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The factorization of a large digit integer in polynomial time is a challenging computational task to decipher. The exponential growth of computation can be alleviated if the factorization problem is changed to an optimization problem with the quantum computation process with the generalized Grover's algorithm and a suitable analytic algebra. In this article, the generalized Grover's protocol is used to amplify the amplitude of the required states and, in turn, help in the execution of the quantum factorization of tetra and penta primes as a proof of concept for distinct integers, including 875, 1269636549803, and 4375 using 3 and 4 qubits of IBMQ Perth (7-qubit processor). The fidelity of quantum factorization with the IBMQ Perth qubits was near unity., Comment: 12 pages, 6 figures

Multimedia security is a vital sector due to its significant impact on the development of industry 5.0. The current multimedia security systems depend on complex mathematical calculations, proven theoretically and practically in their inability to provide complete protection of information against internal and external attacks and penetration attempts. Unfortunately, the advancement of the quantum computer allowing the decryption of secured multimedia data by classical cryptographic algorithms will influence smart industries since no one can imagine the actual processing power of the quantum computer. Therefore, we have developed an efficient quantum image encryption technique for multimedia applications using generalized affine transform and logistic map. The designed generalized quantum circuits for the developed approach are tested and evaluated using the IBM cloud-based quantum computer. The proposed algorithms' performance and computational complexity analysis are measured and proved its efficiency against various criteria. Furthermore, a hybrid approach to reduce the circuit complexity and quantum cost using the Espresso algorithm to approximately 50\% for the cost of adding one more qubit to the circuit is presented. Finally, the robustness and security analysis against various noise attacks proved that the proposed quantum image encryption method forms a secured and accurately measurable quantum image processing system.

The vehicle routing problem (VRP) is an NP-hard optimization problem that has been an interest of research for decades in science and industry. The objective is to plan routes of vehicles to deliver goods to a fixed number of customers with optimal efficiency. Classical tools and methods provide good approximations to reach the optimal global solution. Quantum computing and quantum machine learning provide a new approach to solving combinatorial optimization of problems faster due to inherent speedups of quantum effects. Many solutions of VRP are offered across different quantum computing platforms using hybrid algorithms such as quantum approximate optimization algorithm and quadratic unconstrained binary optimization. In this work, we build a basic VRP solver for 3 and 4 cities using the variational quantum eigensolver on a fixed ansatz. The work is further extended to evaluate the robustness of the solution in several examples of noisy quantum channels. We find that the performance of the quantum algorithm depends heavily on what noise model is used. In general, noise is detrimental, but not equally so among different noise sources., Comment: 15 Pages, 5 figures, 15 tables. arXiv admin note: substantial text overlap with arXiv:2112.15408

Simulation of time dynamical physical problems has been a challenge for classical computers due to their time-complexity. To demonstrate the dominance of quantum computers over classical computers in this regime, here we simulate a semi-empirical model where two neutral particles interact through Lennard-Jones potential in a one-dimensional system. We implement the above scenario on the IBM quantum experience platform using a 5-qubit real device. We construct the Hamiltonian and then efficiently map it to quantum operators onto quantum gates using the time-evolutionary unitary matrix obtained from the Hamiltonian. We verify the results collected from the QASM-simulator and compare it with that of the 5-qubit real chip ibmqx2., Comment: The manuscript contains 14 pages and 16 figures

It is well-known that decoherence is a crucial barrier in realizing various quantum information processing tasks; on the other hand, it plays a pivotal role in explaining how a quantum system's fragile state leads to the robust classical state. Zurek [Nat. Phys. 5, 181-188 (2009)] has developed the theory which successfully describes the emergence of classical objectivity of quantum system via decoherence, introduced by the environment. Here, we consider two systems for a model universe, in which the first system shows a random quantum state, and the other represents the environment. We take 2-, 3-, 4-, 5- and 6-qubit quantum circuits, where the system consists of one qubit and the rest qubits represent the environment qubits. We experimentally realize the Darwinism state constructed by this system's ensemble on two real devices, ibmq_athens and ibmq_16_melbourne. We then use the results to investigate quantum-classical correlation and the mutual information present between the system and the environment., Comment: 8 figures, 10 pages

Diners dilemma is one of the most interesting problems in both economic and game theories. Here, we solve this problem for n (number of players) =4 with quantum rules and we are able to remove the dilemma of diners between the Pareto optimal and Nash equilibrium points of the game. We find the quantum strategy that gives maximum payoff for each diner without affecting the payoff and strategy of others. We use the quantum principles of superposition and entanglement that gives supremacy over any classical strategies. We present the circuit implementation for the game, design it on the IBM quantum simulator and verify the strategies in the quantum model.

