Bilaterally Symmetrical Transformation between Independent Operators and Rotations

This report describes an approach for representation of quantum operators through rotations and rotation through quantum operators. The approach of the proposed method transforms rotation in a kind of a unitary matrix that corresponds to the rotation. Operations with qubits are very similar to the rotation, but with an added phase coefficient. This fact is used to create a process for rotation between unitary matrices. This approach could be used to modifying the controls to apply in a different basis.

Formalized Operators with Phase Encoding

In this article the concept of phase encoding/decoding is used to analyze and formalize a simple quantum algorithm—the Deutsch’s algorithm. The algorithm is formalized in two different ways through an analysis, based on phase encoding/decoding, carried out by the formalized elementary operators developed by the author of this article. Concrete examples of different possible realizations of the formalized with Raychev’s operators Deutsch’s algorithms are offered.

Computational Cluster with Entangled States

In this article the inherent computational power of the quantum entangled cluster states examined by measurement-based quantum computations is studied. By defining a common framework of rules for measurement of quantum entangled cluster states based on classical computations, the precise and detailed meaning of the computing power of the correlations in the quantum cluster states is made. This study exposes a connection, arousing interest, between the infringement of the realistic models that are local and the computing power of the quantum entangled cluster states.

Fundamental Limit for Universal Entanglement Detection

The entanglement, one of the central mysteries of the quantum mechanics, plays a significant role in a variety of applications of the quantum information theory. A natural question in theoretical and experimental importance is whether it is possible to detect a universal entanglement without full diagnostics. The diagnostics relies on a set of quantum trajectories and their records from measurements. This model reflects the probability that each of the measurements may be damaged from interference and decoherence, and may also be associated with recording of continuous signals for an end-time period. The goal is then to retrieve the quantum state such as it had been in the beginning of this measurement process. The proposed solution relies on explicit expression of the probability function through effective matrices contained in the quantum approximation and solutions of ad-joint quantum filters. In this article, we prove а no-go theorem, which outlines this possibility for non-adaptive schemes, which use only single-copy measurements. We also examine in detail а previously conducted experiment, for which it is claimed that detects the entanglement of two-qubit states through adaptive single-copy measurements without full diagnostics. With the conduct of the experiment and the analysis of the data, we demonstrate that the information collected is really sufficient to reconstruct the state. These results reveal a fundamental limit of the single-copy measurements upon the entanglement detection, and provide a common framework for learning the detection of other interesting properties of the quantum states, such as the positivity of partial transposition and the k-symmetric-extendibility.

Interactive Quantum Development Environment (IQDE)

This report presents a second version of the Interactive Quantum Development Environment (IQDE), virtualized parallel simulation platform for optimized testing of quantum software. IQDE is an interactive quantum simulator intended for implementation of a classical computer that can simulate numerous controlled and time-dependent operations. The research presents different relations between the operations that can be typically simulated. The virtualized simulation platform carries out numerous single-node and multi-node optimizations, including vectorization, parallelization, cache sharing, as well as overlapping of the computations with the communication. A common strategy for modeling for shared memory is implemented, as well as realistic parallel simulation with cluster management of the parallelization. А detailed analysis of the implementation is performed in order to be demonstrated that the simulator achieves good operation and high efficiency of the hardware, which is only limited by the available memory and the bandwidth of the machine.

Formalized Quantum Model for Solving the Eigenfunctions

This report describes a fundamental model of a quantum circuit for finding complex eigenvalues of Hamiltonian matrices on the quantum computers through the use of an iteration algorithm for estimation of the phase. In addition to this, we demonstrate the use of the model for simulating the resonant states for quantum systems.