We initiate the study of quantum algorithms for optimizing approximately convex functions. Given a convex set K Rn and a function F: Rn Rsuch that there exists a convex function f: K R satisfying supx K|F(x) f(x)| /n, our quantum algorithm finds an x K such that F(x) minx KF(x) using O(n3) quantum evaluation queries to F. This achieves a polynomial quantum speedup compared to the best-known classical algorithms. As an application, we give a quantum algorithm for zeroth-order stochastic convex bandits with O(n5 log2 T) regret, an exponential speedup in T compared to the classical Ω( T) lower bound. Technically, we achieve quantum speedup in nby exploiting a quantum framework of simulated annealing and adopting a quantum version of the hit-and-run walk. Our speedup in T for zeroth-order stochastic convex bandits is due to a quadratic quantum speedup in multiplicative error of mean estimation.

Optimization theory is a central research topic in computer science, mathematics, operations research, etc. Currently, many efficient algorithms for optimizing convex functions have been proposed (see for instance [10]), but much less is known for nonconvex optimization.

Link prediction is one of the fundamental problems in graph theory, critical for understanding and forecasting the evolution of complex systems like social and biological networks. While classical heuristics capture certain aspects of graph topology, they often struggle to optimally integrate local and global structural information or adapt to complex dependencies. Quantum computing offers a powerful alternative by leveraging superposition for simultaneous multi-path exploration and interference-driven integration of both local and global graph features. In this work, we introduce QSearchNet, a quantum-inspired framework based on Discrete-Time Quantum Walk (DTQW) dynamics and Grover's amplitude amplification. QSearchNet simulates a topology-aware quantum evolution to propagate amplitudes across multiple nodes simultaneously. By aligning interference patterns through quantum reflection and oracle-like phase-flip operation, it adaptively prioritizes multi-hop dependencies and amplifies structurally relevant paths corresponding to potential connections. Experiments on diverse real-world networks demonstrate competitive performance, particularly with hard negative samples under realistic evaluation conditions.

Quantum Diffusion Models (QDMs) are an emerging paradigm in Generative AI that aims to use quantum properties to improve the performances of their classical counterparts. However, existing algorithms are not easily scalable due to the limitations of near-term quantum devices. Following our previous work on QDMs, here we propose and implement two physics-inspired protocols. In the first, we use the formalism of quantum stochastic walks, showing that a specific interplay of quantum and classical dynamics in the forward process produces statistically more robust models generating sets of MNIST images with lower Fréchet Inception Distance (FID) than using totally classical dynamics. In the second approach, we realize an algorithm to generate images by exploiting the intrinsic noise of real IBM quantum hardware with only four qubits. Our work could be a starting point to pave the way for new scenarios for large-scale algorithms in quantum Generative AI, where quantum noise is neither mitigated nor corrected, but instead exploited as a useful resource.

Variational quantum algorithms represent a promising approach to quantum machine learning where classical neural networks are replaced by parametrized quantum circuits. However, both approaches suffer from a clear limitation, that is a lack of interpretability. Here, we present a variational method to quantize projective simulation (PS), a reinforcement learning model aimed at interpretable artificial intelligence. Decision making in PS is modeled as a random walk on a graph describing the agent's memory. To implement the quantized model, we consider quantum walks of single photons in a lattice of tunable Mach-Zehnder interferometers trained via variational algorithms. Using an example from transfer learning, we show that the quantized PS model can exploit quantum interference to acquire capabilities beyond those of its classical counterpart. Finally, we discuss the role of quantum interference for training and tracing the decision making process, paving the way for realizations of interpretable quantum learning agents.

