Search Results (45)

We present a theoretical framework integrating quantum optimization with DNA-based molecular storage for enhanced image compression, validated via classical simulation in IBM Qiskit. The proposed Quantum-DNA Image Compression (Q-DIC) framework formulates DNA codon selection as a quantum search problem, applying Grover’s algorithm to achieve $\mathrm{O}\left(\sqrt{N}\right)$ speedup in exploring the 4⁸ = 65,536-codon solution space. Key contributions include (1) novel multi-objective cost functions balancing reconstruction fidelity, thermodynamic stability, and synthesis feasibility; (2) quantum-inspired stabilizer codes achieving 10⁸-fold error suppression with 23% overhead reduction versus Reed–Solomon codes; (3) NISQ-compatible implementation achieving 12.3× compression on current quantum hardware. Simulation experiments across diverse image categories demonstrate 8.9× realistic compression ratio (18.3× theoretical maximum). Hardware validation on IBM Quantum systems achieved 10.8–11.2× compression, confirming practical viability. Critical assessment identifies implementation gaps: current hardware supports hundreds of gates versus the required amount of 60,000–800,000, and DNA synthesis costs require 1000× reduction for economic viability. Despite being simulation-based, this work establishes rigorous foundations for quantum–molecular hybrid architectures and provides a validated pathway for experimental confirmation. Full article

We investigate optimizing quantum tree search algorithms by employing a nested Grover Algorithm. This approach seeks to enhance results compared to previous Grover-based methods by expanding the tree of partial assignments to a specific depth and conducting a quantum search within the subset of remaining assignments. The study explores the implications and constraints of this approach, providing a foundation for quantum artificial intelligence applications. Instead of utilizing conventional heuristic functions that are incompatible with quantum tree search, we introduce the partial candidate solution, which indicates a node at a specific depth of the tree. By employing such a function, we define the concatenated oracle, which enables us to decompose the quantum tree search using Grover’s algorithm. With a branching factor of 2 and a depth of m, the costs of Grover’s algorithm are $O\left(2^{m/2}\right)$. The concatenated oracle allows us to reduce the cost to $O(m·2^{m/4})$ for m partial candidate solutions. Full article

Blockchain technology has emerged as the backbone of cryptocurrencies and decentralized finance, yet its long-term resilience is increasingly threatened by advances in quantum computing. Quantum algorithms, such as Shor’s algorithm, can undermine public-key cryptography, while Grover’s algorithm accelerates brute-force search, weakening proof-of-work schemes. In this paper, we propose a Quantum Blockchain Framework that integrates quantum communication protocols, quantum consensus mechanisms, and quantum-resistant cryptography. We construct a theoretical model of quantum-secured distributed ledgers, where qubits, entanglement, and quantum key distribution (QKD) enhance security and efficiency. Applications to cryptocurrency are explored, highlighting how quantum blockchain can mitigate security risks, improve consensus speed, and enable quantum-native digital assets. Full article

Quantum computing is an emerging field in computing technology that harnesses the principles of quantum mechanics—including superposition, entanglement, and quantum tunneling—to process information in fundamentally new ways. While classical computers use bits that represent states of either 0 or 1, quantum computers use quantum bits, or qubits. Unlike classical bits, a qubit can exist in a superposition of the logical states 0 and 1 simultaneously. This property allows quantum-powered systems to perform certain complex computations much faster than classical computing systems. Quantum computing holds great potential to transform many sectors by enabling breakthroughs in quantum cryptography, information retrieval, optimization, and artificial intelligence. Through quantum algorithms such as Grover’s and Shor’s algorithms, quantum computers can significantly accelerate the speed of data searching and break encryption systems that would take classical computers billions of years to crack. While still in the relatively early stages of development, quantum computers hold considerable potential to shape our next generation of computing. Full article

