Conditional Value-at-Risk (CVaR) is a central tail-risk measure in stochastic structural mechanics, yet its accurate evaluation under high-dimensional, spatially correlated material uncertainty remains computationally prohibitive for classical Monte Carlo methods. Leveraging bounded-expectation reformulations of CVaR compatible with quantum amplitude estimation, we develop a quantum-enhanced inference framework that casts CVaR evaluation as a statistically consistent, confidence-constrained maximum-likelihood amplitude estimation problem. The proposed method extends iterative quantum amplitude estimation (IQAE) by embedding explicit maximum-likelihood inference within a rigorously controlled interval-tracking architecture. To ensure global correctness under finite-shot noise and the non-injective oscillatory response induced by Grover amplification, we introduce a stabilized inference scheme incorporating multi-hypothesis feasibility tracking, periodic low-depth disambiguation, and a bounded restart mechanism governed by an explicit failure-probability budget. This formulation preserves the quadratic oracle-complexity advantage of amplitude estimation while providing finite-sample confidence guarantees and reduced estimator variance. The framework is demonstrated on benchmark problems with spatially correlated lognormal Young's modulus fields generated using a Nystrom low-rank Gaussian kernel model. Numerical results show that the proposed estimator achieves substantially lower oracle complexity than classical Monte Carlo CVaR estimation at comparable confidence levels, while maintaining rigorous statistical reliability. This work establishes a practically robust and theoretically grounded quantum-enhanced methodology for tail-risk quantification in stochastic continuum mechanics.

Technically, our online quantum algorithm "quantizes" classical algorithms based

We propose Q-Policy, a hybrid quantum-classical reinforcement learning (RL) framework that mathematically accelerates policy evaluation and optimization by exploiting quantum computing primitives. Q-Policy encodes value functions in quantum superposition, enabling simultaneous evaluation of multiple state-action pairs via amplitude encoding and quantum parallelism. We introduce a quantum-enhanced policy iteration algorithm with provable polynomial reductions in sample complexity for the evaluation step, under standard assumptions. To demonstrate the technical feasibility and theoretical soundness of our approach, we validate Q-Policy on classical emulations of small discrete control tasks. Due to current hardware and simulation limitations, our experiments focus on showcasing proof-of-concept behavior rather than large-scale empirical evaluation. Our results support the potential of Q-Policy as a theoretical foundation for scalable RL on future quantum devices, addressing RL scalability challenges beyond classical approaches.

In the modern financial industry system, the structure of products has become more and more complex, and the bottleneck constraint of classical computing power has already restricted the development of the financial industry. Here, we present a photonic chip that implements the unary approach to European option pricing, in combination with the quantum amplitude estimation algorithm, to achieve a quadratic speedup compared to classical Monte Carlo methods. The circuit consists of three modules: a module loading the distribution of asset prices, a module computing the expected payoff, and a module performing the quantum amplitude estimation algorithm to introduce speed-ups. In the distribution module, a generative adversarial network is embedded for efficient learning and loading of asset distributions, which precisely capture the market trends. This work is a step forward in the development of specialized photonic processors for applications in finance, with the potential to improve the efficiency and quality of financial services.

We present a novel quantum algorithm for estimating Gibbs partition functions in sublinear time with respect to the logarithm of the size of the state space. This is the first speed-up of this type to be obtained over the seminal nearly-linear time algorithm of \v{S}tefankovi\v{c}, Vempala and Vigoda [JACM, 2009]. Our result also preserves the quadratic speed-up in precision and spectral gap achieved in previous work by exploiting the properties of quantum Markov chains. As an application, we obtain new polynomial improvements over the best-known algorithms for computing the partition function of the Ising model, counting the number of $k$-colorings, matchings or independent sets of a graph, and estimating the volume of a convex body. Our approach relies on developing new variants of the quantum phase and amplitude estimation algorithms that return nearly unbiased estimates with low variance and without destroying their initial quantum state. We extend these subroutines into a nearly unbiased quantum mean estimator that reduces the variance quadratically faster than the classical empirical mean. No such estimator was known to exist prior to our work. These properties, which are of general interest, lead to better convergence guarantees within the paradigm of simulated annealing for computing partition functions.

Identifying the best arm of a multi-armed bandit is a central problem in bandit optimization. We study a quantum computational version of this problem with coherent oracle access to states encoding the reward probabilities of each arm as quantum amplitudes. Specifically, we show that we can find the best arm with fixed confidence using $\tilde{O}\bigl(\sqrt{\sum_{i=2}^n\Delta^{\smash{-2}}_i}\bigr)$ quantum queries, where $\Delta_{i}$ represents the difference between the mean reward of the best arm and the $i^\text{th}$-best arm. This algorithm, based on variable-time amplitude amplification and estimation, gives a quadratic speedup compared to the best possible classical result. We also prove a matching quantum lower bound (up to poly-logarithmic factors).

Adversarial attacks represent a serious menace for learning algorithms and may compromise the security of future autonomous systems. A theorem by Khoury and Hadfield-Menell (KH), provides sufficient conditions to guarantee the robustness of active learning algorithms, but comes with a caveat: it is crucial to know the smallest distance among the classes of the corresponding classification problem. We propose a theoretical framework that allows us to think of active learning as sampling the most promising new points to be classified, so that the minimum distance between classes can be found and the theorem KH used. The complexity of the quantum active learning algorithm is polynomial in the variables used, like the dimension of the space $m$ and the size of the initial training data $n$. On the other hand, if one replicates this approach with a classical computer, we expect that it would take exponential time in $m$, an example of the so-called `curse of dimensionality'.