arXiv subjects

Haochen Xu

Publications and source records attributed to Haochen Xu.

10 recordsLinked to original sources

arXiv2026

PureSuperQMA(exp) = BellPureSymQMA(poly) = QMA via Dimension-Free Bosonic Argmax

Pure-state consistency problems naturally lead to quantum proof systems in which a single pure witness must satisfy many acceptance constraints. The corresponding class $\mathsf{PureSuperQMA}$ was previously known to lie between $\mathsf{QMA}$ and $\mathsf{QMA}(2)$, and Kamminga and Rudolph (ITCS'26) conjectured that both containments are strict. In this paper, we prove the following surprising complexity collapses $$ \mathsf{QMA} = \mathsf{PureSuperQMA} = \mathsf{PureSuperQMA}(\text{exp}) = \mathsf{BellPureSymQMA}(\text{poly}) $$ Here $\mathsf{PureSuperQMA}(\text{exp})$ allows exponentially many checks which are uniformly indexed and efficiently generated, while requiring an inverse-polynomial violation margin and an inverse-polynomial fraction of violated checks for the NO cases. $\mathsf{BellPureSymQMA}(\text{poly})$ is a related model that requires the prover to give the verifier polynomially many copies of a pure state, which the verifier measures separately with logarithmic output length for each local measurement, before processing the outcomes jointly. The main technical ingredient is a dimension-free stability bound for symmetric tensor states. Our simulations use polynomially many witness registers and combine a random-pair SWAP test with a permutation-invariant lift of the original verification procedure. The key step is to show that, on the symmetric subspace, the extremal verification value is close to that of some tensor-power witness with dimension-independent error. Applying this argument to the two verification models yields both simulations. As a consequence, exact $k$-local pure-state consistency is $\mathsf{QMA}$-complete for every fixed $k\ge2$, and so are the corresponding exact bosonic and fermionic pure $N$-representability problems.

quant-ph↗

arXiv2026

Optimal Quantum de Finetti Theorems via Argmax Rounding

We prove optimal finite quantum de Finetti upper bounds. Given a bosonic state $\rho_N\in D(\mathrm{Sym}^N(\mathbb C^d))$, there is a probability measure $\nu$ on the unit sphere such that \[ \left\| \rho_N^{(2)}-\int |u\rangle\langle u|^{\otimes 2}\,d\nu(u) \right\|_1 \le \frac{\sqrt{d-1}}{N-1}. \] By purification, the bosonic theorem also gives the optimal $O(d/N)$ upper bound for arbitrary exchangeable states. These results settle the dimension dependence left open by Christandl, K\"onig, Mitchison, and Renner (CMP 2007). The proof casts de Finetti approximation as sum-of-squares rounding and applies the argmax method of Jeronimo, Wu, and Xu (manuscript 2026). More generally, $t$-site marginals satisfy $O(t\sqrt d/N)$ bosonic and $O(td/N)$ permutation-invariant bounds. Our proof formulates de Finetti approximation as the integrality gap of a symmetric-extension semidefinite program and rounds an optimum by the argmax principle. The sharp bounds have several consequences. For every fixed $\varepsilon\in(0,1)$, we construct a channel with input dimension $D=\exp(O_\varepsilon(\sqrt d\log d))=\exp(o(d))$ whose outputs are $\varepsilon$-close to separable states of local dimension $d$ and whose image contains every such separable state, thereby refuting Watrous's disentangler conjecture. We also obtain deterministic $\exp(\widetilde O(\sqrt d/\varepsilon))$-time algorithms for explicit Best Separable State without perfect completeness and for trace-distance separability testing. Finally, spectral truncation gives the first dimension-free bosonic de Finetti theorem in Hilbert--Schmidt distance, with the optimal rate $\Theta(N^{-1/2})$ when the dimension may grow.

