相关论文: The computational complexity of PEPS

We use projected entangled-pair states (PEPS) to calculate the large deviations (LD) statistics of the dynamical activity of the two dimensional East model, and the two dimensional symmetric simple exclusion process (SSEP) with open…

We establish a direct connection between general tensor networks and deep feed-forward artificial neural networks. The core of our results is the construction of neural-network layers that efficiently perform tensor contractions, and that…

We introduce a new paradigm for scaling simulations with projected entangled-pair states (PEPS) for critical strongly-correlated systems, allowing for reliable extrapolations of PEPS data with relatively small bond dimensions $D$. The key…

We present PEPSKit.jl, a Julia package for simulating two-dimensional quantum many-body systems with infinite projected entangled-pair states (iPEPS). PEPSKit.jl builds on the TensorKit.jl package for tensor computations and provides…

Projected entangled pair states (PEPS) provide exact representations for many non-chiral topologically ordered states whereas their range of applicability to interacting chiral topological phases remains largely unsettled. In this context,…

Proving that the parent Hamiltonian of a Projected Entangled Pair State (PEPS) is gapped remains an important open problem. We take a step forward in solving this problem by showing two results: first, we identify an approximate…

An algorithm for imaginary time evolution of a fermionic projected entangled pair state (PEPS) with ancillas from infinite temperature down to a finite temperature state is presented. As a benchmark application, it is applied to spinless…

Fermionic Gaussian Projected Entangled Pair States are fermionic tensor network state constructions which describe the physics of ground states of non-interacting fermionic Hamiltonians. As non-interacting states, one may study and analyze…

This paper introduces a hybrid approach combining Green's function Monte Carlo (GFMC) method with projected entangled pair state (PEPS) ansatz. This hybrid method regards PEPS as a trial state and a guiding wave function in GFMC. By…

An infinite projected entangled-pair state (iPEPS) is a variational tensor network ansatz for 2D wave functions in the thermodynamic limit where the accuracy can be systematically controlled by the bond dimension $D$. We show that for the…

The creation of complex entangled states, resources that enable quantum computation, can be achieved via simple 'probabilistic' operations which are individually likely to fail. However, typical proposals exploiting this idea carry a severe…

Although tensor network states constitute a broad range of exotic quantum states, their realization is challenging and often requires resources whose depth scales with system size. In this work, we explore criteria on the local tensors for…

We determine the computational difficulty of finding ground states of one-dimensional (1D) Hamiltonians which are known to be Matrix Product States (MPS). To this end, we construct a class of 1D frustration free Hamiltonians with unique MPS…

Projected squeezed (PS) states are multipartite entangled states generated by unitary spin squeezing, followed by a collective quantum measurement and post-selection. They can lead to an appreciable decrease in the state preparation time of…

We present and implement an efficient variational method to simulate two-dimensional finite size fermionic quantum systems by fermionic projected entangled pair states. The approach differs from the original one due to the fact that there…

We analyse the use of entangled states to perform quantum computations non locally among distant nodes in a quantum network. The complexity associated with the generation of multiparticle entangled states is quantified in terms of the…

A typical quantum state obeying the area law for entanglement on an infinite 2D lattice can be represented by a tensor network ansatz -- known as an infinite projected entangled pair state (iPEPS) -- with a finite bond dimension $D$. Its…

We investigate the algebraic complexity of tensor calulus. We consider a generalization of iterated matrix product to tensors and show that the resulting formulas exactly capture VP, the class of polynomial families efficiently computable…

Generating ground states of any local Hamiltonians seems to be impossible in quantum polynomial time. In this paper, we give evidence for the impossibility by applying an argument used in the quantum-computational-supremacy approach. More…

Quantum many-body systems are challenging targets for computational physics due to their large degrees of freedom. The tensor networks, particularly Tensor Product States (TPS) and Projected Entangled Pair States (PEPS), effectively…