Masking of data is a method to protect information by shielding it from a third party, however keeping it usable for further usages like application development, building program extensions to name a few. Whereas it is possible for classical information encoded in composite quantum states to be completely masked from reduced sub-systems, it has to be checked if quantum information can also be masked when the future possibilities of a quantum computer are increasing day by day. Newly proposed no-masking theorem [Phys. Rev. Lett. 120, 230501 (2018)], one of the no-go theorems, demands that except for some restricted sets of non-orthogonal states, it's impossible to mask arbitrary quantum states. Here, we explore the possibility of masking in the IBM quantum experience platform by designing the quantum circuits and running them on the 5-qubit quantum computer. We choose two particular states considering both the orthogonal and non-orthogonal basis states and illustrate their masking through both the theoretical calculation as well as verification in the quantum computer. By quantum state tomography, it is concluded that the experimental results are collected with high fidelity and hence the possibility of masking is realized., Comment: 12 figures, 14 pages

Quantum error correcting codes (QECC) are the key ingredients both for fault-tolerant quantum computation and quantum communication. Teleportation-based error correction (TEC) helps in detecting and correcting operational and erasure errors by performing X and Z measurements during teleportation. Here we demonstrate the TEC protocol for the detection and correction of a single bit-flip error by proposing a new quantum circuit. A single phase-flip error can also be detected and corrected using the above protocol. For the first time, we illustrate detection and correction of erasure error in the superconducting qubit-based IBM's 14-qubit quantum computer., Comment: 26 pages, 5 figures

The negative hydrogen ion is the first three body quantum problem whose ground state energy is calculated using the `Chandrasekhar Wavefunction' that accounts for the electron-electron correlation. Solving multi-body systems is a daunting task in quantum mechanics as it includes choosing a trial wavefunction and the calculation of integrals for the system that becomes almost impossible for systems with three or more particles. This difficulty can be addressed by quantum computers. They have emerged as a tool to address different electronic structure problems with remarkable efficiency. They have been realized in various fields and proved their efficiency over classical computers. Here, we show the quantum simulation of H^{-} ion to calculate it's ground state energy in IBM quantum computer. The energy is found to be -0.5339355468 Hartree with an error of 0.8376% as compared to the theoretical value. We observe that the quantum computer is efficient in preparing the correlated wavefunction of H^{-} and calculating it's ground state energy. We use a recently developed algorithm known as `Variational Quantum Eigensolver' and implement it in IBM's 5-qubit quantum chip `ibmqx2'. The method consists of a quantum part i.e., state preparation and measurement of expectation values using the quantum computer, and the classical part i.e., the optimization routine run in a classical computer for energy convergence. An optimization routine is performed on classical computer by running quantum chemistry program and codes in QISKit to converge the energy to the minimum. We also present a comparison of different optimization routines and encoding methods used to converge the energy value to the minimum. The technique can be used to solve various many body problems with great efficiency., Comment: 16 pages, 6 figures

The Klein Gordon equation was the first attempt at unifying special relativity and quantum mechanics. While initially discarded this equation of "many fathers" can be used in understanding spinless particles that consequently led to the discovery of pions and other subatomic particles. The equation leads to the development of Dirac equation and hence quantum field theory. It shows interesting quantum relativistic phenomena like Klein Paradox and "Zitterbewegung", a rapid vibrating movement of quantum relativistic particles. The simulation of such quantum equations initially motivated Feynman to propose the idea of quantum computation. While many such simulations have been done till date in various physical setups, this is the first time a digital quantum simulation of Klein Gordon equation is proposed on IBM's quantum computer. Here we simulate the time-dependent Klein Gordon equation in a barrier potential and clearly observe the tunnelling of the particle and anti-particle through a strong potential claiming Klein Paradox. The simulation technique used here inspires the quantum computing community for further studying Klein Gordon equation and applying it to more complicated quantum mechanical systems., Comment: 21 pages, 2 figures

A quantum algorithm is a set of instructions for a quantum computer, however, unlike algorithms in classical computer science their results cannot be guaranteed. Quantum search algorithm can be described as the rotation of state vectors in a Hilbert space. The state vectors uniformly rotate by iterative sequences until they hit the target position. To optimize the algorithm, it is necessary to have the precise knowledge about some parameters like the number of target positions and total number of states. Here, we demonstrate the implementation of optimal fixed-point quantum search algorithm in IBMQ simulator developed by IBM corporation. We perform the search algorithm for one-iteration for two, three, four and five qubit systems and confirm the accuracy of our results through histogram., Comment: 13 pages, 7 figures, Abstract and overall text modified

As one of the most prominent subfields of quantum communication research, remote state preparation (RSP) plays a crucial role in quantum networks. Here we present a deterministic remote state preparation scheme to prepare an arbitrary two-qubit state via a seven-qubit entangled channel created from Borras \emph{et al.} state. Quantum noises are inherent to each and every protocol for quantum communication that is currently in use, putting the integrity of quantum communication systems and their dependability at risk. The initial state of the system was a pure quantum state, but as soon as there was any noise injected into the system, it transitioned into a mixed state. In this article, we discuss the six different types of noise models namely bit-flip noise, phase-flip noise, bit-phase-flip noise, amplitude damping, phase damping and depolarizing noise. The impact these noises had on the entangled channel may be seen by analysing the density matrices that have been altered as a result of the noise. For the purpose of analysing the impact of noise on the scheme, the fidelity between the original quantum state and the remotely prepared state has been assessed and graphically represented. In addition, a comprehensive security analysis is performed, demonstrating that the suggested protocol is safe against internal and external attacks., Comment: 13 Pages, 3 figures