Drafts by Bikash K. Behera
A quantum router is a device that is proposed to direct a quantum data signal in a quantum networ... more A quantum router is a device that is proposed to direct a quantum data signal in a quantum network system. Here, we demonstrate a Hamiltonian based quantum router on a four-qubit system using the IBM quantum experience platform. Transfer of information through message qubit to the desired output qubit in a router is performed by following a certain condition. Using quantum state tomography, we show that message from the input qubit gets transferred to a particular output qubit with 0.99 fidelity. Our study also presents the time evolution of the system Hamiltonian for a four-qubit quantum router. Finally, with a three output qubit router example, we illustrate the scalability of the quantum router system using the Hamiltonian required.
The news of achieving quantum supremacy by Google AI has received critical acclaim by a number of... more The news of achieving quantum supremacy by Google AI has received critical acclaim by a number of researchers in the field of quantum computing. Here, we implement a cross-entropy benchmarking procedure on the IBM quantum computer and report the results obtained. The backend used for this purpose is IBM Ourense. Through this experiment, we observe an exponential decay in the fidelity. Noticing that the observations are similar to ones obtained by Google AI, we conclude that by increasing the number of qubits, it is possible to achieve quantum supremacy on IBM's quantum computer.
Tic-Tac-Toe is a well-known game that almost everyone has played in their childhood. It is genera... more Tic-Tac-Toe is a well-known game that almost everyone has played in their childhood. It is generally played on paper or a classical computer. Recognizing the potential and power of quantum computers, we believe the future is quantum computing, where quantum computers might replace conventional computers due to their high efficiency at handling exceptional levels of complexity. We make our version of Quantum Tic-Tac-Toe by modifying some rules and adding some different types of moves. Through this, we want to show that a game as simple as Tic-Tac-Toe could be made much more exciting and fun by involving quantum circuits. The players have an option to choose from two different types of moves. The classical move which measures the box and results in collapse and the quantum move which entangles two separate boxes and favours the player if the control box collapses in his favour. We give a detailed explanation of the working of the quantum circuit along with the rules and strategies of the game. We have also described the algorithm in detail and provided the code for the game.
We implement a general circuit for superdense coding using 2n and 2n+1 qubits. We develop a circu... more We implement a general circuit for superdense coding using 2n and 2n+1 qubits. We develop a circuit which generates all entangled states encoding every possible combinations of input string. It is shown that 2n bits of information can be sent using n qubits and 2n+1 bits can be sent using n+1 qubits achieving the Holevo bound. It can be shown that our protocol can be extended to achieve superdense coding using even number of qudits transmitting 4 bits of message per qudit and the implementation of the protocol is shown for a two qudit system. We design and execute quantum circuits for the 4-qubit superdense coding using IBM quantum experience platform and verify the simulational results with the theoretically predicted ones.
Entanglement swapping plays a key role in quantum communication network and can be achieved by di... more Entanglement swapping plays a key role in quantum communication network and can be achieved by different kind of interaction processes between the entangled channels. Here, we propose a quantum circuit and design it on IBM quantum experience platform for entanglement swapping between the two qubits of a channel into entanglement between two such separate channels which have never interacted in a three channel system. We create three pairs of entangled qubits and applying series of quantum gates we entagle two of them which have never interacted directly throughout the process. Further, we demonstrate the delayed choice measurement by using entanglement swapping on the IBM QX which is also a entanglement swapping procedure between the qubits without any past interaction between them. To attempt this, we create two pairs of entangled qubits and delayed the measurement of two qubits one from each pair by using series of Identity gates. Then, we develop a choice making circuit which is a quantum random number generator for measurement of the two qubits either in the computational basis or in the Bell basis. This process projects the other two already measured qubits either into entangled state or into the separable state depending on the choice of measuring basis.
