Rotation of bits: a classical and quantum perspective

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.

Open quantum systems and thermal non-equilibrium processes

In this paper, we investigate the effects of convexity and concavity of states on entanglement of the system under thermal non-equilibrium condition. In this regard, we consider a system consisting of two spin 1/2 particles with Dzyaloshinskii–Moriya (DM) interaction that follows the Tsallis statistics.Also, according to the desired statistics, the effect of environment parameters and the convexity or concavity of the input states on the output behavior of the SWAP gate is obtained.

A method of mapping and nearest neighbor optimization for 2-D quantum circuits

In some practical quantum physical architectures, the qubits need to be distributed on 2-dimensional (2-D) grid structure to implement quantum computation. In order to map an 1-dimensional (1-D) quantum circuit into a 2-D grid structure and satisfy the nearest neighbor constraint of qubit interaction in the grid structure, a mapping method from 1-D quantum circuit to 2-D grid structure is proposed in this paper. This method firstly determines the order of placing qubits, and then presents the layout strategy of qubits in 2-D grid. We also proposed an algorithm for establishing interaction paths between non-adjacent qubits in 2-D grid structure, which can satisfy the physical constraints of the interaction of quantum bits in the grid in the process of mapping an 1-D quantum circuit to a 2-D grid structure. For some benchmark circuits, after using the method of this paper to place qubits, it is possible to make every 2-qubit gate in the circuit have a nearest neighbor, so that there is no need to use SWAP gate to establish channel routing. Compared with the latest available methods, the average optimization rate is 82.38%.