The Heisenberg uncertainty principle puts a limit on how precisely we can measure certain properties of quantum objects. But researchers may have found a way to bypass this limitation using a quantum version of a neural network. Given, for example, a chemically useful molecule, how can you predict what properties it might have in an hour or tomorrow? To make such predictions, researchers start by measuring its current properties. But for quantum objects, including some molecules, this can be unexpectedly difficult because each measurement can interfere with or change the outcome of the next measurement.

This work advances the theoretical understanding of quantum learning by establishing a new family of upper bounds on the expected generalization error of quantum learning algorithms, leveraging the framework introduced by Caro et al. (2024) and a new definition for the expected true loss. Our primary contribution is the derivation of these bounds in terms of quantum and classical Rényi divergences, utilizing a variational approach for evaluating quantum Rényi divergences, specifically the Petz and a newly introduced modified sandwich quantum Rényi divergence. Analytically and numerically, we demonstrate the superior performance of the bounds derived using the modified sandwich quantum Rényi divergence compared to those based on the Petz divergence. Furthermore, we provide probabilistic generalization error bounds using two distinct techniques: one based on the modified sandwich quantum Rényi divergence and classical Rényi divergence, and another employing smooth max Rényi divergence.

Action selection based on flags is a Reinforcement Learning (RL) exploration policy that improves the exploration of the state space through the use of flags, which can identify the most promising actions to take in each state. The quantum counterpart of this exploration policy further improves upon this by taking advantage of a quadratic speedup for sampling flagged actions. This approach has already been successfully employed for the game of Checkers. In this work, we describe the application of this method to the context of Connect Four, in order to study its performance in a different setting, which can lead to a better generalization of the technique. We also kept track of a metric that wasn't taken into account in previous work: the average number of iterations to obtain a flagged action. Since going second is a significant disadvantage in Connect Four, we also had the intent of exploring how this more complex scenario would impact the performance of our approach. The experiments involved training and testing classical and quantum RL agents that played either going first or going second against a Randomized Negamax opponent. The results showed that both flagged exploration policies were clearly superior to a simple epsilon-greedy policy. Furthermore, the quantum agents did in fact sample flagged actions in less iterations. Despite obtaining tagged actions more consistently, the win rates between the classical and quantum versions of the approach were identical, which could be due to the simplicity of the training scenario chosen.

A Perceptron is a fundamental building block of a neural network. The flexibility and scalability of perceptron make it ubiquitous in building intelligent systems. Studies have shown the efficacy of a single neuron in making intelligent decisions. Here, we examined and compared two perceptrons with distinct mechanisms, and developed a quantum version of one of those perceptrons. As a part of this modeling, we implemented the quantum circuit for an artificial perception, generated a dataset, and simulated the training. Through these experiments, we show that there is an exponential growth advantage and test different qubit versions. Our findings show that this quantum model of an individual perceptron can be used as a pattern classifier. For the second type of model, we provide an understanding to design and simulate a spike-dependent quantum perceptron. Our code is available at \url{https://github.com/ashutosh1919/quantum-perceptron}

We give a quantum approximation scheme (i.e., $(1 + \varepsilon)$-approximation for every $\varepsilon > 0$) for the classical $k$-means clustering problem in the QRAM model with a running time that has only polylogarithmic dependence on the number of data points. More specifically, given a dataset $V$ with $N$ points in $\mathbb{R}^d$ stored in QRAM data structure, our quantum algorithm runs in time $\tilde{O} \left( 2^{\tilde{O}(\frac{k}{\varepsilon})} \eta^2 d\right)$ and with high probability outputs a set $C$ of $k$ centers such that $cost(V, C) \leq (1+\varepsilon) \cdot cost(V, C_{OPT})$. Here $C_{OPT}$ denotes the optimal $k$-centers, $cost(.)$ denotes the standard $k$-means cost function (i.e., the sum of the squared distance of points to the closest center), and $\eta$ is the aspect ratio (i.e., the ratio of maximum distance to minimum distance). This is the first quantum algorithm with a polylogarithmic running time that gives a provable approximation guarantee of $(1+\varepsilon)$ for the $k$-means problem. Also, unlike previous works on unsupervised learning, our quantum algorithm does not require quantum linear algebra subroutines and has a running time independent of parameters (e.g., condition number) that appear in such procedures.

Quantum computing is a promising paradigm based on quantum theory for performing fast computations. Quantum algorithms are expected to surpass their classical counterparts in terms of computational complexity for certain tasks, including machine learning. In this paper, we design, implement, and evaluate three hybrid quantum k-Means algorithms, exploiting different degree of parallelism. Indeed, each algorithm incrementally leverages quantum parallelism to reduce the complexity of the cluster assignment step up to a constant cost. In particular, we exploit quantum phenomena to speed up the computation of distances. The core idea is that the computation of distances between records and centroids can be executed simultaneously, thus saving time, especially for big datasets. We show that our hybrid quantum k-Means algorithms can be more efficient than the classical version, still obtaining comparable clustering results.

Generative Adversarial Networks are becoming a fundamental tool in Machine Learning, in particular in the context of improving the stability of deep neural networks. At the same time, recent advances in Quantum Computing have shown that, despite the absence of a fault-tolerant quantum computer so far, quantum techniques are providing exponential advantage over their classical counterparts. We develop a fully connected Quantum Generative Adversarial network and show how it can be applied in Mathematical Finance, with a particular focus on volatility modelling.

Machine learning, a process used to train artificial intelligences, can take an extremely long time – but a quantum trick could massively speed things up for tasks involving particles of light called photons. In the classical version of this experiment, without any added quantum effects, the AI would only be able to move the photon to one specific state at a time, being rewarded when it made a correct guess. However, in the quantum version of the experiment, the AI could put the photon in a superposition of more than one state. "If the robot goes right, it does not receive a reward, but if it goes left it receives a reward. That's the classical version of the experiment, but the quantum version would allow it to go left and right simultaneously at each guess, requiring far fewer guesses before it learns to always go left. Machine learning, a process used to train artificial intelligences, can take an extremely long time – but a quantum trick could massively speed things up for tasks involving particles of light called photons. In the classical version of this experiment, without any added quantum effects, the AI would only be able to move the photon to one specific state at a time, being rewarded when it made a correct guess. However, in the quantum version of the experiment, the AI could put the photon in a superposition of more than one state. "If the robot goes right, it does not receive a reward, but if it goes left it receives a reward.

Machine learning, a process used to train artificial intelligences, can take an extremely long time – but a quantum trick could massively speed things up for tasks involving particles of light called photons. In reinforcement learning, an algorithm runs through the same problem over and over again and is given a numerical reward only when it reaches the correct answer. That process teaches it to find the correct answer more quickly when pitted against similar problems later on. Now Valeria Saggio at the University of Vienna in Austria and her colleagues have added a quantum twist to accelerate this process. They set up an experiment involving a photon moving through a wave guide and ending up in one of four possible states.

A new version of the ancient Chinese board game Go that uses quantum entanglement to add an element of randomness could make it a tougher test for artificial intelligences than regular board games. "Board games have long been good test beds for AI because these games provide closed worlds with specific and simple rules," says Xian-Min Jin at Shanghai Jiao Tong University in China. In Go, players take turns to place a stone on a board, trying to surround and capture the opponent's stones.