Related papers: Reconstruction of Randomly Sampled Quantum Wavefun…
This paper proposes a novel method for learning highly nonlinear, multivariate functions from examples. Our method takes advantage of the property that continuous functions can be approximated by polynomials, which in turn are representable…
We study the recovery of the underlying graphs or permutations for tensors in the tensor ring or tensor train format. Our proposed algorithms compare the matricization ranks after down-sampling, whose complexity is $O(d\log d)$ for $d$-th…
We study Sigma-Delta quantization methods coupled with appropriate reconstruction algorithms for digitizing randomly sampled low-rank matrices. We show that the reconstruction error associated with our methods decays polynomially with the…
In this paper, we investigate the sample complexity of recovering tensors with low symmetric rank from symmetric rank-one measurements. This setting is particularly motivated by the study of higher-order interactions and the analysis of…
We introduce a change of perspective on tensor network states that is defined by the computational graph of the contraction of an amplitude. The resulting class of states, which we refer to as tensor network functions, inherit the…
We investigate two methods to reconstruct Hamiltonians of quantum matter, using a quantum spin chain to test them. The first method uses correlation functions and the second method uses entanglement spectra. The two methods are not specific…
Quantum state tomography is a key technique for quantum information processing, but is challenging due to the exponential growth of its complexity with the system size. In this work, we propose an algorithm which iteratively finds the best…
We introduce a variational quantum computing approach for quantum state reconstruction within a discretized logical framework, using experimental measurement data as input. By mapping the reconstruction cost function onto an Ising model,…
We adapt the bialgebra and Hopf relations to expose internal structure in the ground state of a Hamiltonian with $Z_2$ topological order. Its tensor network description allows for exact contraction through simple diagrammatic rewrite rules.…
The evaluation of partition functions is a central problem in statistical physics. For lattice systems and other discrete models the partition function may be expressed as the contraction of a tensor network. Unfortunately computing such…
Preparing the ground state of a given Hamiltonian and estimating its ground energy are important but computationally hard tasks. However, given some additional information, these problems can be solved efficiently on a quantum computer. We…
We present efficient circuits that can be used for the phase space tomography of quantum states. The circuits evaluate individual values or selected averages of the Wigner, Kirkwood and Husimi distributions. These quantum gate arrays can be…
Given a tensor network state, how can we determine conserved operators (including Hamiltonians) for which the state is an eigenstate? We answer this question by presenting a method to extract geometrically $k$-local conserved operators that…
We introduce a new notion of entropy for quantum states, called contextual entropy, and show how it unifies Shannon and von Neumann entropy. The main result is that from the knowledge of the contextual entropy of a quantum state of a…
This paper presents an efficient algorithm for robust network reconstruction of Linear Time-Invariant (LTI) systems in the presence of noise, estimation errors and unmodelled nonlinearities. The method here builds on previous work on robust…
The success of tensor network approaches in simulating strongly correlated quantum systems crucially depends on whether the many body states that are relevant for the problem can be encoded in a local tensor network. Despite numerous…
Reconstruction of a quantum state is of prime importance for quantum-information science. Specifically, means of efficient determination of a state of atoms of room-temperature vapor may enable applications in quantum computations and…
An area law is proved for the Renyi entanglement entropy of possibly degenerate ground states in one-dimensional gapped quantum systems. Suppose in a chain of $n$ spins the ground states of a local Hamiltonian with energy gap $\epsilon$ are…
Machine-learning-based variational Monte Carlo simulations are a promising approach for targeting quantum many-body ground states, especially in two dimensions and in cases where the ground state is known to have a non-trivial sign…
Traditional quantum physics solves ground states for a given Hamiltonian, while quantum information science asks for the existence and construction of certain Hamiltonians for given ground states. In practical situations, one would be…