In the optical well and dissipative model system, the synchronization of the double spin model co... more In the optical well and dissipative model system, the synchronization of the double spin model could be obtained with the Hamiltonian operator. We have simulated this operator by designing a circuit with precise gate measurement and executed on the IBM Q Experience platform through different N states with controlled energy separation ($\omega$) where we can check quantum synchronization in the dissipation in the lattice. Our result shows the relation between entanglement system of the states, the relation between the different energy separation ($\omega$) with the spin-spin coupling ($\lambda$) in the lattice and finally we analyze the one-time correlation of the synchronizing measure of phase locking of N number of states.
Chess is an extremely ancient board game, which can be played using physical chess boards and can... more Chess is an extremely ancient board game, which can be played using physical chess boards and can be enjoyed virtually by using classical computers. Gradually, as the quantum computers are being developed , their potential applications in various complex challenges are being realized. Upon the arrival of quantum computers at the scene, games can now be played on a quantum computer by designing quantum circuits on it. Though classical computers are enough to play the game virtually, quantum computers will always be better for tackling more and more complexity in a game. Since classical computation is used chess engines, in future, the engines can be made faster by using quantum computation, primarily because of their ability to use fewer steps to obtain at the same result as that of classical computers. And we can achieve the same with quantum computers by designing quantum circuits. However, an 8×8 chessboard is quite large and the existence of various pieces makes the circuit quite complex for us to build, so here we present quantum circuits for a 3×3 chessboard with only pawns in it. From here, it can be extrapolated to create, circuits for an 8×8 board and various other pieces. These quantum circuits can be designed on a quantum computer to play chess by any two users. We explain the working of the quantum circuits in detail with the algorithm behind the movement of pawns on the chessboard, in future, we can use this to later develop a quantum chess engine which will boost the quality of chess.
Scientists have been hard and fast at work attempting to develop the next revolutionary concept t... more Scientists have been hard and fast at work attempting to develop the next revolutionary concept that will significantly change the way of data transfer, security, processing speeds, etc. Extensive study in this field has opened the possibilities of quantum physics being used as a basis for improvising the current network and computing systems. The focus as of now is on finding a way to break the classical barrier of limitations. We can, therefore, try to construct a quantum internet using the concepts of quantum computing. Here, we work towards implementing a couple of components of a quantum network, such as a quantum channel and a single layer of quantum intercommunication. Error correction in the network is also illustrated. More specifically, the application layer of the quantum internet model and two protocols of the transport layer are discussed.
With the development in the field of quantum physics, several methods for building a quantum comp... more With the development in the field of quantum physics, several methods for building a quantum computer have come up. One such method is the use of superconducting qubits. The interactions amongst qubits are of greater importance for the designing of a sophisticated quantum computer. The paper discusses the dependence of the circuit size, and circuit depth on the interaction and connection between different qubits present in quantum hardware. Here, we present a procedure which helps one in determining the optimal interactions between different qubits of a quantum chip to execute a given circuit in the most efficient way possible. In this paper, we illustrate it with an example of a 5-qubit structure. In general, this procedure can be used for any arbitrary user-defined circuit. Given the allowed interactions, one can accurately determine the configuration for which the circuit runs in the least number of clock cycles with the lowest gate operations and noise-based errors.
Cryptography is the science of encoding of a message in such a way that it can securely be commun... more Cryptography is the science of encoding of a message in such a way that it can securely be communicated between the involved parties even in the presence of a third party or adversary. With the rise of quantum era, several protocols with theoretical security, violating the quantum properties of photons such as phase, polarization etc., have been discovered. One such protocol is the differential phase shift protocol. Experimental implementation of the protocol has been done in several research works but the implementation of the protocol on a quantum computer has never been discussed before. In this paper, we simulate the DPS QKD protocol on the IBM QX online quantum computing platform. The protocol is implemented and the results are analysed and compared with the the actual results while performing the protocol.
Cryptography is the science of encoding of a message in such a way that it can securely be commun... more Cryptography is the science of encoding of a message in such a way that it can securely be communicated between the involved parties even in the presence of a third party or adversary. With the rise of quantum era, several protocols with theoretical security, violating the quantum properties of photons such as phase, polarization etc., have been discovered. One such protocol is the differential phase shift protocol. Experimental implementation of the protocol has been done in several research works but the implementation of the protocol on a quantum computer has never been discussed before. In this paper, we simulate the DPS QKD protocol on the IBM QX online quantum computing platform. The protocol is implemented and the results are analysed and compared with the the actual results while performing the protocol.
