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Authors develop new nonparametric methods for verification and monitoring for quantum randomness based on the ranged correlation function (RCF) and a sequence of the ranged amplitudes (SRA). We carried out RCF-analysis of different topology subsamples from raw data of the prototype of a quantum random number generator on homodyne detection. It is shown that in the real system there are weak local regression relations, for which it is possible to introduce a robust criterion of significance, and also precise SRA-identification of long samples statistics is made. The obtained results extend the traditional entropy methods of the useful randomness analysis and open the way for creation of new strict quality quantum standards and defense for physical random numbers generators.

Single-photon detectors based on avalanche photodiodes (SPAD) are key elements of many modern highly sensitive optical systems. One of the bottlenecks of such detectors is a afterpulsing effect which limits a detection rate and requires an optimal hold-off time. In this letter we propose a novel approach for statistical analysis of SPAD dark counts and we demonstrate its usefulness for the search of the experimental condition where the afterpulsing effect can be strongly eliminated. This approach exploits a sequence of ranked time intervals between the dark counts and does not contain a complex mathematical analysis of the experimental data. We show that the approach can be efficiently applied for a small number of the dark counts and it seems to be very beneficial for practical characterization of SPAD devices.

A quantitative assessment of the progress of small prototype quantum processors towards fault-tolerant quantum computation is a problem of current interest in experimental and theoretical quantum information science. We introduce a necessary and fair criterion for quantum error correction (QEC), which must be achieved in the development of these quantum processors before their sizes are sufficiently big to consider the well-known QEC threshold. We apply this criterion to benchmark the ongoing effort in implementing QEC with topological color codes using trapped-ion quantum processors and, more importantly, to guide the future hardware developments that shall be required in order to demonstrate beneficial QEC with small topological quantum codes. In doing so, we present a thorough description of a realistic trapped-ion toolbox for QEC, and a physically-motivated error model that goes beyond standard simplifications in the QEC literature. Our large-scale numerical analysis shows that two-species trapped-ion crystals in high-optical aperture segmented traps, with the improvements hereby described, are a very promising candidate for fault-tolerant quantum computation.

When traversing a symmetry breaking second order phase transition at a finite rate, topological defects form whose number dependence on the quench rate is given by simple power laws. We propose a general approach for the derivation of such scaling laws that is based on the analytical transformation of the associated equations of motion to a universal form rather than employing plausible physical arguments. We demonstrate the power of this approach by deriving the scaling of the number of topological defects in both homogenous and non-homogenous settings. The general nature and extensions of this approach is discussed., Comment: 4 pages

Traversal of a symmetry-breaking phase transition at a finite rate can lead to causallyseparated regions with incompatible symmetries and the formation of defects at their boundaries. The defect formation follows universal scaling laws prescribed by the Kibble-Zurek mechanism (KZM) important to the study of phase transitions in fields as diverse as quantum and statistical mechanics, condensed matter physics and cosmology. Here, we observe the KZM in a crystal of cold trapped ions, which is conducive to the precise control of structural phases and the detection of defects. The experiment confirms a scaling law with an exponent of 2.68 +/- 0.06, as predicted from the KZM in the finite inhomogeneous case. Such precision makes it feasible to use ion crystals for quantitative tests of classical and quantum statistical mechanics.

We suggest a new method of calculation of the equilibrium correlation functions of an arbitrary order for the interacting Fermi-gas model in the frame of the static fluctuation approximation (SFA) method. This method based only on the single and controllable approximation allows to obtain the so-called far-distance equations (FDEs). These equations connecting the quantum states of a Fermi particle with variables of the local field operator contains all necessary information related to calculation of the desired correlation functions and basic thermodynamic parameters of the many-body system considered. The basic expressions for the mean energy and heat capacity for electron gas at low temperatures in the limit of high density were obtained. All expressions are given in the units of r_s,where r_s determines the ratio of a mean distance between electrons to the Bohr radius a_0. In these expressions we calculated the terms of the order r_s and r_s^2, correspondingly. It was shown also that the SFA allows to find the terms related with high orders of the decomposition with respect to the parameter r_s., Comment: 22 pages, 5 figures

The implementation of fault-tolerant quantum gates on encoded logic qubits is considered. It is shown that transversal implementation of logic gates based on simple geometric control ideas is problematic for realistic physical systems suffering from imperfections such as qubit inhomogeneity or uncontrollable interactions between qubits. However, this problem can be overcome by formulating the task as an optimal control problem and designing efficient algorithms to solve it. In particular, we can find solutions that implement all of the elementary logic gates in a fixed amount of time with limited control resources for the five-qubit stabilizer code. Most importantly, logic gates that are extremely difficult to implement using conventional techniques even for ideal systems, such as the T-gate for the five-qubit stabilizer code, do not appear to pose a problem for optimal control., Comment: 18 pages, ioptex, many figures

The energy spectrum of eigenvalues of the equal spin-spin interactions (ESSI) Hamiltonian has been found. The obtained spectrum is free from limitations imposed on number of spins and parameters of the ESSI Hamiltonian. This model can be used for consideration of spin dynamics of mesoscopic systems and molecules with large number of nuclei spins.