相关论文: Matrix Product State Representations

An algebraic investigation on bicomplex numbers is carried out here. Particularly matrices and linear maps defined on them are discussed. A new kind of cartesian product, referred to as an idempotent product, is introduced and studied. The…

We investigate the use of matrix product states (MPS) to approximate ground states of critical quantum spin chains with periodic boundary conditions (PBC). We identify two regimes in the (N,D) parameter plane, where N is the size of the…

We demonstrate how to simulate both discrete and continuous stochastic evolution of a quantum many body system subject to measurements using matrix product states. A particular, but generally applicable, measurement model is analyzed and a…

BosonSampling is a well-defined scheme for demonstrating quantum supremacy with photons in near term. Although relying only on multi-photon interference in nonadaptive linear-optical networks, it is hard to simulate classically. Here we…

We present a comparative study of the permutation matrix representation (PMR) method for Hamiltonian simulation alongside other leading quantum algorithms. Our analysis focuses on resource costs for simulating both time-independent and…

In this work we introduce an ansatz for continuous matrix product operators for quantum field theory. We show that (i) they admit a closed-form expression in terms of finite number of matrix-valued functions without reference to any lattice…

We present several improvements of the infinite matrix product state (iMPS) algorithm for finding ground states of one-dimensional quantum systems with long-range interactions. As a main new ingredient we introduce the superposed…

We study the Matrix theory from a purely canonical viewpoint. In particular, we identify free particle asymptotic states of the model corresponding to the 11D supergraviton multiplet along with the split of the matrix model Hamiltonian into…

To compute approximate solutions for combinatorial optimization problems, we describe variational methods based on the product state (PS) and matrix product state (MPS) ansatzes. We perform variational energy minimization with respect to a…

We study the second-order quantum phase-transition of massive real scalar field theory with a quartic interaction ($\phi^4$ theory) in (1+1) dimensions on an infinite spatial lattice using matrix product states (MPS). We introduce and apply…

We consider the general problem of determining the steady state of stochastic nonequilibrium systems such as those that have been used to model (among other things) biological transport and traffic flow. We begin with a broad overview of…

State preparation is a necessary component of many quantum algorithms. In this work, we combine a method for efficiently representing smooth differentiable probability distributions using matrix product states with recently discovered…

We find an efficient approach to approximately convert matrix product states (MPSs) into restricted Boltzmann machine wave functions consisting of a multinomial hidden unit through a canonical polyadic (CP) decomposition of the MPSs. This…

Consider a symmetric quantum state on an n-fold product space, that is, the state is invariant under permutations of the n subsystems. We show that, conditioned on the outcomes of an informationally complete measurement applied to a number…

We investigate ensembles of Matrix Product States (MPSs) generated by quantum circuit evolution followed by projection onto MPSs with a fixed bond dimension $\chi$. Specifically, we consider ensembles produced by: (i) random sequential…

We introduce the concept of quantum field tomography, the efficient and reliable reconstruction of unknown quantum fields based on data of correlation functions. At the basis of the analysis is the concept of continuous matrix product…

Many one-dimensional lattice particle models with open boundaries, like the paradigmatic Asymmetric Simple Exclusion Process (ASEP), have their stationary states represented in the form of a matrix product, with matrices that do not…

The generalized q-deformed valence-bond-solid groundstate of one-dimensional higher integer spin model is studied. The Schwinger boson representation and the matrix product representation of the exact groundstate is determined, which…

There has been a problem of gauge ambiguities with the Rabi Hamiltonian due to the fact that it can be derived from two formally different but physically equivalent fundamental Hamiltonians. This problem has recently been resolved for…

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…