no code implementations • 27 Nov 2023 • Zherui Chen, Yuchen Lu, Hao Wang, Yizhou Liu, Tongyang Li
Finally, based on the observations when comparing QLD with classical Fokker-Plank-Smoluchowski equation, we propose a time-dependent QLD by making temperature and $\hbar$ time-dependent parameters, which can be theoretically proven to converge better than the time-independent case and also outperforms a series of state-of-the-art quantum and classical optimization algorithms in many non-convex landscapes.
no code implementations • 5 Jun 2023 • Yecheng Xue, Xiaoyu Chen, Tongyang Li, Shaofeng H. -C. Jiang
$k$-Clustering in $\mathbb{R}^d$ (e. g., $k$-median and $k$-means) is a fundamental machine learning problem.
no code implementations • 21 Feb 2023 • Han Zhong, Jiachen Hu, Yecheng Xue, Tongyang Li, LiWei Wang
While quantum reinforcement learning (RL) has attracted a surge of attention recently, its theoretical understanding is limited.
no code implementations • 12 Oct 2022 • Andrew M. Childs, Tongyang Li, Jin-Peng Liu, Chunhao Wang, Ruizhe Zhang
We also prove a $1/\epsilon^{1-o(1)}$ quantum lower bound for estimating normalizing constants, implying near-optimality of our quantum algorithms in $\epsilon$.
1 code implementation • 29 Sep 2022 • Yizhou Liu, Weijie J. Su, Tongyang Li
Classical algorithms are often not effective for solving nonconvex optimization problems where local minima are separated by high barriers.
no code implementations • 26 Sep 2022 • Tongyang Li, Ruizhe Zhang
As an application, we give a quantum algorithm for zeroth-order stochastic convex bandits with $\tilde{O}(n^{5}\log^{2} T)$ regret, an exponential speedup in $T$ compared to the classical $\Omega(\sqrt{T})$ lower bound.
no code implementations • 1 Jun 2022 • Xinyi Chen, Elad Hazan, Tongyang Li, Zhou Lu, Xinzhao Wang, Rui Yang
In the fundamental problem of shadow tomography, the goal is to efficiently learn an unknown $d$-dimensional quantum state using projective measurements.
no code implementations • 30 May 2022 • Zongqi Wan, Zhijie Zhang, Tongyang Li, Jialin Zhang, Xiaoming Sun
In this paper, we study MAB and SLB with quantum reward oracles and propose quantum algorithms for both models with $O(\mbox{poly}(\log T))$ regrets, exponentially improving the dependence in terms of $T$.
no code implementations • NeurIPS 2021 • Chenyi Zhang, Tongyang Li
Compared to the previous state-of-the-art algorithms by Jin et al. with $\tilde{O}((\log n)^{4}/\epsilon^{2})$ or $\tilde{O}((\log n)^{6}/\epsilon^{1. 75})$ iterations, our algorithm is polynomially better in terms of $\log n$ and matches their complexities in terms of $1/\epsilon$.
no code implementations • 11 Dec 2020 • Tongyang Li, Chunhao Wang, Shouvanik Chakrabarti, Xiaodi Wu
We give a sublinear classical algorithm that can interpolate smoothly between these two cases: for any fixed $q\in (1, 2]$, we solve the matrix game where $\mathcal{X}$ is a $\ell_{q}$-norm unit ball within additive error $\epsilon$ in time $\tilde{O}((n+d)/{\epsilon^{2}})$.
no code implementations • 20 Jul 2020 • Chenyi Zhang, Jiaqi Leng, Tongyang Li
Compared to the classical state-of-the-art algorithm by Jin et al. with $\tilde{O}(\log^{6} (n)/\epsilon^{1. 75})$ queries to the gradient oracle (i. e., the first-order oracle), our quantum algorithm is polynomially better in terms of $\log n$ and matches its complexity in terms of $1/\epsilon$.
1 code implementation • 14 Jul 2020 • Daochen Wang, Xuchen You, Tongyang Li, Andrew M. Childs
Identifying the best arm of a multi-armed bandit is a central problem in bandit optimization.
1 code implementation • NeurIPS 2019 • Shouvanik Chakrabarti, Yiming Huang, Tongyang Li, Soheil Feizi, Xiaodi Wu
The study of quantum generative models is well-motivated, not only because of its importance in quantum machine learning and quantum chemistry but also because of the perspective of its implementation on near-term quantum machines.
no code implementations • 14 Oct 2019 • Nai-Hui Chia, András Gilyén, Tongyang Li, Han-Hsuan Lin, Ewin Tang, Chunhao Wang
Motivated by quantum linear algebra algorithms and the quantum singular value transformation (SVT) framework of Gily\'en, Su, Low, and Wiebe [STOC'19], we develop classical algorithms for SVT that run in time independent of input dimension, under suitable quantum-inspired sampling assumptions.
no code implementations • 4 Apr 2019 • Tongyang Li, Shouvanik Chakrabarti, Xiaodi Wu
We design sublinear quantum algorithms for the same task running in $\tilde{O}(\sqrt{n} +\sqrt{d})$ time, a quadratic improvement in both $n$ and $d$.
no code implementations • 2 Feb 2019 • András Gilyén, Tongyang Li
The presented approach is a natural fit for distributional property testing both in the classical and the quantum case, demonstrating the first speed-ups for testing properties of density operators that can be accessed coherently rather than only via sampling; for classical distributions our algorithms significantly improve the precision dependence of some earlier results.
no code implementations • 10 Jan 2019 • Nai-Hui Chia, Tongyang Li, Han-Hsuan Lin, Chunhao Wang
In this paper, we present a proof-of-principle sublinear-time algorithm for solving SDPs with low-rank constraints; specifically, given an SDP with $m$ constraint matrices, each of dimension $n$ and rank $r$, our algorithm can compute any entry and efficient descriptions of the spectral decomposition of the solution matrix.