The discovery of topological order has revised the understanding of quantum matter and provided the theoretical foundation for many quantum error–correcting codes. Realizing topologically ordered ...states has proven to be challenging in both condensed matter and synthetic quantum systems. We prepared the ground state of the toric code Hamiltonian using an efficient quantum circuit on a superconducting quantum processor. We measured a topological entanglement entropy near the expected value of –ln2 and simulated anyon interferometry to extract the braiding statistics of the emergent excitations. Furthermore, we investigated key aspects of the surface code, including logical state injection and the decay of the nonlocal order parameter. Our results demonstrate the potential for quantum processors to provide insights into topological quantum matter and quantum error correction.
Let
be a second-order linear uniformly elliptic operator defined on functions of
variables. We study the set
of solutions of the inequality
with a Neumann type boundary condition
. An estimate of the ...form
, where
is the Nikol’skii space,
is the inner product on
, and
is a nonnegative nonzero function in the Schwartz space
, is established. If
(
) and the sequence
converges to a function
in
, then
and
converges to
in the Sobolev space
, where
.
We study integrally bounded solutions of the differential equation
, where
is a linear differential operator of order
defined on functions
(
) and
is a finite-dimensional Euclidean space). The ...right-hand side
is an integrally bounded function on
ranging in
and satisfying the inequality
,
,
. Conditions are given on the operator
and the function
that guarantee an inverse inequality of the following form for the solutions
under consideration:
where the constant
is independent of the choice of a real number
and function
.
The origin and nature of extreme energy cosmic rays (EECRs), which have energies above the
5
⋅
10
19
eV
—the Greisen-Zatsepin-Kuzmin (GZK) energy limit, is one of the most interesting and complicated ...problems in modern cosmic-ray physics. Existing ground-based detectors have helped to obtain remarkable results in studying cosmic rays before and after the GZK limit, but have also produced some contradictions in our understanding of cosmic ray mass composition. Moreover, each of these detectors covers only a part of the celestial sphere, which poses problems for studying the arrival directions of EECRs and identifying their sources. As a new generation of EECR space detectors, TUS (Tracking Ultraviolet Set-up), KLYPVE and JEM-EUSO, are intended to study the most energetic cosmic-ray particles, providing larger, uniform exposures of the entire celestial sphere. The TUS detector, launched on board the Lomonosov satellite on April 28, 2016 from Vostochny Cosmodrome in Russia, is the first of these. It employs a single-mirror optical system and a photomultiplier tube matrix as a photo-detector and will test the fluorescent method of measuring EECRs from space. Utilizing the Earth’s atmosphere as a huge calorimeter, it is expected to detect EECRs with energies above
10
20
eV
.
It will also be able to register slower atmospheric transient events: atmospheric fluorescence in electrical discharges of various types including precipitating electrons escaping the magnetosphere and from the radiation of meteors passing through the atmosphere. We describe the design of the TUS detector and present results of different ground-based tests and simulations.
Steiner symmetrizations of anisotropic integral functionals of multivariate calculus of variations defined on the set of compactly supported functions in the Sobolev class are studied. Applications ...of the results to embedding theorems for anisotropic Orlicz–Sobolev spaces are outlined, and lower bounds for the values of multidimensional variational problems are found.
Quantum algorithms offer a dramatic speedup for computational problems in material science and chemistry. However, any near-term realizations of these algorithms will need to be optimized to fit ...within the finite resources offered by existing noisy hardware. Here, taking advantage of the adjustable coupling of gmon qubits, we demonstrate a continuous two-qubit gate set that can provide a threefold reduction in circuit depth as compared to a standard decomposition. We implement two gate families: an imaginary swap-like (iSWAP-like) gate to attain an arbitrary swap angle, θ, and a controlled-phase gate that generates an arbitrary conditional phase, ϕ. Using one of each of these gates, we can perform an arbitrary two-qubit gate within the excitation-preserving subspace allowing for a complete implementation of the so-called Fermionic simulation (fSim) gate set. We benchmark the fidelity of the iSWAP-like and controlled-phase gate families as well as 525 other fSim gates spread evenly across the entire fSim (θ, ϕ) parameter space, achieving a purity-limited average two-qubit Pauli error of 3.8 × 10−3 per fSim gate.
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A key step toward demonstrating a quantum system that can address difficult problems in physics and chemistry will be performing a computation beyond the capabilities of any classical computer, thus ...achieving so-called quantum supremacy. In this study, we used nine superconducting qubits to demonstrate a promising path toward quantum supremacy. By individually tuning the qubit parameters, we were able to generate thousands of distinct Hamiltonian evolutions and probe the output probabilities. The measured probabilities obey a universal distribution, consistent with uniformly sampling the full Hilbert space. As the number of qubits increases, the system continues to explore the exponentially growing number of states. Extending these results to a system of 50 qubits has the potential to address scientific questions that are beyond the capabilities of any classical computer.
The article deals with utilizing the method of qualitative assessment of welding zone dynamic resistance based on a Hamming neural network to increase versatility and reliability of computer ...diagnostics for resistance spot welding. We propose a mechanism for encoding information on dynamic resistance into bipolar signals required for the neural network tuning and operation. The algorithm of welding diagnostics was developed and implemented with specialized software. The results of the neural network training and testing are presented. As the analysis shows, the relative error in predicting destruction force does not exceed 10%. The approach proposed in this article complies with the requirements of ISO 9000:2015 standard for continuous monitoring and documentation of each welded connection and allows for increased accuracy of computer diagnostics of welds.
We study a wedge
of solutions of the inequality
, where
is a linear elliptic operator of order
. For the elements of the wedge, we establish an interior estimate of the form
where
is a compact subset ...of
,
is the Nikol’skii space,
is the Lebesgue space of integrable functions, and the constant
is independent of the function
. Similar estimates that hold up to the boundaries are proved for the functions from
satisfying the boundary conditions.
The review focuses on allergen-specific immunotherapy (AIT), a treatment method for atopic diseases, including allergic rhinitis. The theoretical and practical basics, development prospects, ...indications and contraindications to AIT, peculiarities of AIT execution in allergic rhinitis, and tolerogenic effects of immunotherapy are considered. Advantages and disadvantages of each of the two preferable routes of allergen administration in AIT, subcutaneous and sublingual, are described. The main goals of further AIT advancement include shortening of treatment protocols with no significant loss of efficacy, creation of a safer adverse effect profile, and distribution of AIT in developing countries.
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