Vol.:(0123456789) SN Computer Science (2021) 2:450 https://doi.org/10.1007/s42979-021-00847-7 SN Computer Science REVIEW ARTICLE Analysis of Five Techniques for the Internal Representation of a Digital Image Inside a Quantum Processor Mario Mastriani 1  · Sundaraja Sitharama Iyengar 1  · Latesh Kumar 1 Received: 20 February 2021 / Accepted: 1 September 2021 © The Author(s), under exclusive licence to Springer Nature Singapore Pte Ltd 2021 Abstract In this paper, fve techniques of representing a digital image inside a quantum processor are compared. The techniques are: fexible representation of quantum images (FRQI), novel enhanced quantum representation (NEQR), generalized quantum image representation (GQIR), multi-channel representation for quantum images (MCQI), and quantum Boolean image processing (QBIP). The comparison will be based on implementations on the Quirk simulator, and on the IBM Q Experi- ence processors, from the point of view of performance, robustness (noise immunity), deterioration of the outcomes due to decoherence, and technical viability. Keywords Flexible representation of quantum images · Generalized quantum image representation · Multi-channel representation for quantum images · Novel enhanced quantum representation · Quantum Boolean image processing · Quantum image processing Introduction Since its inception nearly 2 decades ago, Quantum Image Processing (QImP) has always dealt with the same problem, i.e., the internal representation of a digital image inside a quantum circuit efciently, where such circuits can be opti- cal or of superconductors. In the case of superconducting quantum platforms, they are freely available to the entire scientifc community for approximately 5 years, which has allowed testing the diferent techniques for the internal rep- resentation of an image on a real physical machine without the need for theoretical speculations. However, during the last 5 years, we have witnessed a complete absence of such implementations. There are few examples of them tested on simulators [1, 2] like Qiskit of IBM Q Experience [3] in which the quantum processing units (QPU) from the same company are unused when both options are equally avail- able to the general community. Simultaneously, few other works are illustrated in example [4], where the implementa- tion of QPUs are shown forcefully on QPUs from diferent companies [3, 5], with the problems of various techniques of internal image representation even on simulators [3, 5–8]. From all the accumulated experience in Quantum Infor- mation Processing, the scientifc community knows that the problem with simulators is that they represent a necessary but not sufcient condition, i.e., if something works in a simulator, e.g., Qiskit, it still needs to be tested on a QPU, but if something does not work in a simulator then do not even bother to move to the QPU because it evident that our quantum algorithm under test has problems. Something similar happens with standard versus premium [3] QPUs, where the latter has less decoherence than the former and is generally not as freely accessible as the former. Henceforth, if we carry out implementation on a standard QPU with a notable presence of decoherence and the outcomes are not exact then we can associate such inaccuracy with the afore- mentioned decoherence, but if the implementation is done on a premium QPU with low decoherence and the results are still inaccurate then we conclude saying the problem persist with our quantum algorithm. Conversely, we focus on below two queries when appeared with any technique of internal representation of a digital image inside a QPU: 1. Does this constitute a true Classical-to-Quantum (Cl2Qu) interface? * Mario Mastriani mmastria@fu.edu 1 Knight Foundation School of Computing and Information Sciences, Florida International University, 11200 S.W. 8th Street, Miami, FL 33199, USA