Related papers: Statistical properties of random matrix product st…
I introduce a Markov chain Monte Carlo (MCMC) scheme in which sampling from a distribution with density pi(x) is done using updates operating on an "ensemble" of states. The current state x is first stochastically mapped to an ensemble,…
Quantum state tomography via local measurements is an efficient tool for characterizing quantum states. However it requires that the original global state be uniquely determined (UD) by its local reduced density matrices (RDMs). In this…
Over the last decade tensor network states (TNS) have emerged as a powerful tool for the study of quantum many body systems. The matrix product states (MPS) are one particular case of TNS and are used for the simulation of 1+1 dimensional…
Wilson's numerical renormalization group (NRG) method for solving quantum impurity models yields a set of energy eigenstates that have the form of matrix product states (MPS). White's density matrix renormalization group (DMRG) for treating…
Tensor networks like matrix product states (MPSs) and matrix product operators (MPOs) are powerful tools for representing exponentially large states and operators, with applications in quantum many-body physics, machine learning, numerical…
Sampling problems have emerged as a central avenue for demonstrating quantum advantage on noisy intermediate-scale quantum devices. However, physical noise can fundamentally alter their computational complexity, often making them…
(Please refer to arXiv:1810.08050, which has completely different aims but contains all the main contents of this paper) In this work, we propose to access the information of criticality and excitations of one-dimensional quantum systems by…
A standard approach to generate random pure quantum states relies on sampling from the Haar measure. However, the entanglement properties of such states present a fundamental challenge for their general applicability. Here, we introduce the…
This paper presents a method for calculating steady state probabilities of $M|E_r|c|K$ queueing systems. The infinitesimal generator matrix is used to define all possible states in the system and their transition probabilities. While this…
I present here some results on the statistical behaviour of large random matrices in an ensemble where the probability distribution is not a function of the eigenvalues only. The perturbative expansion can be cast in a closed form and the…
Matrix Product States (MPS) are used for the simulation of the real-time dynamics induced by an electric quench on the vacuum state of the massive Schwinger model. For small quenches it is found that the obtained oscillatory behavior of…
A system composed of identical spins and described by a quantum mechanical pure state is analyzed within the statistical framework presented in Part I of this work. We explicitly derive the typical values of the entropy, of the energy, and…
It has been recently shown that a state generated by a one-dimensional noisy quantum computer is well approximated by a matrix product operator with a finite bond dimension independent of the number of qubits. We show that full quantum…
To every product of $2\times2$ matrices, there corresponds a one-dimensional Schr\"{o}dinger equation whose potential consists of generalised point scatterers. Products of {\em random} matrices are obtained by making these interactions and…
The classical Gaussian ensembles of random matrices can be constructed by maximizing Boltzmann-Gibbs-Shannon's entropy, S_{BGS} = - \int d{\bf H} [P({\bf H})] \ln [P({\bf H})], with suitable constraints. Here we construct and analyze…
A key challenge for quantum computers is the efficient preparation of many-body entangled states across many qubits. In this work, we demonstrate the preparation of matrix product states (MPS) using a renormalization-group(RG)-based quantum…
We show how to efficiently simulate pure quantum states in one dimensional systems that have both finite energy density and vanishingly small energy fluctuations. We do so by studying the performance of a tensor network algorithm that…
We present an implementation of an efficient algorithm for the calculation of the spectrum of one-dimensional quantum systems with periodic boundary conditions. This algorithm is based on a matrix product representation for quantum states…
The Gram matrix of a set of quantum pure states plays key roles in quantum information theory. It has been highlighted that the Gram matrix of a pure-state ensemble can be viewed as a quantum state, and the quantumness of a pure-state…
When working with quantum states, analysis of the final quantum state generated through probabilistic measurements is essential. This analysis is typically conducted by constructing the density matrix from either partial or full tomography…