| 1. |
- Sotnikov, O. M., et al.
(författare)
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Certification of quantum states with hidden structure of their bitstrings
- 2022
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Ingår i: NPJ QUANTUM INFORMATION. - : Springer Nature. - 2056-6387. ; 8:1
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Tidskriftsartikel (refereegranskat)abstract
- The rapid development of quantum computing technologies already made it possible to manipulate a collective state of several dozens of qubits, which poses a strong demand on efficient methods for characterization and verification of large-scale quantum states. Here, we propose a numerically cheap procedure to distinguish quantum states which is based on a limited number of projective measurements in at least two different bases and computing inter-scale dissimilarities of the resulting bit-string patterns via coarse-graining. The information one obtains through this procedure can be viewed as a 'hash function' of quantum state-a simple set of numbers which is specific for a concrete wave function and can be used for certification. We show that it is enough to characterize quantum states with different structure of entanglement, including the chaotic quantum states. Our approach can also be employed to detect phase transitions in quantum magnetic systems.
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| 2. |
- Bagrov, Andrey A., et al.
(författare)
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Multiscale structural complexity of natural patterns
- 2020
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Ingår i: Proceedings of the National Academy of Sciences of the United States of America. - : NATL ACAD SCIENCES. - 0027-8424 .- 1091-6490. ; 117:48, s. 30241-30251
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Tidskriftsartikel (refereegranskat)abstract
- Complexity of patterns is key information for human brain to differ objects of about the same size and shape. Like other innate human senses, the complexity perception cannot be easily quantified. We propose a transparent and universal machine method for estimating structural (effective) complexity of two-dimensional and three-dimensional patterns that can be straightforwardly generalized onto other classes of objects. It is based on multistep renormalization of the pattern of interest and computing the overlap between neighboring renormalized layers. This way, we can define a single number characterizing the structural complexity of an object. We apply this definition to quantify complexity of various magnetic patterns and demonstrate that not only does it reflect the intuitive feeling of what is "complex" and what is "simple" but also, can be used to accurately detect different phase transitions and gain information about dynamics of nonequilibrium systems. When employed for that, the proposed scheme is much simpler and numerically cheaper than the standard methods based on computing correlation functions or using machine learning techniques.
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| 3. |
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| 4. |
- Ageev, Dmitry S., et al.
(författare)
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Coleman-Weinberg potential in p-adic field theory
- 2020
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Ingår i: European Physical Journal C. - : SPRINGER. - 1434-6044 .- 1434-6052. ; 80:9
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we study lambda phi(4) scalar field theory defined on the unramified extension of p-adic numbers Q(pn). For different "space-time" dimensions n, we compute one-loop quantum corrections to the effective potential. Surprisingly, despite the unusual properties of non-Archimedean geometry, the Coleman-Weinberg potential of p-adic field theory has structure very similar to that of its real cousin. We also study two formal limits of the effective potential, p -> 1 and p -> infinity. We show that the p -> 1 limit allows to reconstruct the canonical result for real field theory from the p-adic effective potential and provide an explanation of this fact. On the other hand, in the p -> infinity limit, the theory exhibits very peculiar behavior with emerging logarithmic terms in the effective potential, which has no analogue in real theories.
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| 5. |
- Ageev, Dmitry S., et al.
(författare)
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Deterministic chaos and fractal entropy scaling in Floquet conformal field theories
- 2021
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Ingår i: Physical Review B. - : American Physical Society. - 2469-9950 .- 2469-9969. ; 103:10
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Tidskriftsartikel (refereegranskat)abstract
- In this Letter, we study two-dimensional Floquet conformal field theory, where the external periodic driving is described by iterated logistic or tent maps. These maps are known to be typical examples of dynamical systems exhibiting the order-chaos transition, and we show that, as a result of such driving, the entanglement entropy scaling develops fractal features when the corresponding dynamical system approaches the chaotic regime. For the driving set by the logistic map, the fractal contribution to the scaling dominates, making entanglement entropy a highly oscillating function of the subsystem size.
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| 6. |
- Bagrov, Andrey A., et al.
(författare)
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Kinetic samplers for neural quantum states
- 2021
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Ingår i: Physical Review B. - : American Physical Society. - 2469-9950 .- 2469-9969. ; 104:10
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Tidskriftsartikel (refereegranskat)abstract
- Neural quantum states are a recently introduced class of variational many-body wave functions that are very flexible in approximating diverse quantum states. Optimization of an NQS ansatz requires sampling from the corresponding probability distribution defined by squared wave function amplitude. For this purpose, we propose to use kinetic sampling protocols and demonstrate that in many important cases such methods lead to much smaller autocorrelation times than the Metropolis-Hastings sampling algorithm while still allowing to easily implement lattice symmetries (unlike autoregressive models). We also use uniform manifold approximation and projection algorithm to construct two-dimensional isometric embedding of Markov chains and show that kinetic sampling helps attain a more homogeneous and ergodic coverage of the Hilbert space basis.
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| 7. |
- Iliasov, Askar, et al.
(författare)
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Anisotropic destruction of the Fermi surface in inhomogeneous holographic lattices
- 2020
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Ingår i: Journal of High Energy Physics (JHEP). - 1126-6708 .- 1029-8479. ; :1
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Tidskriftsartikel (refereegranskat)abstract
- We analyze fermionic response of strongly correlated holographic matter in presence of inhomogeneous periodically modulated potential mimicking the crystal lattice. The modulation is sourced by a scalar operator that explicitly breaks the translational symmetry in one direction. We compute the fermion spectral function and show that it either exhibits a well defined Fermi surface with umklapp gaps opening on the Brillouin zone boundary at small lattice wave vector, or, when the wave vector is large, the Fermi surface is anisotropically deformed and the quasiparticles get significantly broadened in the direction of translation symmetry breaking. Making use of the ability of our model to smoothly extrapolate to the homogeneous Q-lattice like setup, we show that this novel effect is not due to the periodic modulation of the potential and Umklapp physics, but rather due to the anisotropic features of the holographic horizon. That means it encodes novel physics of strongly correlated critical systems which may be relevant for phenomenology of exotic states of electron matter.
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