Search Results (17)

This paper proposes a quantum algorithm, named Dicke state quantum search (DSQS), to set qubits in the Dicke state $|D_k^n⟩$ of D states in superposition to locate the target inputs or solutions of specific patterns among $2^n$ unstructured input instances, where n is the number of input qubits and $D=\left({\displaystyle \genfrac{}{}{0pt}{}{n}{k}}\right)=\mathrm{O}\left(n^k\right)$ for $min(k,n-k)\ll n/2$. Compared to Grover’s algorithm, a famous quantum search algorithm that calls an oracle and a diffuser O($\sqrt{2^n}$) times, DSQS requires no diffuser and calls an oracle only once. Furthermore, DSQS does not need to know the number of solutions in advance. We prove the correctness of DSQS with unitary transformations, and show that each solution can be found by DSQS with an error probability less than 1/3 through O($n^k$) repetitions, as long as $min(k,n-k)\ll n/2$. Additionally, this paper proposes a classical algorithm, named DSQS-VCP, to generate quantum circuits based on DSQS for solving the k-vertex cover problem (k-VCP), a well-known NP-complete (NPC) problem. Complexity analysis demonstrates that DSQS-VCP operates in polynomial time and that the quantum circuit generated by DSQS-VCP has a polynomial qubit count, gate count, and circuit depth as long as $min(k,n-k)\ll n/2$. We thus conclude that the k-VCP can be solved by the DSQS-VCP quantum circuit in polynomial time with an error probability less than 1/3 under the condition of $min(k,n-k)\ll n/2$. Since the k-VCP is NP-complete, NP and NPC problems can be polynomially reduced to the k-VCP. If the reduced k-VCP instance satisfies $min(k,n-k)\ll n/2$, then both the instance and the original NP/NPC problem instance to which it corresponds can be solved by the DSQS-VCP quantum circuit in polynomial time with an error probability less than 1/3. All statements of polynomial algorithm execution time in this paper apply only to VCP instances and similar instances of other problems, where $min(k,n-k)\ll n/2$. Thus, they imply neither NP ⊆ BQP nor P = NP. In this restricted regime of $min(k,n-k)\ll n/2$, the Dicke state subspace has a polynomial size of $D=\left({\displaystyle \genfrac{}{}{0pt}{}{n}{k}}\right)=\mathrm{O}\left(n^k\right)$, and our DSQS algorithm samples from it without asymptotic superiority over exhaustive enumeration. Nevertheless, DSQS may be combined with other quantum algorithms to better exploit the strengths of quantum computation in practice. Experimental results using IBM Qiskit packages show that the DSQS-VCP quantum circuit can solve the k-VCP successfully. Full article

In this paper, electrical discharge images are classified using AI with quantum machine learning techniques. These discharges were originated in dielectric mineral oils and were detected by a high-resolution optical sensor. The captured images were processed in a Scikit-image environment to obtain a reduced number of features or qubits for later training of quantum circuits. Two quantum binary classification models were developed and compared in the Qiskit environment for four discharge binary combinations. The first was a quantum variational model (QVM), and the second was a conventional support vector machine (SVM) with a quantum kernel model (QKM). The execution of these two models was realized on three fault-tolerant physical quantum IBM computers. The novelty of this article lies in its application to a real problem, unlike other studies that focus on simulated or theoretical data sets. In addition, a study is carried out on the impact of the number of qubits in QKM, and it is shown that increasing the number of qubits in this model significantly improves the accuracy in the classification of the four binary combinations studied. In the QVM, with two qubits, an accuracy of 92% was observed in the first discharge combination in the three quantum computers used, with a margin of error of 1% compared to the simulation obtained on classical computers. Full article

In this paper, we use a simplified quantum counter to implement Grover’s algorithm-based quantum circuits to tackle the NP-hard exact cover problem (ECP). The ECP seeks a subcollection of sets such that every element is covered by exactly one set. Leveraging Grover’s algorithm, our quantum circuits achieve a quadratic speedup, querying the oracle O($\sqrt{N}$) times, compared to O(N) for classical methods, where $N=2^n$ is the total number of unstructured input instances and n is the number of input (quantum) bits. For the whole quantum circuit, the simplified quantum counter saves $(4mb-4m)\lfloor \pi /4\sqrt{N/M}\rfloor$ quantum gates and reduces the quantum circuit depth by $\left(2mb\right)\lfloor \pi /4\sqrt{N/M}\rfloor$ compared to Heidari et al.’s design, where $b=\lfloor logn\rfloor +1$ is the number of counting qubits used in a counter. Experimental results obtained using IBM Qiskit packages confirm the effectiveness of our quantum circuits. Full article

