Related papers: Matrix product operator representations
Quantum simulation is a promising near term application for mesoscale quantum information processors, with the potential to solve computationally intractable problems at the scale of just a few dozen interacting quantum systems. Recent…
Quantum algorithms for simulation of Hamiltonian evolution are often based on product formulae. The fractal methods give a systematic way to find arbitrarily high-order product formulae, but result in a large number of exponentials. On the…
Thus far, sparse representations have been exploited largely in the context of robustly estimating functions in a noisy environment from a few measurements. In this context, the existence of a basis in which the signal class under…
Matrix product states (MPSs) and matrix product operators (MPOs) allow an alternative formulation of the density matrix renormalization group algorithm introduced by White. Here, we describe how non-abelian spin symmetry can be exploited in…
We investigate the power of quantum systems for the simulation of Hamiltonian time evolutions on a cubic lattice under the constraint of translational invariance. Given a set of translationally invariant local Hamiltonians and short range…
Slater determinants are product states of filled quantum fermionic orbitals. When they are expressed in a configuration space basis chosen a priori, their entanglement is bound and controlled. This suggests that an exact representation of…
We study the classical compilation of quantum circuits for the preparation of matrix product states (MPS), which are quantum states of low entanglement with an efficient classical description. Our algorithm represents a near-term…
We propose a tensor-network (TN) approach for solving classical optimization problems that is inspired by spectral filtering and sampling on quantum states. We first shift and scale an Ising Hamiltonian of the cost function so that all…
Algorithms developed to solve many-body quantum problems, like tensor networks, can turn into powerful quantum-inspired tools to tackle problems in the classical domain. In this work, we focus on matrix product operators, a prominent…
Matrix models, as quantum mechanical systems without explicit spatial dependence, provide valuable insights into higher-dimensional gauge and gravitational theories, especially within the framework of string theory, where they can describe…
The study of tensor network theory is an important field and promises a wide range of experimental and quantum information theoretical applications. Matrix product state is the most well-known example of tensor network states, which…
A protocol to obtain the matrix product state representation of a class of boson states is introduced. The proposal is presented in the context of linear systems and is tested by performing simulations of a reference model. The method can…
In stochastic modeling, there has been a significant effort towards finding predictive models that predict a stochastic process' future using minimal information from its past. Meanwhile, in condensed matter physics, matrix product states…
A central primitive in quantum tensor network simulations is the problem of approximating a matrix product state with one of a lower bond dimension. This problem forms the central bottleneck in algorithms for time evolution and for…
We describe quantum many--body systems in terms of projected entangled--pair states, which naturally extend matrix product states to two and more dimensions. We present an algorithm to determine correlation functions in an efficient way. We…
Quantum trajectories and superoperator algorithms implemented within the matrix product state (MPS) framework are powerful tools to simulate the real-time dynamics of open dissipative quantum systems. As for the unitary case, the reachable…
Based on the matrix realignment and partial transpose, we develop an approach to entangling power and operator entanglement of quantum unitary operators. We demonstrate efficiency of the approach by studying several unitary operators on…
We present efficient quantum algorithms for simulating time-dependent Hamiltonian evolution of general input states using an oracular model of a quantum computer. Our algorithms use either constant or adaptively chosen time steps and are…
Simulations of quantum chemistry and quantum materials are believed to be among the most important potential applications of quantum information processors, but realizing practical quantum advantage for such problems is challenging. Here,…
We present a general method for simulating lattice gauge theories in low dimensions using infinite matrix product states (iMPS). A central challenge in Hamiltonian formulations of gauge theories is the unbounded local Hilbert space…