Depatment of Physical Sciences

Since the advent of quantum computation, there have been attempts to apply the power of quantum mechanics to robotics and develop quantum equivalent of classical robots-quantum robots. In this paper, we review a very simple yet powerful vehicular design: classical Braitenberg vehicles. We discuss the working of a classical Braitenberg vehicle and the various problems which lead us to propose a novel improvement by automating the Braitenberg vehicles using classical finite automata, Moore machines. We improve upon the classical automated Braitenberg vehicle by introducing an intrinsic nature to the vehicle such that it stops its motion without requiring external signals. We achieve this by using entanglement and this leads to our design of a quantum automated Braitenberg vehicle. Finally, we propose an improvement to the quantum automated Braitenberg vehicle by incorporating the possibility of external control over its movement. We implement the circuits in IBM Quantum Experience platform and obtain encouraging results matching with our theoretical predictions. This paper makes important contributions to the understanding of quantum robots: an experimental verification of the quantum logic on a real quantum computer with reasonably good results despite decoherence and errors in quantum gate applications, the idea of introducing intrinsic complex behaviour using quantum mechanics, the idea of flexibility in developing manual external controls, and achieving better results than classical robots using lesser number of gates.

Error detection and correction has been a fundamental branch of quantum information, attempting to minimize decay of information through decoherence. Several error correcting codes have been developed over the years, out of which Reed-Solomon code is one of the most useful ones. We test the reliability of the quantum equivalent of the classical Reed-Solomon code and present the circuit implementation of quantum Reed-Solomon code for encoding-decoding using two approaches; using auxiliary CNOTs as previously established and without auxiliary CNOTs as our improvement to the existing algorithm. We compare the results obtained from these approaches and comment on the general reliability of the quantum Reed-Solomon error correction algorithm for error correction. For the same, we encode a threequbit GHZ cluster state in IBM 16-qubit quantum computer, manually introduce errors, and analyze cumulative probabilities of error detection. We also discuss possible improvements to the existing quantum Reed-Solomon error detection algorithm using quantum singular value decomposition, interpolation, partial greatest common divisor, and polynomial long division.

Error detection and correction has been a fundamental branch of quantum information, attempting to minimize decay of information through decoherence. Several error correcting codes have been developed over the years, out of which Reed-Solomon code is one of the most useful ones. We test the reliability of the quantum equivalent of the classical Reed-Solomon code and present the circuit implementation of quantum Reed-Solomon code for encoding-decoding using two approaches; using auxiliary CNOTs as previously established and without auxiliary CNOTs as our improvement to the existing algorithm. We compare the results obtained from these approaches and comment on the general reliability of the quantum Reed-Solomon error correction algorithm for error correction. For the same, we encode a threequbit GHZ cluster state in IBM 16-qubit quantum computer, manually introduce errors, and analyze cumulative probabilities of error detection. We also discuss possible improvements to the existing quantum Reed-Solomon error detection algorithm using quantum singular value decomposition, interpolation, partial greatest common divisor, and polynomial long division.

The goal of teleportation is to transfer the state of one particle to another particle. In coined quantum walks, conditional shift operators can introduce entanglement between position space and coin space. This entan-glement resource can be used as a quantum channel for teleportation, as proposed by Wang, Shang and Xue [Quantum Inf. Process. 16, 221 (2017)]. Here, we demonstrate the implementation of quantum teleportation using quantum walks on a five-qubit quantum computer and a 32-qubit simulator provided by IBM quantum experience beta platform. We show the teleportation of single-qubit, two-qubit and three-qubit quantum states with circuit implementation on the quantum devices. The teleportation of Bell, W and GHZ states has also been demonstrated as special cases of the above states.