Flexi-grid technology has revolutionized optical networking by enabling Elastic Optical Networks (EONs) that offer greater flexibility and dynamism compared to traditional fixed-grid systems. As data traffic continues to grow exponentially, the need for efficient and scalable solutions to the routing and spectrum assignment (RSA) problem in EONs becomes increasingly critical. The RSA problem, being NP-Hard, requires solutions that can simultaneously address both spatial routing and spectrum allocation. This paper proposes a novel quantum-based approach to solving the RSA problem. By formulating the problem as a Quadratic Unconstrained Binary Optimization (QUBO) model, we employ the Quantum Approximate Optimization Algorithm (QAOA) to effectively solve it. Our approach is specifically designed to minimize end-to-end delay while satisfying the continuity and contiguity constraints of frequency slots. Simulations conducted using the Qiskit framework and IBM-QASM simulator validate the effectiveness of our method. We applied the QAOA-based RSA approach to small network topology, where the number of nodes and frequency slots was constrained by the limited qubit count on current quantum simulator. In this small network, the algorithm successfully converged to an optimal solution in less than 30 iterations, with a total runtime of approximately 10.7 s with an accuracy of $78.8\%$. Additionally, we conducted a comparative analysis between QAOA, integer linear programming, and deep reinforcement learning methods to evaluate the performance of the quantum-based approach relative to classical techniques. This work lays the foundation for future exploration of quantum computing in solving large-scale RSA problems in EONs, with the prospect of achieving quantum advantage as quantum technology continues to advance. Full article

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. Full article

The rapid development and extensive application of the Internet of Things (IoT) have brought new challenges and opportunities to the field of communication. By integrating quantum secure communication with the IoT, we can provide a higher level of security and privacy protection to counteract security threats in the IoT. In this paper, a hybrid quantum communication scheme using six-qubit entangled states as a channel is proposed for specific IoT application scenarios. This scheme achieves hierarchical control of communication protocols on a single quantum channel. In the proposed scheme, device A transmits data to device B through quantum teleportation, while device B issues control commands to device A through remote quantum state preparation technology. These two tasks are controlled by control nodes C and D, respectively. The transmission of information from device A to device B is a relatively less important task, which can be solely controlled by control node C. On the other hand, issuing control commands from device B to device A is a more crucial task requiring joint control from control nodes C and D. This paper describes the proposed scheme and conducts simulation experiments using IBM’s Qiskit Aer quantum computing simulator. The results demonstrate that the fidelity of the quantum teleportation protocol (QTP) and the remote state preparation protocol (RSP) reach an impressive value of 0.999, fully validating the scheme’s feasibility. Furthermore, the factors affecting the fidelity of the hybrid communication protocol in an IoT environment with specific quantum noise are analyzed. By combining the security of quantum communication with the application scenarios of the IoT, this paper presents a new possibility for IoT communication. Full article

In this study, we design an algorithm to work on gate-based quantum computers. Based on the algorithm, we construct a quantum circuit that represents the surplus process of a cedant under a reinsurance agreement. This circuit takes into account a variety of factors: initial reserve, insurance premium, reinsurance premium, and specific amounts related to claims, retention, and deductibles for two different non-proportional reinsurance contracts. Additionally, we demonstrate how to perturb the actuarial stochastic process using Hadamard gates to account for unpredictable damage. We conclude by presenting graphs and numerical results to validate our capital modelling approach. Full article

This paper describes a practical approach to the quantum theory using the simulation and processing technology available today. The proposed project allows us to create an exploration graph so that for an initial starting configuration of the qubits, all possible states are created given a set of gates selected by the user. For each node in the graph, we can obtain various types of information such as the applied gates from the initial state (the transition route), necessary cost, representation of the quantum circuit, as well as the amplitudes of each state. The project is designed not as an end goal, but rather as a processing platform that allows users to visualize and explore diverse solutions for different quantum problems in a much easier manner. We then describe some potential applications of this project in other research fields, illustrating the way in which the states from the graph can be used as nodes in a new interpretation of a quantum neural network; the steps of a hybrid processing chain are presented for the problem of finding one or more states that verify certain conditions. These concepts can also be used in academia, with their implementation being possible with the help of the Python programming language, the NumPy library, and Qiskit—the open-source quantum framework developed by IBM. Full article

