Related papers: Calculus of continuous matrix product states
We show that all zero energy eigenstates of an arbitrary $m$--state quantum spin chain Hamiltonian with nearest neighbor interaction in the bulk and single site boundary terms, which can also describe the dynamics of stochastic models, can…
This paper addresses the problem of checking invariant properties for a large class of symbolic transition systems, defined by a combination of SMT theories and quantifiers. State variables can be functions from an uninterpreted sort…
We present a general variational approach to determine the steady state of open quantum lattice systems via a neural network approach. The steady-state density matrix of the lattice system is constructed via a purified neural network ansatz…
Much progress has been made in the field of quantum computing using continuous variables over the last couple of years. This includes the generation of extremely large entangled cluster states (10,000 modes, in fact) as well as a fault…
The representation of numbers by product states in quantum mechanics can be extended to the representation of words and word sequences in languages by product states. This can be used to study quantum systems that generate text that has…
Generalized symmetries have emerged as a powerful organizing principle for exotic quantum phases. However, their role in open quantum systems, especially for non-invertible cases, remains largely unexplored. We address this by applying a…
The projection of time-dependent variational principle (TDVP) for matrix product states enables us to perform long-time simulations of one-dimensional quantum systems with the conservation of the total energy and the norm of wave functions.…
In this paper we apply the formalism of translation invariant (continuous) matrix product states in the thermodynamic limit to $(1+1)$ dimensional critical models. Finite bond dimension bounds the entanglement entropy and introduces an…
Motivated by studies of typical properties of quantum states in statistical mechanics, we introduce phase-random states, an ensemble of pure states with fixed amplitudes and uniformly distributed phases in a fixed basis. We first show that…
A causal input-output system may be described by a function space for inputs, a function space for outputs, and a causal operator mapping the input space into the output space. A particular representation of the state of such a system at…
We study entanglement-related properties of random quantum states which are unitarily invariant, in the sense that their distribution is left unchanged by conjugation with arbitrary unitary operators. In the large matrix size limit, the…
Quantum technologies exploit entanglement to enhance various tasks beyond their classical limits including computation, communication and measurements. Quantum metrology aims to increase the precision of a measured quantity that is…
The preparation of quantum Gibbs states at finite temperatures is a cornerstone of quantum computation, enabling applications in quantum simulation of many-body systems, machine learning via quantum Boltzmann machines, and optimization…
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…
By combining the continuous matrix product state (cMPS) representation for quantum fields in the continuum with standard optimization techniques for matrix product states (MPS) on the lattice, we obtain an approximation $|\Psi\rangle$,…
A one dimensional XX spin chain of finite length coupled to reservoirs at both ends is solved exactly in terms of a matrix product state ansatz. An explicit representation of matrices of fixed dimension 4 independent of the chain length is…
We study a class of Markov chains that model the evolution of a quantum system subject to repeated measurements. Each Markov chain in this class is defined by a measure on the space of matrices. It is then given by a random product of…
In this paper we construct the continuous Matrix Product State (MPS) representation of the vacuum of the field theory corresponding to the continuous limit of an Ising model. We do this by exploiting the observation made by Hastings and…
The variational method is a powerful approach to solve many-body quantum problems non perturbatively. However, in the context of relativistic quantum field theory (QFT), it needs to meet 3 seemingly incompatible requirements outlined by…
Continuous-Variable (CV) devices are a promising platform for demonstrating large-scale quantum information protocols. In this framework, we define a general quantum computational model based on a CV hardware. It consists of vacuum input…