[PDF] Top 20 Tensor Network Representation of Many-Body Quantum States and Unitary Operators

... into many directions, such as Symmetry Enriched Topological phases[22], SPT with n-form symmetries ...a quantum-many body system is the pattern of entanglement individual constituents of the ... See full document

... for quantum supremacy because it inherently increases the depth of the ...the quantum chaotic state for models involving a far greater number of qubits than those constructed with aggregated ... See full document

... are used, as we do here), so through the SVD we are able to compress the state quite efficiently beyond what we initially might expect. 2.5 Conclusion We have presented an efficient, numerically stable, and controllably ... See full document

... case. Quantum trajectory techniques, in contrast, carry a computational cost (assuming the single sample evolution relies on a matrix product state Ansatz with bond dimension ˆD) of the order Oðηd 4 ˆD 2 Þþ Oðηd 3 ... See full document

... generic many-body quantum systems which are hard to access with other ...chiral states in two dimensions are hard to represent by tensor networks, but can be captured by RBM ... See full document

... In the TTN setting, instead, the update step directly replaces two adjacent tensors with a matrix A associated to the lowest eigenvector of an effective Hamiltonian. The matrix A is at most a χ 2 -by-χ 2 square matrix. ... See full document

... a quantum many-body system can be defined by a Hilbert space H and a Hamiltonian H describing the evolution of states in ...23 states for just a single mole of, ...ground states ... See full document

... matrix representation, the matrix dimension D has to be increased in order to allow for classical correlations to be represented as well as quantum ...matrix representation presented in section IV ... See full document

... of quantum gauge theories comes from Monte Carlo sampling of the path integral corresponding to Wilson’s lattice gauge the- ory (LGT) formulation ...and tensor network ap- proaches [15–23]. The ... See full document

... Hermitian operators, i.e., all possible combinations of the tensor product of two Pauli ...initial states for ρ ij , we can uniquely determine the matrix elements c αβ (t), from which we can finally ... See full document

... of tensor networks were introduced in the context of an MPS-based DMRG ...most tensor network papers and talks was introduced and utilised ...in tensor network algorithms, were ... See full document

... dispersion relations of the quasiparticles. In particular, one lesson from our study is that the conformal field theories cannot be used to described such properties of short-range models at finite temperatures. Lastly, ... See full document

... of unitary space and provide examples of operators in the unitary space, with special attention to unitary ...those operators. In the third chapter we will define unitary ... See full document

... of quantum chaos in all three representations of the quantum ...identifying quantum chaotic dynamics more generally, whereas RMT is limited in small and large systems or rapidly becomes misleading ... See full document

... interacting many-body states, ranging from paired states of fermions to topological ...with many open questions, ranging from specific questions such as the effect of spontaneous ... See full document

... 1.1.4 Many-body models and computation One of the primary motivations to study the exotic materials considered in this thesis is their potential use as platforms for quantum ...of ... See full document

... Chapter 5 Discussion and Outlook In Chapters 2 and 3 we showed numerical evidence that ergodic systems generically heat-up to infinite temperature with periodic driving, whereas many-body localized systems ... See full document

... pure quantum systems to be entangled with each other. Quantum comparison may be used in quantum information applications, and here one often benefits from ...entangled states in order to ... See full document

... reconstruction error due to the finite number of measurements. Results of this simulation are shown in FIG. S3 for N ∈ {8, 20, 32, 48, 64} spins. The left part of the figure shows that the estimation error decreases ... See full document

... uous support and encouragement during my Ph.D. studies. Many thanks to Xie for taking me into the exciting areas of condensed matter theory and quantum informa- tion science. Xie always inspires me with her ... See full document