Related papers: Quantum-Inspired Algorithm for Classical Spin Hami…
Tensor network states and specifically matrix-product states have proven to be a powerful tool for simulating ground states of strongly correlated spin models. Recently, they have also been applied to interacting fermionic problems,…
Matrix Product Operators (MPOs) are at the heart of the second-generation Density Matrix Renormalisation Group (DMRG) algorithm formulated in Matrix Product State language. We first summarise the widely known facts on MPO arithmetic and…
The rapid growth of entanglement under unitary time evolution is the primary bottleneck for modern tensor-network techniques--such as Matrix Product States (MPS)--when computing time-dependent expectation values. This {entanglement barrier}…
Tensor Networks (TN) are approximations of high-dimensional tensors designed to represent locally entangled quantum many-body systems efficiently. This study provides a comprehensive comparison between classical TNs and TN-inspired quantum…
We adopt a two-dimensional tensor-network (TN) ansatz to simulate variational quantum algorithms on two-dimensional qubit architectures, demonstrating its capability to accurately simulate deep circuits through the Quantum Approximate…
Quantum-inspired algorithms can deliver substantial speedups over classical state-of-the-art methods by executing quantum algorithms with tensor networks on conventional hardware. Unlike circuit models restricted to unitary gates, tensor…
We address the problem of implementing bottleneck layers from classical pre-trained neural networks on a quantum computer, with the goal of exploring intrinsically quantum ansatz for representing large linear layers within hybrid…
We recently introduced a method to approximate functions of Hermitian Matrix Product Operators or Tensor Trains that are of the form $\mathsf{Tr} f(A)$. Functions of this type occur in several applications, most notably in quantum physics.…
Proposed hybrid algorithms encode a combinatorial cost function into a problem Hamiltonian and optimize its energy by varying over a set of states with low circuit complexity. Classical processing is typically only used for the choice of…
The Schmidt decomposition is the go-to tool for measuring bipartite entanglement of pure quantum states. Similarly, it is possible to study the entangling features of a quantum operation using its operator-Schmidt, or tensor product…
We propose a hybrid quantum-classical algorithm for approximating the ground state and ground state energy of a Hamiltonian. Once the Ansatz has been decided, the quantum part of the algorithm involves the calculation of two overlap…
Matrix product state has become the algorithm of choice when studying one-dimensional interacting quantum many-body systems, which demonstrates to be able to explore the most relevant portion of the exponentially large quantum Hilbert space…
Compactly representing and efficently applying linear operators are fundamental ingredients in tensor network methods for simulating quantum many-body problems and solving high-dimensional problems in scientific computing. In this work, we…
We perform a comprehensive analysis of the quantum-enhanced Monte Carlo method [Nature, 619, 282-287 (2023)], aimed at identifying the optimal working point of the algorithm. We observe an optimal mixing Hamiltonian strength and analyze the…
In the path integral formulation of the evolution of an open quantum system coupled to a Gaussian, non-interacting environment, the dynamical contribution of the latter is encoded in an object called the influence functional. Here, we…
Tensor-Network (TN) states are efficient parametric representations of ground states of local quantum Hamiltonians extensively used in numerical simulations. Here we encode a TN ansatz state directly into a quantum simulator, which can…
We investigate quantum algorithms derived from tensor networks to simulate the static and dynamic properties of quantum many-body systems. Using a sequentially prepared quantum circuit representation of a matrix product state (MPS) that we…
A pivotal task for quantum computing is to speed up solving problems that are both classically intractable and practically valuable. Among these, combinatorial optimization problems have attracted tremendous attention due to their broad…
We introduce a novel method of efficiently simulating the non-equilibrium steady state of large many-body open quantum systems with highly non-local interactions, based on a variational Monte Carlo optimization of a matrix product operator…
Quantum annealing is a heuristic algorithm for searching the ground state of an Ising model. Heuristic algorithms aim to obtain near-optimal solutions with a reasonable computation time. Accordingly, many algorithms have so far been…