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

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### 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

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### Tensor Network States: Optimizations and Applications in Quantum Many-Body Physics and Machine Learning

... 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

152

### Development of Tensor Network Algorithms for Studying Classical and Quantum Many Body Systems

... 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

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### Positive Tensor Network Approach for Simulating Open Quantum Many-Body Systems

... 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

6

### Symmetries and Many-Body Excitations with Neural-Network Quantum States

... 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

7

### Probabilistic low-rank factorization accelerates tensor network simulations of critical quantum many-body ground states

... 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

10

### Tensor networks and geometry for the modelling of disordered quantum many body systems

... 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

11

### Quantum trajectories and open many-body quantum systems

... 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

66

### Gauging quantum states : from global to local symmetries in many-body systems

... 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

11

### Time evolution of open quantum many-body systems

... 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

7

### Tensor networks and geometry for the modelling of disordered quantum many body systems

... 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

205

### Surviving Quantum Chaos: Weak Thermalization, Prethermalization and Quantum Many Body Scar States

... 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

213

### Unitary Operators

... 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

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### Many-body quantum chaos and entanglement in a quantum ratchet

... 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

6

### Quantum trajectories and open many-body quantum systems

... 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

67

### Tensor Network Methods for Quantum Phases

... 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

212

### Periodically-driven quantum many-body systems, many-body localization and machine learning

... 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

138

### Comparing the states of many quantum systems

... 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

13

### Efficient tomography of a quantum many-body system

... 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

23

### Information Scrambling in Quantum Many-Body Systems

... 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

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