This paper proposes a quantum computing approach for insurance capital modelling. Using an open-source software development kit, Qiskit, an algorithm for working on a superconducting type IBM quantum computer is developed and implemented to predict the capital of insurance companies in the classical surplus process. With the fundamental properties of quantum mechanics, Dirac notation and Feynman’s path calculation are shown. Furthermore, custom quantum insurance premium and claim gates are investigated in order to build a quantum circuit with respect to initial reserve, premium and claim amounts. Some numerical results are presented and discussed at the end of the paper. Full article

This paper explores the idea of a quantum exchange protocol between two entities, validated by (at least) a third one. Two entities, part of a greater system, decide they want to trade quantum goods: their exchange is configurable, and allows them to select the type of good, from a selected preset, and the desired quantity, up to a maximum value (one of the quantum goods can be interpreted as quantum money/a form of quantum currency). Certain qubits should also be used as a way of storing the details of the transfer, after it has been validated (acting in a similar way to a quantum ledger). The quantum circuits of the proposed design are implemented using the Python programming language with the help of Qiskit, IBM’s open-source quantum framework. Full article

We indicate the quantum tree search qiskit implementation by popular examples from symbolical artificial intelligence, the 3-puzzle, 8-puzzle and the ABC blocks world. Qiskit is an open-source software development kit (SDK) for working with quantum computers at the level of circuits and algorithms from IBM. The objects are represented by symbols and adjectives. Two principles are presented. Either the position description (adjective) is fixed and the class descriptors moves (is changed) or, in the reverse interpretation, the class descriptor is fixed and the position descriptor (adjective) moves (is changed). We indicate how to decompose the permutation operator that executes the rules by the two principles. We demonstrate that the the branching factor is reduced by Grover’s amplification to the square root of the average branching factor and not to the maximal branching factor as previously assumed. Full article

This paper presents a communication algorithm in which a grayscale image, shared between two parties, can be used to transmit a secret message, by applying the idea introduced in the B92 quantum protocol. The least significant qubits of the pixels’ representation in certain regions of the image are used. With the help of a server, the algorithm generates a random message, which can further act as a secret key for cryptographic algorithms in order to secure the data that two parties might want to exchange later on. The chosen representation of the image is NEQR (novel enhanced quantum representation) and the platform used for testing the described idea is IBM Quantum Experience, along with the open-source Python framework called Qiskit. This solution allows users to design, implement quantum circuits (containing various quantum gates), and simulate them using real devices and local simulators. An implementation using this platform for a sample image and the corresponding results are also presented in this paper. Full article

The solution of nonlinear Boolean equations in a binary field plays a crucial part in cryptanalysis and computational mathematics. To speed up the process of solving Boolean equations is an urgent task that needs to be addressed. In this paper, we propose a method for solving Boolean equations based on the Grover algorithm combined with preprocessing using classical algorithms, optimizing the quantum circuit for solving the equations, and implementing the automatic generation of quantum circuits. The method first converted Boolean equations into Boolean expressions to construct the oracle in the Grover algorithm. The quantum circuit was emulated based on the IBM Qiskit framework and then simulated the Grover algorithm on this basis. Finally, the solution of the Boolean equation was implemented. The experimental results proved the feasibility of using the Grover algorithm to solve nonlinear Boolean equations in a binary field, and the correct answer was successfully found under the conditions that the search space was 2²¹ and three G iterations were used. The method in this paper increases the solving scale and solving speed of Boolean equations and enlarges the application area of the Grover algorithm. Full article

This work presents a quantum associative memory (Alpha-Beta HQAM) that uses the Hamming distance for pattern recovery. The proposal combines the Alpha-Beta associative memory, which reduces the dimensionality of patterns, with a quantum subroutine to calculate the Hamming distance in the recovery phase. Furthermore, patterns are initially stored in the memory as a quantum superposition in order to take advantage of its properties. Experiments testing the memory’s viability and performance were implemented using IBM’s Qiskit library. Full article

We characterize for the first time the performances of IBM quantum chips as quantum batteries, specifically addressing the single-qubit Armonk processor. By exploiting the Pulse access enabled to some of the IBM Quantum processors via the Qiskit package, we investigate the advantages and limitations of different profiles for classical drives used to charge these miniaturized batteries, establishing the optimal compromise between charging time and stored energy. Moreover, we consider the role played by various possible initial conditions on the functioning of the quantum batteries. As the main result of our analysis, we observe that unavoidable errors occurring in the initialization phase of the qubit, which can be detrimental for quantum computing applications, only marginally affect energy transfer and storage. This can lead counter-intuitively to improvements of the performances. This is a strong indication of the fact that IBM quantum devices are already in the proper range of parameters to be considered as good and stable quantum batteries comparable to state-of-the-art devices recently discussed in the literature. Full article