The key to our discussion is a set of `fixed point' conditions which characterize the form of the matrix product unitary operators after blocking sites. In both cases, the map \( for classifying 1D locality preserving unitaries. In the case of quantum walks, the index is integer-valued, whereas for cellular automata, it takes values in the group of positive rationals. Second, the index labels connected components of such systems: equality of the index is necessary and sufficient for the existence of a continuous deformation of SĢ. First, two systems SĢ can be “pieced together”, in the sense that there is a system S which acts like SĢ have the same index. The index supplies a complete characterization of two properties of the discrete dynamics. For two types of such systems - namely quantum walks and cellular automata - we make this intuition precise by defining an index, a quantity that measures the “net flow of quantum information” through the system. If a one-dimensional quantum lattice system is subject to one step of a reversible discrete-time dynamics, it is intuitive that as much “quantum information” as moves into any given block of cells from the left, has to exit that block to the right. Some parallels with the free fermion Floquet topological phases are discussed, and possible experimental implementations are mentioned. We explicitly compute this index for specific models, and show that the nontrivial topology leads to edge thermalization, which provides an interesting link between bulk topology and chaos at the edge. Surprisingly, we show that they are classified by a quantized index, taking the form of the logarithm of a rational number, which can be related to the flow of quantum information. These chiral phases do not require any symmetry, and in fact owe their existence to the absence of energy conservation in driven systems. The construction proceeds by introducing exactly soluble models with chiral edges, which in the presence of many body localization in the bulk are argued to lead to stable chiral phases. We construct and classify chiral topological phases in driven (Floquet) systems of strongly interacting bosons, with finite-dimensional site Hilbert spaces, in two spatial dimensions. Finally, we give several examples of MPU possessing different symmetries. ![]() In the first case, we give a full characterization of all equivalence classes. In particular, we characterize the tensors corresponding to MPU that are invariant under conjugation, time reversal, or transposition. We also discuss the effect of symmetries on the MPU classification. We use this canonical form to prove an Index Theorem for MPUs which gives the precise conditions under which two MPUs are adiabatically connected, providing an alternative derivation to that of for QCAs. We prove that all MPUs have a strict causal cone, making them Quantum Cellular Automata (QCAs), and derive a canonical form for MPUs which relates different MPU representations of the same unitary through a local gauge. in the description of time evolutions of one-dimensional systems. In this work, we develop the structure theory of Matrix Product Unitary operators (MPUs) which appear e.g. Because the item is digital file that can not be returned once download, there are no returns, exchanges or refunds.Matrix Product Vectors form the appropriate framework to study and classify one-dimensional quantum systems. Actual colors may vary slightly due to different color monitors. For help with digital downloads, please see the etsy help article: You are purchasing the Digital File only. ![]() ![]() You can feel free to contact us before purchasing to make sure the desired size is available. If you need a specific size, we can resize the files for you for no extra charge. 5x7 Ratio file for printing on international paper size: A5, A4, A3, A2, A1 ![]() 11x14 Ratio file for printing on 11x14 inchesĥ. You can choose the size that matches your need.ġ. You will receive 5 HIGH RESOLUTION JPG files at 300 dpi (pixels per inch). Very easy to download and print! You can print if from your home computer or at your local print shop. This is an instant DIGITAL DOWNLOAD wall art printable. Napoleon Crossing the Alps Pixel Art, Printable Wall Art, Pixelated Famous Art, 8 Bit, Historical Print, Vintage Poster, Digital Downloads JPG JPEG
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