Error detection and correction has been a fundamental branch of quantum information, attempting to minimize decay of information through decoherence. Several error correcting codes have been developed over the years, out of which Reed-Solomon code is one of the most useful ones. We test the reliability of the quantum equivalent of the classical Reed-Solomon code and present the circuit implementation of quantum Reed-Solomon code for encoding-decoding using two approaches; using auxiliary CNOTs as previously established and without auxiliary CNOTs as our improvement to the existing algorithm. We compare the results obtained from these approaches and comment on the general reliability of the quantum Reed-Solomon error correction algorithm for error correction. For the same, we encode a three-qubit GHZ cluster state in IBM 16-qubit quantum computer, manually introduce errors, and analyze cumulative probabilities of error detection. We also discuss possible improvements to the existing quantum Reed-Solomon error detection algorithm using quantum singular value decomposition, interpolation, partial greatest common divisor, and polynomial long division. Implementation of quantum Reed-Solomon error detection on IBM quantum computer

It is known that the horizon of quantum supremacy is located at 50 qubit threshold, i.e., quantum computation with more than 50 qubits can no longer be simulated by classical simulation. The above supremacy is determined mainly by state vector simulation method and a path integral simulation algorithm. Here we present a variant of recursive path-summing algorithm proposed by Shi [arXiv:1710.09364] which can simulate the quantum circuits with lesser time-and memory-complexity. The proposed algorithm is compared with the state vector simulation method and is concluded that quantum supremacy can be more accurately measured from the above algorithm as compared to the state vector method. Random quantum circuits are taken as inputs of the algorithm and the comparison of both the algorithm is made. Furthermore, a quantum circuit is run on the real chip and path-integral has been calculated. In brief, we present here a classical algorithm for simulation of any random quantum circuits by making a tree depicting the evolution of the quantum system , in an approach reminiscent of the many-worlds interpretation of quantum mechanics.

Though algorithms for quantum simulation of Quantum Harmonic Oscillator (QHO) have been proposed, still they have not yet been experimentally verified. Here, for the first time, we demonstrate a quantum simulation of QHO in the presence of both time-varying and constant force field for both one and two dimensional case. New quantum circuits are developed to simulate both the one and two-dimensional QHO and are implemented on the real quantum chip "ibmqx4". Experimental data, clearly illustrating the dynamics of QHO in the presence of time-dependent force field, are presented in graphs for different frequency parameters in the Hamiltonian picture.

Quantum Information Splitting (QIS) is an important technique widely used in quantum teleportation, where a sender sends quantum information (state) to particular recipients by doing some operations on their qubits. Only all of the receivers can collectively work out to recover the content which was sent by the sender. Here, we provide a new efficient scheme for splitting up of quantum information using five-qubit cluster states. We demonstrate our work by performing experiments on the IBM quantum computer and conclude that a two-qubit arbitrary state can be split by using a five-qubit cluster state. We properly implement the schemes on the quantum computer by designing appropriate quantum circuits and collect experimental results with good fidelity .

Quantum Key Distribution (QKD) is one of the major applications in the field of quantum cryptography. For security reasons, all the QKD designs have to be resilient against any attackers, who may try to passively or actively attack the quantum or classical link between the parties and gain hold of illegitimate information. Here, we propose a three party QKD using the three-qubit entangled states (GHZ state) and a complete graph type network architecture comprising both quantum and classical channels among four (or more) participants. The network architecture itself provides sufficient confusion to any potential attacker. Furthermore, we use the non-local correlations provided by two-qubit Bell states through the quantum channels, and the concept of hash values and a request-acknowledge type communication through the classical channels to add to the robustness of the scheme. We explicate the proposed algorithm in detail along with the analysis on the security of the system.

The negative hydrogen ion is the first three body quantum problem whose ground state energy is theoretically calculated using the "Chandrasekhar Wavefunction" that accounts for the electron-electron correlation 1. The best value of ground state energy is obtained by photodetachment experiment using lasers in the laboratory. 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. Here, we show the quantum simulation of H − ion to calculate it's ground state energy in IBM quantum computer. We observe that the quantum computer is efficient in preparing the correlated wavefunction of H − and shows it as a bound entity as the ground state energy is found to be lower than that of Hydrogen atom. We use a recently developed algorithm known as "Variational Quantum Eigensolver" 2,3 and implement it in IBM's 5-qubit quantum chips "ibmqx2" and "ibmqx4". An optimization routine is performed on a 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 circuit is parametrized by 12 arbitrary angles and is thus used to create different trial wavefuntions by varying the parameters. The technique can be used to solve various many body problems 4 with great efficiency.