Classical computers allow security of cryptographic protocols based on the mathematical complexit... more Classical computers allow security of cryptographic protocols based on the mathematical complexity of encoding functions and the shared key. This implies that high computational power can have a positive outcome in breaking cryptographic protocols that employ classical computers. Quantum machines claim to possess such power. Two parties interested in communicating with each other take up the process of measuring entangled states in order to construct a secret key which is safeguarded against an eavesdropper capable of performing quantum operations. At first, experimental verification of the BB84 protocol using three bases has been performed in this paper, out of which sub-cases have been considered based on whether or not Eve has attempted an attack. The following part includes experimental realization of the B92 protocol which was introduced by Charles Bennett in the year 1992. Possibility of an Eve's attack is considered and implemented. Succeeding part relies on experimental implementation of the protocol that was introduced by Acin, Massar and Pironio in the year 2006 [New J. Phys. 8, 126 (2006)]. All the implementations have been done using the IBM Quantum Experience platform.
Artificial intelligence and machine learning paves the way to achieve greater technical feats. In... more Artificial intelligence and machine learning paves the way to achieve greater technical feats. In this endeavor to hone these techniques, quantum machine learning is budding to serve as an important tool. Using the techniques of deep learning and supervised learning in the quantum framework, we are able to propose a quantum neural network and showcase its implementation. We consider the application of cancer detection to demonstrate the working of our quantum neural network. Our focus is to train the network of ten qubits in a way so that it can learn the label of the given data set and optimize the circuit parameters to obtain the minimum error. Thus, through the use of many algorithms, we are able to give an idea of how a quantum neural network can function.
Quantum computers promise to efficiently solve important problems that are intractable on a conve... more Quantum computers promise to efficiently solve important problems that are intractable on a conventional computer. Quantum computational algorithms have the potential to be a exciting way of studying quantum cosmology. In quantum cosmology, we try to learn about the dynamics of the universe without constructing a complete theory of quantum gravity. Since the universal wavefunction exists in an infinite-dimensional superspace over all possible 3D metrics and modes of matter configurations, we take minisuperspaces for our work by constraining the degrees of freedom to particular 3D metrics and uniform scalar field configurations. In our work, we consider a wide variety of cosmological models. We begin by analyzing an anisotropic universe with cosmological constant and classical radiation. We then study the results for higher derivatives, Kaluza-Klein theories and string dilaton in quantum cosmology. We use IBM's Quantum Information Science Kit (QISKit) python library and the Variational Quantum Eigensolver (VQE) algorithm for studying these systems. The VQE algorithm is a hybrid algorithm that uses the variational approach and interleaves quantum and classical computations in order to find the minimum eigenvalue of the Hamiltonian for a given system.
A fundamental concept in quantum-information processing is the connection of a quantum computatio... more A fundamental concept in quantum-information processing is the connection of a quantum computational model to a physical system by transformations of closed-operator algebras. The Jordan-Wigner isomorphism gives the correspondence between the algebra of the computational model and the physical model. An electronic system can be represented in terms of the algebra generated by the fermionic creation and annihilation operators or algebra of the Pauli operators. We discuss quantum simulation of the fermionic model by a quantum computer, which is expressed in the language and algebra of quantum spin-1/2 objects Pauli algebra. We apply this method to the paradigmatic cases of 1D and 2D Fermi-Hubbard models, involving couplings with nearest neighbors. We construct the quantum circuit of this model and simulate the system in the IBM quantum computer.
