PeerJ Computer Science:Quantum Computinghttps://peerj.com/articles/index.atom?journal=cs&subject=12710Quantum Computing articles published in PeerJ Computer ScienceSymbolic model checking quantum circuits in Maudehttps://peerj.com/articles/cs-20982024-06-202024-06-20Canh Minh DoKazuhiro Ogata
This article presents a symbolic approach to model checking quantum circuits using a set of laws from quantum mechanics and basic matrix operations with Dirac notation. We use Maude, a high-level specification/programming language based on rewriting logic, to implement our symbolic approach. As case studies, we use the approach to formally specify several quantum communication protocols in the early work of quantum communication and formally verify their correctness: Superdense Coding, Quantum Teleportation, Quantum Secret Sharing, Entanglement Swapping, Quantum Gate Teleportation, Two Mirror-image Teleportation, and Quantum Network Coding. We demonstrate that our approach/implementation can be a first step toward a general framework to formally specify and verify quantum circuits in Maude. The proposed way to formally specify a quantum circuit makes it possible to describe the quantum circuit in Maude such that the formal specification can be regarded as a series of quantum gate/measurement applications. Once a quantum circuit has been formally specified in the proposed way together with an initial state and a desired property expressed in linear temporal logic (LTL), the proposed model checking technique utilizes a built-in Maude LTL model checker to automatically conduct formal verification that the quantum circuit enjoys the property starting from the initial state.
This article presents a symbolic approach to model checking quantum circuits using a set of laws from quantum mechanics and basic matrix operations with Dirac notation. We use Maude, a high-level specification/programming language based on rewriting logic, to implement our symbolic approach. As case studies, we use the approach to formally specify several quantum communication protocols in the early work of quantum communication and formally verify their correctness: Superdense Coding, Quantum Teleportation, Quantum Secret Sharing, Entanglement Swapping, Quantum Gate Teleportation, Two Mirror-image Teleportation, and Quantum Network Coding. We demonstrate that our approach/implementation can be a first step toward a general framework to formally specify and verify quantum circuits in Maude. The proposed way to formally specify a quantum circuit makes it possible to describe the quantum circuit in Maude such that the formal specification can be regarded as a series of quantum gate/measurement applications. Once a quantum circuit has been formally specified in the proposed way together with an initial state and a desired property expressed in linear temporal logic (LTL), the proposed model checking technique utilizes a built-in Maude LTL model checker to automatically conduct formal verification that the quantum circuit enjoys the property starting from the initial state.Modelling and verification of post-quantum key encapsulation mechanisms using Maudehttps://peerj.com/articles/cs-15472023-09-192023-09-19Víctor GarcíaSantiago EscobarKazuhiro OgataSedat AkleylekAyoub Otmani
Communication and information technologies shape the world’s systems of today, and those systems shape our society. The security of those systems relies on mathematical problems that are hard to solve for classical computers, that is, the available current computers. Recent advances in quantum computing threaten the security of our systems and the communications we use. In order to face this threat, multiple solutions and protocols have been proposed in the Post-Quantum Cryptography project carried on by the National Institute of Standards and Technologies. The presented work focuses on defining a formal framework in Maude for the security analysis of different post-quantum key encapsulation mechanisms under assumptions given under the Dolev-Yao model. Through the use of our framework, we construct a symbolic model to represent the behaviour of each of the participants of the protocol in a network. We then conduct reachability analysis and find a man-in-the-middle attack in each of them and a design vulnerability in Bit Flipping Key Encapsulation. For both cases, we provide some insights on possible solutions. Then, we use the Maude Linear Temporal Logic model checker to extend the analysis of the symbolic system regarding security, liveness and fairness properties. Liveness and fairness properties hold while the security property does not due to the man-in-the-middle attack and the design vulnerability in Bit Flipping Key Encapsulation.