The emergence of quantum computing poses significant threats to conventional public-key cryptography, driving the urgent need for quantum-resistant cryptographic solutions. While quantum key distribution addresses secure key exchange, its dependency on symmetric keys and point-to-point limitations present scalability constraints. Quantum Asymmetric Encryption (QAE) offers a promising alternative by leveraging quantum mechanical principles for security. This paper presents the first practical implementation of a QAE protocol on IBM Quantum devices, building upon the theoretical framework originally proposed by Yoon et al. We develop a generalized Grover Search Algorithm (GSA) framework that supports non-standard initial quantum states through novel diffusion operator designs, extending its applicability beyond idealized conditions. The complete QAE protocol, including key generation, encryption, and decryption stages, is translated into executable quantum circuits and evaluated on both IBM Quantum simulators and real quantum hardware. Experimental results demonstrate significant scalability challenges, with success probabilities deteriorating considerably for larger systems. The 2-qubit implementation achieves near-perfect accuracy (100% on the simulator, and 93.88% on the hardware), while performance degrades to 78.15% (simulator) and 45.84% (hardware) for 3 qubits, and declines critically to 48.08% (simulator) and 7.63% (hardware) for 4 qubits. This degradation is primarily attributed to noise and decoherence effects in current Noisy Intermediate-Scale Quantum (NISQ) devices, highlighting the limitations of single-iteration GSA approaches. Our findings underscore the critical need for enhanced hardware fidelity and algorithmic optimization to advance the practical viability of quantum cryptographic systems, providing valuable insights for bridging the gap between theoretical quantum cryptography and real-world implementations. Full article

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

This manuscript is intended for readers who have a general interest in the subject of quantum computation and provides an overview of the most significant developments in the field. It begins by introducing foundational concepts from quantum mechanics—such as superposition, entanglement, and the no-cloning theorem—that underpin quantum computation. The primary computational models are discussed, including gate-based (circuit) quantum computing, adiabatic quantum computing, measurement-based quantum computing and the quantum Turing machine. A selection of significant quantum algorithms are reviewed, notably Grover’s search algorithm, Shor’s factoring algorithm, and Quantum Singular Value Transformation (QSVT), which enables efficient solutions to linear algebra problems on quantum devices. To assess practical performance, we compare quantum and classical implementations of support vector machines (SVMs) using several synthetic datasets. These experiments offer insight into the capabilities and limitations of near-term quantum classifiers relative to classical counterparts. Finally, we review leading quantum programming platforms—including Qiskit, PennyLane, and Cirq—and discuss their roles in bridging theoretical models with real-world quantum hardware. The paper aims to provide a concise yet comprehensive guide for those looking to understand both the theoretical foundations and applied aspects of quantum computing. Full article

This paper presents a hybrid computational architecture for efficient and robust digital transmission inspired by helical genetic structures. The proposed system integrates advanced modulation schemes, such as multi-pulse-position modulation (MPPM), high-order quadrature amplitude modulation (QAM), and chirp spread spectrum (CSS), along with Reed–Solomon error correction and quantum-assisted search, to optimize performance in noisy and non-line-of-sight (NLOS) optical environments, including VLC channels modeled with log-normal fading. Through mathematical modeling and simulation, we demonstrate that the number of helical transmissions required for genome-scale data can be drastically reduced—up to 95% when using parallel strands and high-order modulation. The trade-off between redundancy, spectral efficiency, and error resilience is quantified across several configurations. Furthermore, we compare classical genetic algorithms and Grover’s quantum search algorithm, highlighting the potential of quantum computing in accelerating decision-making and data encoding. These results contribute to the field of operations research and supply chain communication by offering a scalable, energy-efficient framework for data transmission in distributed systems, such as logistics networks, smart sensing platforms, and industrial monitoring systems. The proposed architecture aligns with the goals of advanced computational modeling and optimization in engineering and operations management. Full article

Chatbots, search engines and Database Query Systems are invaluable sources of information for decision-making processes in the data-driven world in which we live today. In this study, we explore the extent to which classical and Quantum Query Systems can support future decisions, taken at a moment where the query service may be inaccessible and the decision has to be based solely on information collected in the past. We show that encoding information at the quantum level allows Query Systems to support future or delayed decisions. More precisely, Grover’s algorithm can be employed in order to extract the desired answer from a large superposition of question–answer pairs obtained through a single interrogation of the system. The method works best for binary answers and can be applied to queries encompassing hundreds or thousands of questions in one query. Extensions are possible if we allow more than one query to be addressed to the system. By comparison, a classical system would require hundreds or thousands of queries in order to offer the same level of support for delayed decisions. Full article

This paper introduces a novel theoretical framework that reformulates optimal control as a quantum search problem using Grover’s algorithm, leveraging its quadratic speedup. Specifically, the method encodes all possible control inputs into a quantum superposition state and uses a reference value interpreted as a candidate minimum to evaluate which inputs yield a lower control cost. To guide the search, we integrate a quantum comparator circuit to identify the inputs below this reference, and quantum counting to estimate their number. The reference is iteratively updated using a sigmoid-based rule until only one input satisfies the condition, thereby ensuring convergence to the global minimum within the discretized control space. Although full quantum implementation is currently infeasible due to oracle complexity and hardware limitations, we simulate the process using a classical controller as a pseudo-oracle to illustrate the algorithmic structure. This work does not aim to demonstrate performance gains but rather to establish a foundational method for embedding control synthesis within Grover-based quantum circuits. The framework paves the way for scalable quantum control systems once hardware resources permit full realization. Full article

