Quantum Arithmetic for Directly Embedded Arrays

We describe a general-purpose framework to implement quantum algorithms relying upon an efficient handling of arrays. The cornerstone of the framework is the direct embedding of information into quantum amplitudes, thus avoiding hampering square roots. We discuss the entire pipeline, from data loading to information extraction. Particular attention is devoted to the definition of an efficient toolkit of basic quantum operations on arrays. We comment on strong and weak points of the proposed quantum manipulations, especially in relation to an effective exploitation of quantum parallelism. We describe in detail some general-purpose routines as well as their embedding in full algorithms. Their efficiency is critically discussed both locally, at the level of the routine, and globally, at the level of the full algorithm. Finally, we comment on some applications in the quantitative finance domain.

Image processing: why quantum?

Quantum Image Processing has exploded in recent years with dozens of papers trying to take advantage of quantum parallelism in order to offer a better alternative to how current computers are dealing with digital images. The vast majority of these papers define or make use of quantum representations based on very large superposition states spanning as many terms as there are pixels in the image they try to represent. While such a representation may apparently offer an advantage in terms of space (number of qubits used) and speed of processing (due to quantum parallelism), it also harbors a fundamental flaw: only one pixel can be recovered from the quantum representation of the entire image, and even that one is obtained non-deterministically through a measurement operation applied on the superposition state. We investigate in detail this measurement bottleneck problem by looking at the number of copies of the quantum representation that are necessary in order to recover various fractions of the original image. The results clearly show that any potential advantage a quantum representation might bring with respect to a classical one is paid for dearly with the huge amount of resources (space and time) required by a quantum approach to image processing.

Improved quantum dilation and erosion operations

To reduce the time complexity of quantum morphology operations, two kinds of improved quantum dilation and erosion operations are proposed. Quantum parallelism is well used in the design of these operations. Consequently, the time complexity is greatly reduced compared with the previous quantum dilation and erosion operations. The neighborhood information of each pixel is needed in the process of designing quantum dilation and erosion operations. In order to get the neighborhood information, quantum position shifting transformation is utilized, which can make the neighborhood information store in a quantum image set. In this image set, the neighborhood information of pixel at location ([Formula: see text], [Formula: see text]) is stored at the same location ([Formula: see text], [Formula: see text]) of other images in the image set. All the pixels will be processed simultaneously, which is the performance of quantum parallelism. The time complexity analysis shows that these quantum operations have polynomial-time complexity which is much lower than the exponential-time complexity of the previous version.

Abstract quantum computing machines and quantum computational logics

Classical and quantum parallelism are deeply different, although it is sometimes claimed that quantum Turing machines are nothing but special examples of classical probabilistic machines. We introduce the concepts of deterministic state machine, classical probabilistic state machine and quantum state machine. On this basis, we discuss the question: To what extent can quantum state machines be simulated by classical probabilistic state machines? Each state machine is devoted to a single task determined by its program. Real computers, however, behave differently, being able to solve different kinds of problems. This capacity can be modeled, in the quantum case, by the mathematical notion of abstract quantum computing machine, whose different programs determine different quantum state machines. The computations of abstract quantum computing machines can be linguistically described by the formulas of a particular form of quantum logic, termed quantum computational logic.

An Enhanced Cloud Security using Quantum Teleportation

In the cloud environment, it is difficult to provide security to the monolithic collection of data as it is easily accessed by breaking the algorithms which are based on mathematical computations and on the other hand, it takes much time for uploading and downloading the data. This paper proposes the concept of implementing quantum teleportation i.e., telecommunication + transportation in the cloud environment for the enhancement of cloud security and also to improve speed of data transfer through the quantum repeaters. This technological idea is extracted from the law of quantum physics where the particles say photons can be entangled and encoded to be teleported over large distances. As the transfer of photons called qubits allowed to travel through the optical fiber, it must be polarized and encoded with QKD (Quantum Key Distribution) for the security purpose. Then, for the enhancement of the data transfer speed, qubits are used in which the state of quantum bits can be encoded as 0 and 1 concurrently using the Shors algorithm. Then, the Quantum parallelism will help qubits to travel as fast as possible to reach the destination at a single communication channel which cannot be eavesdropped at any point because, it prevents from creating copies of transmitted quantum key due to the implementation of no-cloning theorem so that the communication parties can only receive the intended data other than the intruders.