A fundamental concept in quantum-information processing is the connection of a quantum computatio... more A fundamental concept in quantum-information processing is the connection of a quantum computational model to a physical system by transformations of closed-operator algebras. The Jordan-Wigner isomorphism gives the correspondence between the algebra of the computational model and the physical model. An electronic system can be represented in terms of the algebra generated by the fermionic creation and annihilation operators or algebra of the Pauli operators. We discuss quantum simulation of the fermionic model by a quantum computer, which is expressed in the language and algebra of quantum spin-1/2 objects Pauli algebra. We apply this method to the paradigmatic cases of 1D and 2D Fermi-Hubbard models, involving couplings with nearest neighbors. We construct the quantum circuit of this model and simulate the system in the IBM quantum computer.
In quantum information processing, entanglement criteria remains a core area of research, especia... more In quantum information processing, entanglement criteria remains a core area of research, especially for W-type multimode states. Here, we experimentally realize the scheme of entanglement condition on IBM quantum computer for the above states as proposed by Selvan and Panigrahi [Eur. Phys. J. D \textbf{73}, 127 (2019)]. We test it for three-mode single-photon W state by proposing a quantum circuit for the experimental scheme. According to the scheme, violation of creation/annihilation numbers based operator-inequality confirms the entanglement of three-mode W-type state. Firstly, we prepare the three-mode W-type entangled state, subsequently, design the propose quantum circuit and run it on the 5-qubit quantum computer. We successfully confirm and verify the scheme for a three-mode W-type state by showing the violation of inequality in nine different experimental conditions. For each of the experiments, we use a different number of terms to calculate the magnitude of the operator used in the inequality. Here, we experiment it for three-mode W-type state, that finally paves the way for higher-order modes of electromagnetic fields.
In the present work, we simulate the interesting case of neutrino oscillations by considering the... more In the present work, we simulate the interesting case of neutrino oscillations by considering the two Majorana phases to be non zero on the IBM quantum experience platform. The theme of the paper is to study and understand more about neutrino oscillations by using quantum computing as a tool. Further, we prove that the oscillation probabilities are unchanged by the present choices of Majorana phases and the proof is followed by the time evolution graphs of the neutrinos by considering them as two state and three state quantum mechanical systems. The quantum circuit we propose here is able to give three quantum states by using two qubits on quantum simulator, in principle satisfying the previous theory. We include both quantum simulator and real device results and calculate the fidelity by using theoretical and real device density matrix constructions. It is concluded that the neutrino tomography plots are obtained with good fidelity. Finally, the survival oscillation and the probabilities are plotted which show close resemblance with plots obtained from classical computer.
Quantum machine learning is at the crossroads of two of the most exciting current areas of resear... more Quantum machine learning is at the crossroads of two of the most exciting current areas of research: quantum computing and classical machine learning. It explores the interaction between quantum computing and machine Learning, investigating how results and techniques from one field can be used to solve the problems of the other. With an ever-growing amount of data, current machine learning systems are rapidly approaching the limits of classical computational models. In this sense, quantum computational power can offer advantage in such machine learning tasks. The field of quantum machine learning explores how to devise and implement quantum software that could enable machine learning that is faster than that of classical computers. Fuelled by increasing computing power and algorithmic advances, machine learning techniques have become powerful tools for finding patterns in data. Quantum systems produce atypical patterns that classical systems are thought not to produce efficiently, so it is reasonable to postulate that quantum computers may outperform classical computers on machine learning tasks. Here, we review the previous literature on quantum machine learning and provide the current status of it.
Quantum algorithm, as compared to classical algorithm, plays a notable role in solving linear sys... more Quantum algorithm, as compared to classical algorithm, plays a notable role in solving linear systems of equations with an exponential speedup. Here, we demonstrate a method for solving a particular system of equations by using the concept of well-known Grover's quantum search algorithm. The algorithm finds the solution by rotating the initial state vector in the Hilbert space to get the target solution state. It mainly involves finding particular matrices that solve the set of equations and constructing corresponding quantum circuits using the basic quantum gates. We explicitly illustrate the whole process by taking 48 different set of equations and solving them by using the concept of Grover's algorithm. We propose new quantum circuits for each set of equations and design those on the IBM quantum simulator. We run the quantum circuit for one set of equations and obtain the desired results, and hence verify the working of the algorithm.
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Drafts by Bikash K. Behera