Communication and information technologies shape the world’s systems of today, and those systems shape our society. The security of those systems relies on mathematical problems that are hard to solve for classical computers, that is, the available current computers. Recent advances in quantum computing threaten the security of our systems and the communications we use. In order to face this threat, multiple solutions and protocols have been proposed in the Post-Quantum Cryptography project carried on by the National Institute of Standards and Technologies. The presented work focuses on defining a formal framework in Maude for the security analysis of different post-quantum key encapsulation mechanisms under assumptions given under the Dolev-Yao model. Through the use of our framework, we construct a symbolic model to represent the behaviour of each of the participants of the protocol in a network. We then conduct reachability analysis and find a man-in-the-middle attack in each of them and a design vulnerability in Bit Flipping Key Encapsulation. For both cases, we provide some insights on possible solutions. Then, we use the Maude Linear Temporal Logic model checker to extend the analysis of the symbolic system regarding security, liveness and fairness properties. Liveness and fairness properties hold while the security property does not due to the man-in-the-middle attack and the design vulnerability in Bit Flipping Key Encapsulation.Quantum-effective exact multiple patterns matching algorithms for biological sequenceshttps://peerj.com/articles/cs-9572022-05-122022-05-12Kapil Kumar SoniAkhtar Rasool
This article presents efficient quantum solutions for exact multiple pattern matching to process the biological sequences. The classical solution takes Ο(mN) time for matching m patterns over N sized text database. The quantum search mechanism is a core for pattern matching, as this reduces time complexity and achieves computational speedup. Few quantum methods are available for multiple pattern matching, which executes search oracle for each pattern in successive iterations. Such solutions are likely acceptable because of classical equivalent quantum designs. However, these methods are constrained with the inclusion of multiplicative factor m in their complexities. An optimal quantum design is to execute multiple search oracle in parallel on the quantum processing unit with a single-core that completely removes the multiplicative factor m, however, this method is impractical to design. We have no effective quantum solutions to process multiple patterns at present. Therefore, we propose quantum algorithms using quantum processing unit with C quantum cores working on shared quantum memory. This quantum parallel design would be effective for searching all t exact occurrences of each pattern. To our knowledge, no attempts have been made to design multiple pattern matching algorithms on quantum multicore processor. Thus, some quantum remarkable exact single pattern matching algorithms are enhanced here with their equivalent versions, namely enhanced quantum memory processing based exact algorithm and enhanced quantum-based combined exact algorithm for multiple pattern matching. Our quantum solutions find all t exact occurrences of each pattern inside the biological sequence in
$O((m/C)\sqrt{N})$O((m/C)N)
and
$O((m/C)\sqrt{t})$O((m/C)t)
time complexities. This article shows the hybrid simulation of quantum algorithms to validate quantum solutions. Our theoretical–experimental results justify the significant improvements that these algorithms outperform over the existing classical solutions and are proven effective in quantum counterparts.
This article presents efficient quantum solutions for exact multiple pattern matching to process the biological sequences. The classical solution takes Ο(mN) time for matching m patterns over N sized text database. The quantum search mechanism is a core for pattern matching, as this reduces time complexity and achieves computational speedup. Few quantum methods are available for multiple pattern matching, which executes search oracle for each pattern in successive iterations. Such solutions are likely acceptable because of classical equivalent quantum designs. However, these methods are constrained with the inclusion of multiplicative factor m in their complexities. An optimal quantum design is to execute multiple search oracle in parallel on the quantum processing unit with a single-core that completely removes the multiplicative factor m, however, this method is impractical to design. We have no effective quantum solutions to process multiple patterns at present. Therefore, we propose quantum algorithms using quantum processing unit with C quantum cores working on shared quantum memory. This quantum parallel design would be effective for searching all t exact occurrences of each pattern. To our knowledge, no attempts have been made to design multiple pattern matching algorithms on quantum multicore processor. Thus, some quantum remarkable exact single pattern matching algorithms are enhanced here with their equivalent versions, namely enhanced quantum memory processing based exact algorithm and enhanced quantum-based combined exact algorithm for multiple pattern matching. Our quantum solutions find all t exact occurrences of each pattern inside the biological sequence in
$O((m/C)\sqrt{N})$O((m/C)N)
and
$O((m/C)\sqrt{t})$O((m/C)t)
time complexities. This article shows the hybrid simulation of quantum algorithms to validate quantum solutions. Our theoretical–experimental results justify the significant improvements that these algorithms outperform over the existing classical solutions and are proven effective in quantum counterparts.Graph coloring using the reduced quantum genetic algorithmhttps://peerj.com/articles/cs-8362022-01-032022-01-03Sebastian Mihai ArdeleanMihai Udrescu
Genetic algorithms (GA) are computational methods for solving optimization problems inspired by natural selection. Because we can simulate the quantum circuits that implement GA in different highly configurable noise models and even run GA on actual quantum computers, we can analyze this class of heuristic methods in the quantum context for NP-hard problems. This paper proposes an instantiation of the Reduced Quantum Genetic Algorithm (RQGA) that solves the NP-hard graph coloring problem in O(N1/2). The proposed implementation solves both vertex and edge coloring and can also determine the chromatic number (i.e., the minimum number of colors required to color the graph). We examine the results, analyze the algorithm convergence, and measure the algorithm's performance using the Qiskit simulation environment. Our Reduced Quantum Genetic Algorithm (RQGA) circuit implementation and the graph coloring results show that quantum heuristics can tackle complex computational problems more efficiently than their conventional counterparts.
Genetic algorithms (GA) are computational methods for solving optimization problems inspired by natural selection. Because we can simulate the quantum circuits that implement GA in different highly configurable noise models and even run GA on actual quantum computers, we can analyze this class of heuristic methods in the quantum context for NP-hard problems. This paper proposes an instantiation of the Reduced Quantum Genetic Algorithm (RQGA) that solves the NP-hard graph coloring problem in O(N1/2). The proposed implementation solves both vertex and edge coloring and can also determine the chromatic number (i.e., the minimum number of colors required to color the graph). We examine the results, analyze the algorithm convergence, and measure the algorithm's performance using the Qiskit simulation environment. Our Reduced Quantum Genetic Algorithm (RQGA) circuit implementation and the graph coloring results show that quantum heuristics can tackle complex computational problems more efficiently than their conventional counterparts.