Solving combinatorial optimization problems of the kind that can be codified by quadratic unconstrained binary optimization (QUBO) is a promising application of quantum computation. Some problems of this class suitable for practical applications such as the traveling salesman problem (TSP), the bin packing problem (BPP), or the knapsack problem (KP) have inequality constraints that require a particular cost function encoding. The common approach is the use of slack variables to represent the inequality constraints in the cost function. However, the use of slack variables considerably increases the number of qubits and operations required to solve these problems using quantum devices. In this work, we present an alternative method that does not require extra slack variables and consists of using an unbalanced penalization function to represent the inequality constraints in the QUBO. This function is characterized by larger penalization when the inequality constraint is not achieved than when it is. We evaluate our approach on the TSP, BPP, and KP, successfully encoding the optimal solution of the original optimization problem near the ground state cost Hamiltonian. Additionally, we employ D-Wave Advantage and D-Wave hybrid solvers to solve the BPP, surpassing the performance of the slack variables approach by achieving solutions for up to 29 items, whereas the slack variables approach only handles up to 11 items. This new approach can be used to solve combinatorial problems with inequality constraints with a reduced number of resources compared to the slack variables approach using quantum annealing or variational quantum algorithms.

This work introduces a quantum K-Nearest Neighbor (K-NN) classifier algorithm. The algorithm utilizes angle encoding through a Quantum Random Access Memory (QRAM) using n number of qubit addresses with $\mathrm{O}(log(\mathrm{n}\left)\right)$ space complexity. It incorporates Grover’s algorithm and the quantum SWAP-Test to identify similar states and determine the nearest neighbors with high probability, achieving $\mathrm{O}\left(\sqrt{m}\right)$ search complexity, where m is the qubit address. We implement a simulation of the algorithm using IBM’s Qiskit with GPU support, applying it to the Iris and MNIST datasets with two different angle encodings. The experiments employ multiple QRAM cell sizes (8, 16, 32, 64, 128) and perform ten trials per size. According to the performance, accuracy values in the Iris dataset range from 89.3 ± 5.78% to 94.0 ± 1.56%. The MNIST dataset’s mean binary accuracy values range from 79.45 ± 18.84% to 94.00 ± 2.11% for classes 0 and 1. Additionally, a comparison of the results of this proposed approach with different state-of-the-art versions of QK-NN and the classical K-NN using Scikit-learn. This method achieves a 96.4 ± 2.22% accuracy in the Iris dataset. Finally, this proposal contributes an experimental result to the state of the art for the MNIST dataset, achieving an accuracy of 96.55 ± 2.00%. This work presents a new implementation proposal for QK-NN and conducts multiple experiments that yield more robust results than previous implementations. Although our average performance approaches still need to surpass the classic results, an experimental increase in the size of QRAM or the amount of data to encode is not achieved due to limitations. However, our results show promising improvement when considering working with more feature numbers and accommodating more data in the QRAM.

Interactive technologies such as augmented reality have grown in popularity, but specialized sensors and high computer power must be used to perceive and analyze the environment in order to obtain an immersive experience in real time. However, these kinds of implementations have high costs. On the other hand, machine learning has helped create alternative solutions for reducing costs, but it is limited to particular solutions because the creation of datasets is complicated. Due to this problem, this work suggests an alternate strategy for dealing with limited information: unpaired samples from known and unknown surroundings are used to generate a path on embedded devices, such as smartphones, in real time. This strategy creates a path that avoids virtual elements through physical objects. The authors suggest an architecture for creating a path using imperfect knowledge. Additionally, an augmented reality experience is used to describe the generated path, and some users tested the proposal to evaluate the performance. Finally, the primary contribution is the approximation of a path produced from a known environment by using an unpaired dataset.

Finding groups of similar image blocks within an ample search area is often necessary in different applications, such as video compression, image clustering, vector quantization, and nonlocal noise reduction. A block-matching algorithm that uses a dissimilarity measure can be applied in such scenarios. In this work, a measure that utilizes the quantum Fourier transform or the Swap test based on the Euclidean distance is proposed. Experiments on small cases with ideal and noisy simulations are implemented. In the case of the Swap test, the IBM and IonQ quantum devices have been used, demonstrating potential for future near-term applications.