. While we already have many efficient quantum algorithms to prepare Dicke states, it is not yet clear if we could do so for arbitrary spin eigenfunctions deterministically. Generalizing Bärtschi and Eidenbenz's elegant algorithms for Dicke state preparation, we successfully prepare arbitrary spin eigenfunctions characterized by branching paths and binary spin trees. As a byproduct, we also develop the corresponding classical algorithms to reconstruct all these spin states.

quant-ph↗

arXiv2026

Three-dimensional stochastic wave equation with non-Lipschitz coefficients

We consider the three-dimensional stochastic wave equation (SWE) driven by a multiplicative Gaussian noise that is white in time and colored in space: \[ \frac{\partial^2 u}{\partial t^2} = Δu + b\bigl(u\bigr) + σ\bigl(u\bigr)\,\dot{W}, \] where the drift function $ b $ and diffusion coefficient $σ$ are assumed to be locally Lipschitz and exhibit logarithmic superlinear growth at infinity. We establish the existence and uniqueness of a global mild solution on any fixed time interval $[0,T]$ under suitable assumptions on the spatial covariance function $ f $ of the noise $\dot W(t,x)$. Our results apply, for example, to the case \[ b(u) = u (\log_+ u)^{θ_1} \quad \text{and} \quad σ(u) = u (\log_+ u)^{θ_2}, \] with parameters $θ_1 \in (0,2)$ and $θ_2 \in \bigl(0, \tfrac{\barν+1}{2}\bigr)$, and $\log_+(z)=\log(z\vee e)$, where $\barν$ is determined by the assumptions on $ f $.

math.PR↗

arXiv2026

Ergodicity and asymptotic limits for Langevin interacting systems with singular forces and multiplicative noises

In this paper, we study systems of $N$ interacting particles described by the classical and relativistic Langevin dynamics with singular forces and multiplicative noises. For the classical model, we prove the ergodicity, obtaining an exponential rate of convergence to the invariant Boltzmann-Gibbs distribution, and the small-mass limit, recovering the $N$-particle interacting overdamped Langevin dynamics. For the relativistic model, we establish the ergodicity, obtaining an algebraic mixing rate of any order to the Maxwell-Jüttner distribution, and the Newtonian limit (that is when the speed of light tends to infinity), approximating a system of underdamped Langevin dynamics. The proofs rely on the construction of Lyapunov functions that account for irregular potentials and multiplicative noises.

math.PR↗

arXiv2026

On weak convergence of stochastic wave equation with colored noise on $\mathbb{R}$

In this paper, we study the following stochastic wave equation on the real line $\partial_t^2 u_α=\partial_x^2 u_α+b\left(u_α\right)+σ\left(u_α\right)η_α$. The noise $η_α$ is white in time and colored in space with a covariance structure $\mathbb{E}[η_α(t,x)η_α(s,y)]=δ(t-s)f_α(x-y)$ where $f_α$ is continuous with respect to $α$ in Fourier mode, see Assumption 1.2. We prove the continuity of the probability measure induced by the solution $u_α$, in terms of $α$, with respect to the convergence in law in the topology of continuous functions with uniform metric on compact sets. We also give several examples of $f_α$ such that our theorem applies to.

math.PR↗

arXiv2026

Distributed Exact Quantum Amplitude Amplification Algorithm for Arbitrary Quantum States