A random walk(RW) is one of the most ubiquitous stochastic processes and is employed for both mathematical analyses and applications, such as describing real-world phenomena and constructing various algorithms. Meanwhile, along with the increasing interest in quantum mechanics from both theoretical and applied perspectives, the quantum counterpart of a RW, known as a quantum walk (QW), is also attracting attention [1-4]. A QW includes the effects of quantum superposition or time evolution. In classical RWs, a random walker(RWer) selects in which direction to go probabilistically at each time step, and thus one can track where the RWer is at any time step. On the other hand, in QWs, one cannot tell where a quantum walker (QWer) exists during the time evolution, and the location is determined only after conducting the measurement. QWs have a property that classical RWs do not possess: the coexistence of linear spreading and localization [5, 6]. As a result, QWs show probability distributions that are totally different from those of random walks, which weakly converge to normal distributions. The former behavior, linear spreading, means that the standard deviation of the probability distribution of measurement of quantum walkers (QWers) grows in proportion to the run time t.

Abstract: In this paper, we address the stochastic contextual linear bandit problem, where a decision maker is provided a context (a random set of actions drawn from a distribution). The expected reward of each action is specified by the inner product of the action and an unknown parameter. The goal is to design an algorithm that learns to play as close as possible to the unknown optimal policy after a number of action plays. This problem is considered more challenging than the linear bandit problem, which can be viewed as a contextual bandit problem with a \emph{fixed} context. Surprisingly, in this paper, we show that the stochastic contextual problem can be solved as if it is a linear bandit problem. In particular, we establish a novel reduction framework that converts every stochastic contextual linear bandit instance to a linear bandit instance, when the context distribution is known. When the context distribution is unknown, we establish an algorithm that reduces the stochastic contextual instance to a sequence of linear bandit instances with small misspecifications and achieves nearly the same worst-case regret bound as the algorithm that solves the misspecified linear bandit instances. As a consequence, our results imply a O(dTlogT) high-probability regret bound for contextual linear bandits, making progress in resolving an open problem in (Li et al., 2019), (Li et al., 2021).

As NAND formula algorithm allow us to evaluate quality Quantum computing is a computation paradigm using of a position in a two-player game tree, we illustrate its properties of quantum mechanics to perform information potential application by using it as a training tool for a processing. Many famous quantum algorithms have been quantum agent in a simple two-player game. With the shown to outperform their equivalent classical algorithm[1], speed-up proposed by this algorithm, we are able to perform [2]. Quantum walk is a way to compose many promising evaluation of deeper trees in equivalent time (twice deeper quantum algorithms. It can be viewed as the quantum exploration for a binary tree). By using quantum algorithm analogues of classical random walks [3]. In several studies, to perform such explorations, we expect agents to achieve it has been shown that it could provide some algorithmic better performances in their learning process.

We initiate the study of quantum algorithms for optimizing approximately convex functions. Given a convex set ${\cal K}\subseteq\mathbb{R}^{n}$ and a function $F\colon\mathbb{R}^{n}\to\mathbb{R}$ such that there exists a convex function $f\colon\mathcal{K}\to\mathbb{R}$ satisfying $\sup_{x\in{\cal K}}|F(x)-f(x)|\leq \epsilon/n$, our quantum algorithm finds an $x^{*}\in{\cal K}$ such that $F(x^{*})-\min_{x\in{\cal K}} F(x)\leq\epsilon$ using $\tilde{O}(n^{3})$ quantum evaluation queries to $F$. This achieves a polynomial quantum speedup compared to the best-known classical algorithms. 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. Technically, we achieve quantum speedup in $n$ by exploiting a quantum framework of simulated annealing and adopting a quantum version of the hit-and-run walk. Our speedup in $T$ for zeroth-order stochastic convex bandits is due to a quadratic quantum speedup in multiplicative error of mean estimation.

Protein-protein interaction (PPI) networks consist of the physical and/or functional interactions between the proteins of an organism. Since the biophysical and high-throughput methods used to form PPI networks are expensive, time-consuming, and often contain inaccuracies, the resulting networks are usually incomplete. In order to infer missing interactions in these networks, we propose a novel class of link prediction methods based on continuous-time classical and quantum random walks. In the case of quantum walks, we examine the usage of both the network adjacency and Laplacian matrices for controlling the walk dynamics. We define a score function based on the corresponding transition probabilities and perform tests on four real-world PPI datasets. Our results show that continuous-time classical random walks and quantum walks using the network adjacency matrix can successfully predict missing protein-protein interactions, with performance rivalling the state of the art.