quant-ph↗

arXiv2026

An Argmax Principle for Sum-of-Squares Relaxations on the Sphere

We develop an argmax principle for analyzing sum-of-squares relaxations of optimization problems over the unit sphere. Given a feasible pseudo-expectation, we form a polynomial of high-order pseudo-moments, such as $\Phi_k(u)=\widetilde{\mathbb E}\langle x,u\rangle^{2k}$. Our guiding principle is that its maximizers are rounding candidates: their local and global optimality conditions reveal the reweighed pseudo-expectation inequalities governing SoS convergence. This viewpoint unifies several problems previously analyzed by rather different techniques. We obtain three results. First, for Best Separable State, we give a degree-$O(\sqrt{n/\epsilon})$ SoS analysis for approximating $h_{\mathrm{sep}}(P)$ in the perfect-completeness regime, improving and simplifying Barak, Kothari and Steurer (STOC'17). The dependence is essentially tight for inverse-linear gap under the Exponential-Time Hypothesis, matching hardness from $\mathrm{QMA}(2)$ protocols. Second, for the matrix $2\to4$ norm, degree-$O(\sqrt n/\epsilon)$ SoS gives a multiplicative $(1+\epsilon)$ approximation. Barak et al. (STOC'12) previously gave a comparable-time constant-gap decision algorithm; our result gives a multiplicative guarantee and extends to a family of $p\to q$ norms with even $q$. Finally, for degree-$d$ polynomial optimization, we recover the convergence theorem of Bhattiprolu et al. (FOCS'17) with a shorter, more direct proof: degree-$k$ SoS gives approximation ratio $O_d((n/k)^{d/2-1})$. The paper introduces no new relaxation. Instead, the high-moment argmax gives a common way to read an SoS solution, unifying previously separate convergence analyses and yielding sharper bounds or simpler proofs.

cs.CC↗

arXiv2026

Bayesian Bandit Beamforming with Implicit Channel Learning for RIS under Hybrid Near/Far-Field Propagation

Reconfigurable intelligent surfaces (RISs) can improve high-frequency wireless links by shaping the propagation environment, but their passive architecture makes channel acquisition costly. Conventional estimate-then-optimize methods usually require pilot overhead that scales with the number of reflecting elements, which is undesirable under short coherence times and hybrid near-/far-field propagation. This paper proposes the Bayesian bandit framework for RIS phase-shift configuration with implicit channel learning. The method updates a Gaussian posterior of the cascaded channel from one scalar pilot observation per slot and uses Thompson sampling to balance channel estimation and beamforming gain. We derive a Bayesian regret decomposition that connects Bayesian received-power regret to posterior uncertainty contraction, and further establish a conditional sublinear Bayesian-regret guarantee. To exploit sparse hybrid-field propagation, we develop an energy-focusing angle-distance dictionary and a sparse Bayesian learning (SBL)-based Thompson-sampling algorithm with warm-started hyperparameter refinement. Simulations show that the proposed policies approach the perfect-channel state information (CSI) benchmark in the line-of-sight (LOS)-dominant setting within 10 time block and improve transmission efficiency over the considered baselines in multipath and Rayleigh fading scenarios.

eess.SP↗

arXiv2025

Nonlocal Games in the High-Noise Regime: Optimal Quantum Values and Rigidity

Motivated by the limitations of near-term quantum devices, we study nonlocal games in the high-noise regime, where the two players may share arbitrarily many copies of a noisy entangled state. In this regime, existing rigidity theorems are unable to certify any nontrivial quantum structure. We first characterize the maximal quantum winning probabilities of the CHSH game [Clauser et al. '69], the Magic Square game [Mermin '90], and their 2-out-of-n variants [Chao et al. '18] as explicit functions of the noise rate. These characterizations enable the construction of device-independent protocols for estimating the underlying noise level. Building on these results, we prove noise-robust rigidity theorems showing that these games certify one, two, and n pairs of anticommuting Pauli observables, respectively. To our knowledge, these are the first rigidity results of Pauli measurements that remain sound in the high-noise regime, which has applications in Measurement-Device-Independent (MDI) cryptography and studying the computational power of Multi-prover Interactive Proof System with entanglement and a vanishing completeness-soundness gap ($\text{MIP}^*_0$). Our proofs rely on Sum-of-Squares decompositions and Pauli analysis techniques originating from quantum proof systems and quantum learning theory, respectively.

quant-ph↗

arXiv2025

Explosive Output to Enhance Jumping Ability: A Variable Reduction Ratio Design Paradigm for Humanoid Robots Knee Joint

Enhancing the explosive power output of the knee joints is critical for improving the agility and obstacle-crossing capabilities of humanoid robots. However, a mismatch between the knee-to-center-of-mass (CoM) transmission ratio and jumping demands, coupled with motor performance degradation at high speeds, restricts the duration of high-power output and limits jump performance. To address these problems, this paper introduces a novel knee joint design paradigm employing a dynamically decreasing reduction ratio for explosive output during jump. Analysis of motor output characteristics and knee kinematics during jumping inspired a coupling strategy in which the reduction ratio gradually decreases as the joint extends. A high initial ratio rapidly increases torque at jump initiation, while its gradual reduction minimizes motor speed increments and power losses, thereby maintaining sustained high-power output. A compact and efficient linear actuator-driven guide-rod mechanism realizes this coupling strategy, supported by parameter optimization guided by explosive jump control strategies. Experimental validation demonstrated a 63 cm vertical jump on a single-joint platform (a theoretical improvement of 28.1\% over the optimal fixed-ratio joints). Integrated into a humanoid robot, the proposed design enabled a 1.1 m long jump, a 0.5 m vertical jump, and a 0.5 m box jump.