In the noisy intermediate-scale quantum (NISQ) era, distributed quantum computation has garnered considerable interest, as it overcomes the physical limitations of single-device architectures and enables scalable quantum information processing. In this study, we focus on the challenge of achieving exact amplitude amplification for quantum states with arbitrary amplitude distributions and subsequently propose a Distributed Exact Quantum Amplitude Amplification Algorithm (DEQAAA). Specifically, (1) it supports partitioning across any number of nodes $t$ within the range $2 \leq t \leq n$; (2) the maximum qubit count required for any single node is expressed as $\max \left(n_0,n_1,\dots,n_{t-1} \right) $, where $n_j$ represents the number of qubits at the $j$-th node, with $\sum_{j=0}^{t-1} n_j =n$; (3) it can realize exact amplitude amplification for multiple targets of a quantum state with arbitrary amplitude distributions; (4) we verify the effectiveness of DEQAAA by resolving a specific exact amplitude amplification task involving two targets (8 and 14 in decimal) via MindSpore Quantum, a quantum simulation software, with tests conducted on 4-qubit, 6-qubit, 8-qubit and 10-qubit systems. Notably, through the decomposition of $C^{n-1}PS$ gates, DEQAAA demonstrates remarkable advantages in both quantum gate count and circuit depth as the qubit number scales, thereby boosting its noise resilience. In the 10-qubit scenario, for instance, it achieves a reduction of over $97\%$ in both indicators compared to QAAA and EQAAA, underscoring its outstanding resource-saving performance.

quant-ph↗

arXiv2025

A stochastic heat equation with non-locally Lipschitz coefficients

We consider the stochastic heat equation (SHE) on the torus $\mathbb{T}=[0,1]$, driven by space-time white noise $\dot W$, with an initial condition $u_0$ that is nonnegative and not identically zero: \begin{equation*} \frac{\partial u}{\partial t} = \tfrac{1}{2}\frac{\partial^2 u}{\partial x^2} + b(u) + σ(u)\dot{W}. \end{equation*} The drift $b$ and diffusion coefficient $σ$ are Lipschitz continuous away from zero, although their Lipschitz constants may blow up as the argument approaches zero. We establish the existence of a unique global mild solution that remains strictly positive. Examples include $b(u)=u|\log u|^{A_1}$ and $σ(u)=u|\log u|^{A_2}$ with $A_1\in(0,1)$ and $A_2\in(0,1/4)$.

math.PR↗

arXiv2025

Testing APS conjecture on regular graphs

The maximum energy of the EPR model on a weighted graph is known to be upper-bounded by the sum of the total weight and the value of maximum-weight fractional matching~(MWFM). Recently, Apte, Parekh and Sud~(APS) conjecture that the bound could be strengthened by replacing MWFM with maximum weight matching~(MWM). Here we test this conjecture on a special class of regular graphs that Henning and Yeo constructed many years ago. On this class of regular graphs, MWMs achieve tight lower bounds. As for the maximum energy of the EPR model, we have recently devised a new algorithm called Fractional Entanglement Distribution~(FED) based on quasi-homogeneous fractional matchings, which could achieve rather high accuracy. Applying the FED algorithm to the EPR model on Henning-Yeo graphs, we could thus obtain energy as high as possible and matching value as low as possible, and then make high-precision tests of the APS conjecture. Nevertheless, our numerical results do not show any evidence that the APS conjecture could be violated.

quant-ph↗

arXiv2025

A Refined Algorithm For the EPR model

The Einstein-Podolsky-Rosen~(EPR) model is an analogous model of the anti-ferromagnetic Heisenberg model or the equivalent quantum maximum-cut problem, proposed by R. King two years ago. Adjacent qubits in the model prefer symmetric EPR/Bell parings rather than the antisymmetric one, in order to maximize the energy. Recently, two groups independently develop specific algorithms for the highest-energy state with approximation ratio $\frac{1+\sqrt{5}}{4}\approx.809$, based on maximum fractional matchings. Here we try to refine one of the two algorithms by devising homogeneous/quasi-homogeneous fractional matchings, with the aim to distribute quantum entanglement as much as possible. For regular graphs $G_d$, we immediately obtain increasing approximation ratios $r_d$ with $r_2=\frac{3+\sqrt{5}}{6}\approx.872$. For irregular graphs, we show such a refinement could still guarantee nice performance if the fractional matchings are chosen properly.

quant-ph↗