1,721,167 research outputs found
Introduction to Tensor Network Methods
No full textThis volume of lecture notes briefly introduces the basic concepts needed in any computational physics course: software and hardware, programming skills, linear algebra, and differential calculus. It then presents more advanced numerical methods to tackle the quantum many-body problem: it reviews the numerical renormalization group and then focuses on tensor network methods, from basic concepts to gauge invariant ones. Finally, in the last part, the author presents some applications of tensor network methods to equilibrium and out-of-equilibrium correlated quantum matter.
The book can be used for a graduate computational physics course. After successfully completing such a course, a student should be able to write a tensor network program and can begin to explore the physics of many-body quantum systems. The book can also serve as a reference for researchers working or starting out in the field
Dynamically localized systems: Exponential sensitivity of entanglement and efficient quantum simulations
No full textMethod for analyzing web space data
No full textA method for analyzing data from the web that determine the importance that a chosen subject has in society, e.g., subject matter relating a concert, a scientific discovery, a football match, a person, a corporation, a brand, or a car, and analyze such data that can represent the entire society better than the known techniques. The method according to the invention can avoid malicious alterations and is able to measure and detect the temporal relations among all the web resources that talk about a particular topic or subject matter
Multipartite entanglement generation and fidelity decay in disordered qubit systems
Full text linkWe investigate multipartite entanglement dynamics in disordered spin-1∕2 lattice models exhibiting a transition from integrability to quantum chaos. Borrowing from the generalized entanglement framework, we construct measures for correlations relative to arbitrary local and bilocal spin observables, and show how they naturally signal the crossover between distinct dynamical regimes. Analytical estimates are obtained in the short- and long-time limits. Our results are in qualitative agreement with predictions from the random matrix theory and are relevant to both condensed-matter physics and to the stability of quantum information in disordered quantum computing hardware
Phase diagram and conformal string excitations of square ice using gauge invariant matrix product states
Full text linkWe investigate the ground state phase diagram of square ice — a U(1)
lattice gauge theory in two spatial dimensions — using gauge invariant
tensor network techniques. By correlation function, Wilson loop, and
entanglement diagnostics, we characterize its phases and the transitions
between them, finding good agreement with previous studies. We study the
entanglement properties of string excitations on top of the ground
state, and provide direct evidence of the fact that the latter are
described by a conformal field theory. Our results pave the way to the
application of tensor network methods to confining, two-dimensional
lattice gauge theories, to investigate their phase diagrams and
low-lying excitations
Is quantum computing green? An estimate for an energy-efficiency quantum advantage
Full text linkThe quantum advantage threshold determines when a quantum processing unit
(QPU) is more efficient with respect to classical computing hardware in terms
of algorithmic complexity. The "green" quantum advantage threshold based on
a comparison of energetic efficiency between the two is going to play a
fundamental role in the comparison between quantum and classical hardware.
Indeed, its characterization would enable better decisions on energy-saving
strategies, e.g. for distributing the workload in hybrid quantum-classical
algorithms. Here, we show that the green quantum advantage threshold crucially
depends on (i) the quality of the experimental quantum gates and (ii) the
entanglement generated in the QPU. Indeed, for NISQ hardware and algorithms
requiring a moderate amount of entanglement, a classical tensor network
emulation can be more energy-efficient at equal final state fidelity than
quantum computation. We compute the green quantum advantage threshold for a few
paradigmatic examples in terms of algorithms and hardware platforms, and
identify algorithms with a power-law decay of singular values of bipartitions
with power-law exponent as the green quantum
advantage threshold in the near future.Comment: 12 pages, 7 figures, 2 table; minor revisions in comparison to v1,
e.g., one additional tabl
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