An efficient numerical method is developed using the matrix product formalism for computing the properties at finite energy densities in one-dimensional (1D) many-body localized (MBL) systems. Arguing that any efficient (possibly quantum) algorithm can only have a polynomially small energy resolution, we propose a (rigorous) polynomial-time (classical) algorithm that outputs a diagonal density operator supported on a microcanonical ensemble of an inverse polynomial bandwidth. The proof uses no other conditions for MBL but assumes that the effect of any local perturbation (e.g., injecting conserved charges) is restricted to a region whose radius grows logarithmically with time. A non-optimal version of this algorithm efficiently simulates the quantum phase estimation algorithm in 1D MBL systems; a heuristic version of the algorithm can be easily coded and used to, e.g., detect energy-tuned dynamical quantum phase transitions between MBL phases. We extend the algorithm to two and higher spatial dimensions using the projected entangled pair formalism.An efficient numerical method is developed using the matrix product formalism for computing the properties at finite energy densities in one-dimensional (1D) many-body localized (MBL) systems. Arguing that any efficient (possibly quantum) algorithm can only have a polynomially small energy resolution, we propose a (rigorous) polynomial-time (classical) algorithm that outputs a diagonal density operator supported on a microcanonical ensemble of an inverse polynomial bandwidth. The proof uses no other conditions for MBL but assumes that the effect of any local perturbation (e.g., injecting conserved charges) is restricted to a region whose radius grows logarithmically with time. A non-optimal version of this algorithm efficiently simulates the quantum phase estimation algorithm in 1D MBL systems; a heuristic version of the algorithm can be easily coded and used to, e.g., detect energy-tuned dynamical quantum phase transitions between MBL phases. We extend the algorithm to two and higher spatial dimensions using the projected entangled pair formalism.

arXiv:1508.04756Aug 19, 20153 citations

Entanglement spectroscopy on a quantum computer

Sonika Johri, Damian S. Steiger, Matthias Troyer

The efficient simulation of many-body quantum systems is an important application of quantum computers. However, extracting useful information from a system of qubits is not straightforward. The quantum computing equivalent of the vast array of diagnostic tools that extract information from classical numerical simulation are still being developed. This paper addresses the efficient calculation of quantities that characterize entanglement between different parts of a quantum state using a quantum computer. Illustrative examples of applications as diverse as many-body localization and fractional quantum Hall effect are discussed.The efficient simulation of many-body quantum systems is an important application of quantum computers. However, extracting useful information from a system of qubits is not straightforward. The quantum computing equivalent of the vast array of diagnostic tools that extract information from classical numerical simulation are still being developed. This paper addresses the efficient calculation of quantities that characterize entanglement between different parts of a quantum state using a quantum computer. Illustrative examples of applications as diverse as many-body localization and fractional quantum Hall effect are discussed.

arXiv:1707.07658Physical review. B./Physical review. BNov 20, 201765 citations

Entanglement and efficient simulation of many-body quantum systems

Guifré Vidal

Bulletin of the American Physical SocietyMar 7, 20070 citations

Exploring many-body localization in two dimensions

Christian Groß

Bulletin of the American Physical SocietyJun 8, 20170 citations

Entanglement dynamics of a many-body localized system coupled to a bath

Elisabeth Wybo, Michael Knap, Frank Pollmann

The combination of strong disorder and interactions in closed quantum systems can lead to many-body localization (MBL). However, this quantum phase is not stable when the system is coupled to a thermal environment. We investigate how MBL is destroyed in systems that are weakly coupled to a dephasive Markovian environment by focusing on their entanglement dynamics. We numerically study the third R\'enyi negativity ${R}_{3}$ , a recently proposed entanglement proxy based on the negativity that captures the unbounded logarithmic growth in the closed case and that can be computed efficiently with tensor networks. We also show that the decay of ${R}_{3}$ follows a stretched exponential law, similarly to the imbalance, with, however, a smaller stretching exponent.The combination of strong disorder and interactions in closed quantum systems can lead to many-body localization (MBL). However, this quantum phase is not stable when the system is coupled to a thermal environment. We investigate how MBL is destroyed in systems that are weakly coupled to a dephasive Markovian environment by focusing on their entanglement dynamics. We numerically study the third R\'enyi negativity ${R}_{3}$, a recently proposed entanglement proxy based on the negativity that captures the unbounded logarithmic growth in the closed case and that can be computed efficiently with tensor networks. We also show that the decay of ${R}_{3}$ follows a stretched exponential law, similarly to the imbalance, with, however, a smaller stretching exponent.

arXiv:2004.13072Physical review. B./Physical review. BAug 7, 202042 citations

{R}_{3}

, a recently proposed entanglement proxy based on the negativity that captures the unbounded logarithmic growth in the closed case and that can be computed efficiently with tensor networks. We also show that the decay of

{R}_{3}

follows a stretched exponential law, similarly to the imbalance, with, however, a smaller stretching exponent.