Abstract Bit rotation is an operation similar to shift except that the bits that fall off at one end are put back to the other end. In left rotation, the bits that fall off at left end are put back at right end. In right rotation, the bits that fall off at the right end are put back at the left end. Applications of bit rotation include; registers, cryptography, computing with a single bit string circularly shifted to the right or left based on some position but no work has been done with respect to shifting the bits one position at a time generating emergent bit strings equal to the number of bits-1 from the incident bit string, and then recombining or extracting bit(s) from each of the bit strings or words to form back the incident bit string. In this article, the authors present a new approach of rotating classical bit strings known as CRotate. A quantum approach to bit rotation known as QRotate is presented as well. The quantum perspective uses the concept of bit swapping by avenue of the quantum swap gate in jsqubits. Models and algorithms are duly presented.
Abstract Bit rotation is an operation similar to shift except that the bits that fall off at one end are put back to the other end. In left rotation, the bits that fall off at left end are put back at right end. In right rotation, the bits that fall off at the right end are put back at the left end. Applications of bit rotation include; registers, cryptography, computing with a single bit string circularly shifted to the right or left based on some position but no work has been done with respect to shifting the bits one position at a time generating emergent bit strings equal to the number of bits-1 from the incident bit string, and then recombining or extracting bit(s) from each of the bit strings or words to form back the incident bit string. In this article, the authors present a new approach of rotating classical bit strings known as CRotate. A quantum approach to bit rotation known as QRotate is presented as well. The quantum perspective uses the concept of bit swapping by avenue of the quantum swap gate in jsqubits. Models and algorithms are duly presented.
Abstract A circular shift operator (or cyclic rotation gate) ROTk ROT k applies a rightward (or leftward) shift to an input register of n qubits o by as many positions as encoded by an additional input k∈N k ∈ N . Specifically, the qubit at position x is moved to position (x+k)modn ( x + k ) mod n . While it is known that there exists a quantum rotation operator that can be implemented in O(log(n)) O ( log ( n ) ) -time, through the repeated parallel application of the elementary Swap Swap operators, there is no systematic procedure that concretely constructs the quantum operator ROT ROT for variable size n of the quantum register and a variable parameter k. We fill the gap, providing a systematic implementation of the cyclic rotation operator (denoted ROT ROT ) in a quantum circuit model of computation whose depth is O(log(n)) O ( log ( n ) ) . We show how the circular shift operator can be utilized in quantum approaches to text processing, focusing on the problem of getting all possible cyclic rotations of a string in O(log2(n)) O ( log 2 ( n ) ) depth.
Digital computers are based on devices that can take on only two states, one of which is denoted by 0 and the other by 1. By concatenating several 0s and is together, 0-1 combinations can be formed to represent as many different entities as desired. A combination containing a single 0 or 1 is called a bit. In general, n bits can be used to distinguish among 2 n distinct entities and each addition of a bit doubles the number of possible combinations. Computers use strings of bits to represent numbers, letters, punctuation marks, and any other useful pieces of information. In a classical computer, the processing of information is done by logic gate. A logic gate maps the state of its input bits into another state according to a truth table. Quantum computers require quantum logic, something fundamentally different to classical Boolean logic. This difference leads to a greater efficiency of quantum computation over its classical counterpart. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This chapter represents our first step into quantum information theory (QIT). The key to operating such a transition is to become familiar with the concept of the quantum bit, or qubit , which is a probabilistic superposition of the classical 0 and 1 bits. In the quantum world, the classical 0 and 1 bits become the pure states |0〉 and |1〉, respectively. It is as if a coin can be classically in either heads or tails states, but is now allowed to exist in a superposition of both! Then I show that qubits can be physically transformed by the action of unitary matrices , which are also called operators . I show that such qubit transformations, resulting from any qubit manipulation, can be described by rotations on a 2D surface, which is referred to as the Bloch sphere . The Pauli matrices are shown to generate all such unitary transformations. These transformations are reversible , because they are characterized by unitary matrices ; this property always makes it possible to trace the input information carried by qubits. I will then describe different types of elementary quantum computations performed by elementary quantum gates, forming a veritable “zoo” of unitary operators, called I , X , Y , Z , H , CNOT, CCNOT, CROSSOVER or SWAP, controlled- U , and controlled-controlled- U . These gates can be used to form quantum circuits , involving any number of qubits, and of which several examples and tools for analysis are provided. Finally, the concept of tensor product , as progressively introduced through the above description, is eventually formalized.
Abstract We present a bit-string quantum oblivious transfer protocol based on single-qubit rotations. Our protocol is built upon a previously proposed quantum public-key protocol and its practical security relies on the laws of Quantum Mechanics. Practical security is reflected in the fact that, due to technological limitations, the receiver (Bob) of the transferred bit-string is restricted to performing only ‘few-qubit’ coherent measurements. We also present a single-bit oblivious transfer based on the proposed bit-string protocol. The protocol can be implemented with current technology based on optics.
The advent of computers has significantly diminished the need for manual computation. As technology has evolved, it has led to the creation of classical computers with high performance, throughput, and memory capacity. Classical computers store data in binary format, using bits that can either be 0 or 1, typically represented by low and high voltage levels, respectively. While effective, this method sometimes demands considerable resources for certain computations. In contrast, quantum computers represent the cutting edge of computing technology. They utilize quantum bits or qubits, which exploit quantum mechanical phenomena like superposition and entanglement, allowing for more efficient problem-solving. This paper presents a simplified overview of the core concepts of quantum computing.