cs.RO↗

arXiv2024

Lower-level Duality Based Reformulation and Majorization Minimization Algorithm for Hyperparameter Optimization

Hyperparameter tuning is an important task of machine learning, which can be formulated as a bilevel program (BLP). However, most existing algorithms are not applicable for BLP with non-smooth lower-level problems. To address this, we propose a single-level reformulation of the BLP based on lower-level duality without involving any implicit value function. To solve the reformulation, we propose a majorization minimization algorithm that marjorizes the constraint in each iteration. Furthermore, we show that the subproblems of the proposed algorithm for several widely used hyperparameter turning models can be reformulated into conic programs that can be efficiently solved by the off-the-shelf solvers. We theoretically prove the convergence of the proposed algorithm and demonstrate its superiority through numerical experiments.

math.OC↗

arXiv2023

The Computational Advantage of MIP* Vanishes in the Presence of Noise

Quantum multiprover interactive proof systems with entanglement MIP* are much more powerful than its classical counterpart MIP (Babai et al. '91, Ji et al. '20): while MIP = NEXP, the quantum class MIP* is equal to RE, a class including the halting problem. This is because the provers in MIP* can share unbounded quantum entanglement. However, recent works of Qin and Yao '21 and '23 have shown that this advantage is significantly reduced if the provers' shared state contains noise. This paper attempts to exactly characterize the effect of noise on the computational power of quantum multiprover interactive proof systems. We investigate the quantum two-prover one-round interactive system MIP*[poly, O(1)], where the verifier sends polynomially many bits to the provers and the provers send back constantly many bits. We show noise completely destroys the computational advantage given by shared entanglement in this model. Specifically, we show that if the provers are allowed to share arbitrarily many noisy EPR states, where each EPR state is affected by an arbitrarily small constant amount of noise, the resulting complexity class is equivalent to NEXP = MIP. This improves significantly on the previous best-known bound of NEEEXP (nondeterministic triply exponential time) by Qin and Yao '21. We also show that this collapse in power is due to the noise, rather than the O(1) answer size, by showing that allowing for noiseless EPR states gives the class the full power of RE = MIP*[poly, poly]. Along the way, we develop two technical tools of independent interest. First, we give a new, deterministic tester for the positivity of an exponentially large matrix, provided it has a low-degree Fourier decomposition in terms of Pauli matrices. Secondly, we develop a new invariance principle for smooth matrix functions having bounded third-order Fr\'echet derivatives or which are Lipschitz continous.

quant-ph↗

arXiv2020

Group Network Hawkes Process

In this work, we study the event occurrences of individuals interacting in a network. To characterize the dynamic interactions among the individuals, we propose a group network Hawkes process (GNHP) model whose network structure is observed and fixed. In particular, we introduce a latent group structure among individuals to account for the heterogeneous user-specific characteristics. A maximum likelihood approach is proposed to simultaneously cluster individuals in the network and estimate model parameters. A fast EM algorithm is subsequently developed by utilizing the branching representation of the proposed GNHP model. Theoretical properties of the resulting estimators of group memberships and model parameters are investigated under both settings when the number of latent groups $G$ is over-specified or correctly specified. A data-driven criterion that can consistently identify the true $G$ under mild conditions is derived. Extensive simulation studies and an application to a data set collected from Sina Weibo are used to illustrate the effectiveness of the proposed methodology.

stat.ME↗

arXiv2019

A Latent Topic Model with Markovian Transition for Process Data

We propose a latent topic model with a Markovian transition for process data, which consist of time-stamped events recorded in a log file. Such data are becoming more widely available in computer-based educational assessment with complex problem solving items. The proposed model can be viewed as an extension of the hierarchical Bayesian topic model with a hidden Markov structure to accommodate the underlying evolution of an examinee's latent state. Using topic transition probabilities along with response times enables us to capture examinees' learning trajectories, making clustering/classification more efficient. A forward-backward variational expectation-maximization (FB-VEM) algorithm is developed to tackle the challenging computational problem. Useful theoretical properties are established under certain asymptotic regimes. The proposed method is applied to a complex problem solving item in 2012 Programme for International Student Assessment (PISA 2012).

stat.ME↗