Search Results for author:
Found 21 papers, 5 papers with code
QCircuitNet: A Large-Scale Hierarchical Dataset for Quantum Algorithm Design
In this work, we introduce QCircuitNet, the first benchmark and test dataset designed to evaluate AI's capability in designing and implementing quantum algorithms in the form of quantum circuit codes.
Quantum Algorithms and Lower Bounds for Finite-Sum Optimization
In addition, when $F$ is nonconvex, our quantum algorithm can find an $\epsilon$-critial point using $\tilde{O}(n+\ell(d^{1/3}n^{1/3}+\sqrt{d})/\epsilon^2)$ queries.
Comparisons Are All You Need for Optimizing Smooth Functions
In addition, we also give an algorithm for escaping saddle points and reaching an $\epsilon$-second order stationary point of a nonconvex $f$, using $\tilde{O}(n^{1. 5}/\epsilon^{2. 5})$ comparison queries.
Quantum Langevin Dynamics for Optimization
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.
Near-Optimal Quantum Coreset Construction Algorithms for Clustering
$k$-Clustering in $\mathbb{R}^d$ (e. g., $k$-median and $k$-means) is a fundamental machine learning problem.
Logarithmic-Regret Quantum Learning Algorithms for Zero-Sum Games
We propose the first online quantum algorithm for solving zero-sum games with $\widetilde O(1)$ regret under the game setting.
Provably Efficient Exploration in Quantum Reinforcement Learning with Logarithmic Worst-Case Regret
While quantum reinforcement learning (RL) has attracted a surge of attention recently, its theoretical understanding is limited.
Quantum Algorithms for Sampling Log-Concave Distributions and Estimating Normalizing Constants
We also prove a $1/\epsilon^{1-o(1)}$ quantum lower bound for estimating normalizing constants, implying near-optimality of our quantum algorithms in $\epsilon$.
On Quantum Speedups for Nonconvex Optimization via Quantum Tunneling Walks
Classical algorithms are often not effective for solving nonconvex optimization problems where local minima are separated by high barriers.
Quantum Speedups of Optimizing Approximately Convex Functions with Applications to Logarithmic Regret Stochastic Convex Bandits
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.
Adaptive Online Learning of Quantum States
The problem of efficient quantum state learning, also called shadow tomography, aims to comprehend an unknown $d$-dimensional quantum state through POVMs.
Quantum Multi-Armed Bandits and Stochastic Linear Bandits Enjoy Logarithmic Regrets
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 $T$.
Escape saddle points by a simple gradient-descent based algorithm
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 $1/\epsilon$.
Sublinear classical and quantum algorithms for general matrix games
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 $\tilde{O}((n+d)/{\epsilon^{2}})$.
Quantum algorithms for escaping from saddle points
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 $1/\epsilon$.
Quantum exploration algorithms for multi-armed bandits
Identifying the best arm of a multi-armed bandit is a central problem in bandit optimization.
Quantum Wasserstein Generative Adversarial Networks
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.
Sampling-based sublinear low-rank matrix arithmetic framework for dequantizing quantum machine learning
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.
Sublinear quantum algorithms for training linear and kernel-based classifiers
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 $d$.
Distributional property testing in a quantum world
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.
Quantum-inspired sublinear algorithm for solving low-rank semidefinite programming
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.
