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We introduce Gaussian Matrix Product States (GMPS), a generalization of Matrix Product States (MPS) to lattices of harmonic oscillators. Our definition resembles the interpretation of MPS in terms of projected maximally entangled pairs,…

Quantum Physics · Physics 2012-01-20 Norbert Schuch , Michael M. Wolf , J. Ignacio Cirac

Critical phenomena involve a structural change in the correlations of its constituents. These features can be employed in quantum simulators to assess when a criticality occurred in medium-size systems, for which phase transitions are not…

Quantum Physics · Physics 2014-11-27 Adeline Orieux , Joelle Boutari , Marco Barbieri , Mauro Paternostro , Paolo Mataloni

We present an algorithm for finding ground states of two dimensional spin glass systems based on ideas from matrix product states in quantum information theory. The algorithm works directly at zero temperature and defines an approximate…

Disordered Systems and Neural Networks · Physics 2009-11-13 M. B. Hastings

An area law is proved for the Renyi entanglement entropy of possibly degenerate ground states in one-dimensional gapped quantum systems. Suppose in a chain of $n$ spins the ground states of a local Hamiltonian with energy gap $\epsilon$ are…

Strongly Correlated Electrons · Physics 2015-01-08 Yichen Huang

An important but little-studied property of spin glasses is the stability of their ground states to changes in one or a finite number of couplings. It was shown in earlier work that, if multiple ground states are assumed to exist, then…

Disordered Systems and Neural Networks · Physics 2020-01-22 L. -P. Arguin , C. M. Newman , D. L. Stein

We study an effective Hamiltonian for the standard $\nu=1/3$ fractional quantum Hall system in the thin cylinder regime. We give a complete description of its ground state space in terms of what we call Fragmented Matrix Product States,…

Mathematical Physics · Physics 2022-01-12 Bruno Nachtergaele , Simone Warzel , Amanda Young

Structure in quantum entanglement entropy is often leveraged to focus on a small corner of the exponentially large Hilbert space and efficiently parameterize the problem of finding ground states. A typical example is the use of matrix…

Statistical Mechanics · Physics 2023-04-17 Bart Olsthoorn

We study a model of quantum computation based on the continuously-parameterized yet finite-dimensional Hilbert space of a spin system. We explore the computational powers of this model by analyzing a pilot problem we refer to as the close…

Quantum Physics · Physics 2016-12-30 Mark Adcock , Peter Hoyer , Barry C. Sanders

We compare the results of ground state and spectroscopic measurements carried out on superconducting flux qubits which are effective two-level quantum systems. For a single qubit and for two coupled qubits we show excellent agreement…

We prove an area law for the entanglement entropy in gapped one dimensional quantum systems. The bound on the entropy grows surprisingly rapidly with the correlation length; we discuss this in terms of properties of quantum expanders and…

Quantum Physics · Physics 2018-07-12 M. B. Hastings

We prove that estimating the ground state energy of a translationally-invariant, nearest-neighbour Hamiltonian on a 1D spin chain is QMAEXP-complete, even for systems of low local dimension (roughly 40). This is an improvement over the best…

Quantum Physics · Physics 2017-11-15 Johannes Bausch , Toby Cubitt , Maris Ozols

A generic method to investigate many-body continuous-variable systems is pedagogically presented. It is based on the notion of matrix product states (so-called MPS) and the algorithms thereof. The method is quite versatile and can be…

Strongly Correlated Electrons · Physics 2013-05-29 S. Iblisdir , R. Orus , J. I. Latorre

The purpose of this study is to calculate the entanglement measure for a bipartite system where the two subsystems interact via a central potential, and more importantly, to analyze the conceptual implication in the case of gravitational…

Quantum Physics · Physics 2020-06-16 Jianhao M. Yang

We introduce a natural mathematical definition of boundary states of a bulk gapped ground state, in the operator algebraic framework of $2$-d quantum spin systems. With approximate Haag duality at the boundary, we derive a $C^*$-tensor…

Mathematical Physics · Physics 2025-01-14 Yoshiko Ogata

We study a generalized quantum hard-core dimer model on the square and honeycomb lattices, allowing for first and second neighbor dimers. At generalized RK points, the exact ground states can be constructed, and ground-state correlation…

Strongly Correlated Electrons · Physics 2015-06-03 Hong Yao , Steven A. Kivelson

This paper analyzes general spatially-coupled (SC) systems with multi-dimensional coupling. A continuum approximation is used to derive potential functions that characterize the performance of the SC systems. For any dimension of coupling,…

Information Theory · Computer Science 2013-04-19 Keigo Takeuchi , Toshiyuki Tanaka , Kenta Kasai

In this work, we extend the so-called typicality approach, originally formulated in statistical mechanics contexts, to $SU(2)$-invariant spin-network states. Our results do not depend on the physical interpretation of the spin network;…

General Relativity and Quantum Cosmology · Physics 2016-11-02 Fabio Anzà , Goffredo Chirco

It is experimentally demonstrated that an arbitrary quantum state of a single spin 1/2: a|u> + b|d> can be converted into a superposition of the two ferromagnetic states of a spin cluster: a|uu...uu> + b|dd...dd>. The physical system is a…

Quantum Physics · Physics 2007-05-23 Jae-Seung Lee , A. K. Khitrin

A random vector whose norm and overlap (inner product with an independent copy) concentrates is shown to have random low-dimensional projections that are approximately random Gaussians. Conversely, asymptotically random Gaussian projections…

Probability · Mathematics 2025-12-23 Timothy L. H. Wee , Sekhar Tatikonda

Characterizing the entanglement structure of ground states of local Hamiltonians is a fundamental problem in quantum information. In this work we study the computational complexity of this problem, given the Hamiltonian as input. Our main…

Quantum Physics · Physics 2024-11-08 Adam Bouland , Chenyi Zhang , Zixin Zhou