Complete characterization of the directly implementable quantum gates used in the IBM quantum processors

Quantum process tomography of each directly implementable quantum gate used in the IBM quantum processors is performed to compute gate error in order to check viability of complex quantum operations in the superconductivity-based quantum computers introduced by IBM and to compare the quality of these gates with the corresponding gates implemented using other technologies. Quantum process tomography (QPT) of C-NOT gates have been performed for three configurations available in IBM QX4 processor. For all the other allowed gates QPT have been performed for every allowed position (i.e., by placing the gates in different qubit lines) for IBM QX4 architecture, and thus, gate fidelities are obtained for both single-qubit and 2-qubit gates. Gate fidelities are observed to be lower than the corresponding values obtained in the other technologies, like NMR. Further, gate fidelities for all the single-qubit gates are obtained for IBM QX2 architecture by placing the gates in the third qubit line ($q[2]$). It's observed that the IBM QX4 architecture yields better gate fidelity compared to IBM QX2 in all cases except the case of $\operatorname{Y}$ gate as far as the gate fidelity corresponding to the third qubit line is concerned. In general, the analysis performed here leads to a conclusion that a considerable technological improvement would be inevitable to achieve the desired scalability required for the realization of complex quantum operations.Comment: Quantum Process tomography has been done for all the gates used in IBM QX2 and IBM QX

Experimental realization of nondestructive discrimination of Bell states using a five-qubit quantum computer

A scheme for distributed quantum measurement that allows nondestructive or indirect Bell measurement was proposed by Gupta et al., (Int. J. Quant. Infor. \textbf{5} (2007) 627) and subsequently realized experimentally using an NMR-based three-qubit quantum computer by Samal et al., (J. Phys. B, \textbf{43} (2010) 095508). In the present work, a similar experiment is performed using the five-qubit super-conductivity-based quantum computer, which has been recently placed in cloud by IBM Corporation. The experiment confirmed that the Bell state can be constructed and measured in a nondestructive manner with a reasonably high fidelity. A comparison of the outcomes of this study and the results obtained earlier in the NMR-based experiment has also been performed. The study indicates that to make a scalable SQUID-based computer, errors by the gates (in the present technology) have to be reduced considerably.Comment: 7 figures,13 pages including 1 appendi

Benford's distribution in extrasolar world: Do the exoplanets follow Benford's distribution?

In many real life situations, it is observed that the first digits (i.e., $1,2,\ldots,9$) of a numerical data-set, which is expressed using decimal system, do not follow a random distribution. Instead, smaller numbers are favoured by nature in accordance with a logarithmic distribution law, which is referred to as Benford's law. The existence and applicability of this empirical law have been extensively studied by physicists, accountants, computer scientists, mathematicians, statisticians, etc., and it has been observed that a large number of data-sets related to diverse problems follow this distribution. However, applicability of Benford's law has been hardly tested for extrasolar objects. Motivated by this fact, this paper investigates the existence of Benford's distribution in the extrasolar world using Kepler data for exoplanets. The investigation has revealed the presence of Benford's distribution in various physical properties of these exoplanets. Further, Benford goodness parameters are computed to provide a quantitative measure of coincidence of real data with the ideal values obtained from Benford's distribution. The quantitative analysis and the plots have revealed that several physical parameters associated with the exoplanets (e.g., mass, volume, density, orbital semi-major axis, orbital period, and radial velocity) nicely follow Benford's distribution, whereas some physical parameters (e.g., total proper motion, stellar age and stellar distance) moderately follow the distribution, and some others (e.g., longitude, radius, and effective temperature) do not follow Benford's distribution. Further, some specific comments have been made on the possible generalizations of the obtained result, its potential applications in analyzing data-set of candidate exoplanets, and how interested readers can perform similar investigations on other interesting data-sets.Comment: 7 pages, 3 figures and one potrai

Design and experimental realization of an optimal scheme for teleportion of an nn-qubit quantum state

An explicit scheme (quantum circuit) is designed for the teleportation of an $n$-qubit quantum state. It is established that the proposed scheme requires an optimal amount of quantum resources, whereas larger amount of quantum resources has been used in a large number of recently reported teleportation schemes for the quantum states which can be viewed as special cases of the general $n$-qubit state considered here. A trade off between our knowledge about the quantum state to be teleported and the amount of quantum resources required for the same is observed. A proof of principle experimental realization of the proposed scheme (for a 2-qubit state) is also performed using 5-qubit superconductivity-based IBM quantum computer. Experimental results show that the state has been teleported with high fidelity. Relevance of the proposed teleportation scheme has also been discussed in the context of controlled, bidirectional, and bidirectional-controlled state teleportation.Comment: 11 pages 4 figure