The negative hydrogen ion is the first three body quantum problem whose ground state energy is theoretically calculated using the "Chandrasekhar Wavefunction" that accounts for the electron-electron correlation 1. The best value of ground state energy is obtained by photodetachment experiment using lasers in the laboratory. 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. Here, we show the quantum simulation of H − ion to calculate it's ground state energy in IBM quantum computer. We observe that the quantum computer is efficient in preparing the correlated wavefunction of H − and shows it as a bound entity as the ground state energy is found to be lower than that of Hydrogen atom. We use a recently developed algorithm known as "Variational Quantum Eigensolver" 2,3 and implement it in IBM's 5-qubit quantum chips "ibmqx2" and "ibmqx4". An optimization routine is performed on a 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 circuit is parametrized by 12 arbitrary angles and is thus used to create different trial wavefuntions by varying the parameters. The technique can be used to solve various many body problems 4 with great efficiency.

Cloning an unknown state is an important task in the field of quantum computation as it is one of the basic operations required in any experiment. The no-cloning theorem states that it is impossible to create an identical copy of an arbitrary unknown quantum state. Hence, techniques are developed to clone unknown states to high fidelities, rather than to exact copies. The usual method of cloning is quantum tomography, which measures a set of observables to reconstruct the unknown state. This method proves to be very expensive when the number of copies of the unknown state is limited. Here, we try to clone an unknown state in IBM's QASM simulator using a quantum reinforcement learning protocol [Phys. Rev. A 98, 042315 (2018)] as proposed by Albarran-Arriagada et al., where the "right" amount of punishment/reward function and boundary conditions can give much better fidelity than what tomography can offer in limited copies of the state. Using this method, we can attain above 90% fidelity in under 50 copies. This method proves to be very useful for reconstructing quantum states when only limited copies of the state are available.

Bingo game is one of the most used online games, which is played using classical computers. After realizing the power of quantum computers, researchers have started developing quantum games, which can be played using a quantum computer by designing quantum circuits on it. Though classical computers are good to play the games, quantum computers will always be better for tackling more and more complexity in a game. It is believed that the game can be more efficiently designed on a quantum computer with minimum resource complexity, where more and more strategy-complexity can be introduced in the game and thus can be more interesting and survivable. Here, we present quantum circuits, which can be designed on a quantum computer to play the Bingo game by any two users. We explain the working of the quantum circuits in detail with the rules of the game. It has been shown that, at the end of the game, measurement outcomes of the ancilla qubits can tell which user wins the game.

Continuous-time quantum walk (CTQW) and its experimental realization are of great interest due to its profound application starting from graph matching to quantum search algorithms. Here, we propose quantum circuits for CTQW on cycle graph with 2, 4, and 8 vertices at any time t for given different initial conditions. We present a comparative study of theoretical probability distribution, simulated and implemented output after executing the quantum circuits on the real quantum chip,"ibmq 16 melbourne" provided by IBM quantum experience platform and thus experimentally verify our quantum circuits and provide a demonstration of CTQW on mentioned graphs.

Quantum error correcting codes (QECC) are the key ingredients both for fault-tolerant 9 quantum computation and quantum communication. Teleportation-based error correction 10 (TEC) helps in detecting and correcting operational and erasure errors by performing X and 11 Z measurements during teleportation. Here we demonstrate the TEC protocol for the detec-12 tion and correction of a single bit-flip error by proposing a new quantum circuit. A single 13 phase-flip error can also be detected and corrected using the above protocol. For the first 14 time, we illustrate detection and correction of erasure error in the superconducting qubit-15 based IBM's 14-qubit quantum computer. 16