The rapid integration of the Internet of Medical Things (IoMT) into healthcare systems raises urgent demands for secure communication mechanisms capable of protecting sensitive patient data. Quantum key agreement (QKA), a collaborative approach to key generation based on quantum principles, provides an attractive alternative to traditional quantum key distribution (QKD), as it eliminates dependence on a trusted authority and ensures equal participation from all users. QKA demonstrates particular suitability for IoMT’s decentralized medical networks by eliminating trusted authority dependence while ensuring equitable participation among all participants. This addresses fundamental challenges where centralized trust models introduce vulnerabilities and asymmetric access patterns that compromise egalitarian principles essential for medical data sharing. However, practical QKA applications in IoMT remain limited, particularly for schemes that avoid complex entanglement operations and authenticated classical channels. Among the few QKA protocols employing Grover’s search algorithm (GSA), existing proposals potentially suffer from limitations in fairness and security. In this paper, the author proposes an improved GSA-based QKA protocol that ensures fairness, security, and correctness without requiring an authenticated classical communication channel. The proposed scheme guarantees that each participant’s input equally contributes to the final key, preventing manipulation by any user subgroup. The scheme combines Grover’s algorithm with the decoy photon technique to ensure secure quantum transmission. Security analysis confirms resistance to external attacks, including intercept-resend, entanglement probes, and device-level exploits, as well as insider threats such as parameter manipulation. Fairness is achieved through a symmetric protocol design rooted in quantum mechanical principles. Efficiency evaluation shows a theoretical efficiency of approximately 25%, while eliminating the need for quantum memory. These results position the proposed protocol as a practical and scalable solution for future secure quantum communication systems, particularly within distributed IoMT environments. Full article

We demonstrate a quantum processor based on a 3D linear Paul trap that uses ${}^{171}\mathrm{Yb}^{+}$ ions with eight individually controllable four-level qudits (ququarts), which is computationally equivalent to a sixteen-qubit quantum processor. The design of the developed ion trap provides high secular frequencies and a low heating rate, which, together with individual addressing and readout optical systems, allows executing quantum algorithms. In each of the eight ions, we use four electronic levels coupled by E2 optical transition at 435 nm for qudit encoding. We present the results of single- and two-qubit operations benchmarking and realizing basic quantum algorithms, including the Bernstein–Vazirani and Grover’s search algorithms as well as H₂ and LiH molecular simulations. Our results pave the way to scalable qudit-based quantum processors using trapped ions. Full article

This paper introduces an improved Grover Adaptive Search (GAS) algorithm. The GAS algorithm has been prove to achieve quadratic acceleration in the Constrained Polynomial Binary Optimization (CPBO) problem. Nevertheless, the acceleration effect of the GAS algorithm can be decreased by the poor threshold selection. This article uses the Quantum Approximate Optimization Algorithm (QAOA) to improve the initial threshold selection, thereby accelerating the convergence speed of the original GAS algorithm. The acceleration effect of the improved GAS algorithm is presented by the Max-Cut problem and the CPBO problem. 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

Grover’s algorithm leverages quantum computing to efficiently locate solutions in unstructured search spaces, outperforming classical approaches. Since Grover’s algorithm requires prior knowledge of the number of solutions (M) within a search space of size N, previous studies assume M is estimated beforehand and focus on identifying all solutions. Here, we propose a two-step process that integrates both the estimation of M and the discovery of the solutions, optimizing the interactions between the two steps. To enhance efficiency, the estimation step captures as many solutions as possible, leaving the discovery step to focus on the remaining ones. To ensure accuracy, the discovery step continues searching until the probability of finding additional solutions becomes sufficiently low. We implemented and evaluated our methods, showing that over 80% of solutions were found during the estimation phase, allowing the discovery phase to conclude earlier, while identifying over 99% of solutions on average. In theory, the process requires $\sqrt{NM}$ × log(M) Grover’s iterations in the worst case, but in practice, it typically terminates after iterations proportional to $\sqrt{N}$. We expect that our methods will be applicable to various search problems and inspire further research on efficiently finding all solutions. Full article