Related papers: Gaussian matrix product states cannot efficiently …
We discuss a dynamical matrix model by which probability distribution is associated with Gaussian ensembles from random matrix theory. We interpret the matrix M as a Hamiltonian representing interaction of a bosonic system with a single…
Tensor networks, which are originally developed for characterizing complex quantum many-body systems, have recently emerged as a powerful framework for capturing high-dimensional probability distributions with strong physical…
We consider the gauged free fermionic matrix model, for a single fermionic matrix. In the large $N$ limit this system describes a $c=1/2$ chiral fermion in $1+1$ dimensions. The Gauss' law constraint implies that to obtain a physical state,…
We analyze the quantum phase transition between a semimetal and a superfluid in a model of attractively interacting fermions with a linear dispersion. The quantum critical properties of this model cannot be treated by the Hertz-Millis…
Identifying variational wave functions that efficiently parametrize the physically relevant states in the exponentially large Hilbert space is one of the key tasks towards solving the quantum many-body problem. Powerful tools in this…
We define fermionic convolution and demonstrate its utility in characterizing fermionic non-Gaussian components, which are essential to the computational advantage of fermionic systems. Using fermionic convolution, we propose an efficient…
We present a novel, non-parametric form for compactly representing entangled many-body quantum states, which we call a `Gaussian Process State'. In contrast to other approaches, we define this state explicitly in terms of a configurational…
Matrix Product States can be defined as the family of quantum states that can be sequentially generated in a one-dimensional system. We introduce a new family of states which extends this definition to two dimensions. Like in Matrix Product…
We describe a simple method to find the ground state energy without calculating the expectation value of the Hamiltonian in the time-evolving block decimation algorithm with tensor network states. For example, we consider quantum…
This work explores displaced fermionic Gaussian operators with nonzero linear terms. We first demonstrate equivalence between several characterizations of displaced Gaussian states. We also provide an efficient classical simulation protocol…
Efficient simulation of a quantum system generally relies on structural properties of the quantum state. Motivated by the recent results by Bakshi et al. on the sudden death of entanglement in high-temperature Gibbs states of quantum spin…
The study of generic properties of quantum states has led to an abundance of insightful results. A meaningful set of states that can be efficiently prepared in experiments are ground states of gapped local Hamiltonians, which are well…
Compressible models extend the domain of simulable systems in quantum computers, but little is known about their precise limits of applicability. Using the theory of compressible matchgate circuits, we identify a class of quadratic…
We study frustration-free Hamiltonians of fractional quantum Hall (FQH) states from the point of view of the matrix product state (MPS) representation of their ground and excited states. There is a wealth of solvable models relating to FQH…
We show that the norm squared amplitudes with respect to a local orthonormal basis (the classical restriction) of finite quantum systems on one-dimensional lattices can be exponentially well approximated by Gibbs states of local…
Gaussian process state-space model (GPSSM) is a fully probabilistic state-space model that has attracted much attention over the past decade. However, the outputs of the transition function in the existing GPSSMs are assumed to be…
This work gives a detailed investigation of matrix product state (MPS) representations for pure multipartite quantum states. We determine the freedom in representations with and without translation symmetry, derive respective canonical…
Tensor network states, and in particular Projected Entangled Pair States (PEPS) have been a strong ansatz for the variational study of complicated quantum many-body systems, thanks to their built-in entanglement entropy area law. In this…
We study phases of one-dimensional matrix-product states (MPS) when transformations are restricted to symmetric local circuits supplemented with symmetric measurements and feedforward (G-CMF). Building on the framework introduced in Gunn et…
We study matrix product unitary operators (MPUs) for fermionic one-dimensional (1D) chains. In stark contrast with the case of 1D qudit systems, we show that (i) fermionic MPUs do not necessarily feature a strict causal cone and (ii) not…