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An Area Law for One Dimensional Quantum Systems

- M. Hastings
- Mathematics, Physics
- 14 May 2007

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… Expand

Superadditivity of communication capacity using entangled inputs

- M. Hastings
- Physics
- 1 April 2009

The additivity conjecture of quantum information theory implies that entanglement cannot, even in principle, help to funnel more classical information through a quantum-communication channel. A… Expand

Spectral Gap and Exponential Decay of Correlations

- M. Hastings, T. Koma
- Physics, Mathematics
- 4 July 2005

We study the relation between the spectral gap above the ground state and the decay of the correlations in the ground state in quantum spin and fermion systems with short-range interactions on a wide… Expand

Progress towards practical quantum variational algorithms

- D. Wecker, M. Hastings, M. Troyer
- Physics
- 31 July 2015

The preparation of quantum states using short quantum circuits is one of the most promising near-term applications of small quantum computers, especially if the circuit is short enough and the… Expand

Lieb-Robinson bounds and the generation of correlations and topological quantum order.

- S. Bravyi, M. Hastings, F. Verstraete
- Physics, Medicine
- Physical review letters
- 14 March 2006

The Lieb-Robinson bound states that local Hamiltonian evolution in nonrelativistic quantum mechanical theories gives rise to the notion of an effective light cone with exponentially decaying tails.… Expand

Towards the fast scrambling conjecture

- Nima Lashkari, D. Stanford, M. Hastings, T. Osborne, P. Hayden
- Physics
- 28 November 2011

A bstractMany proposed quantum mechanical models of black holes include highly non-local interactions. The time required for thermalization to occur in such models should reflect the relaxation times… Expand

Area laws in quantum systems: mutual information and correlations.

- M. Wolf, F. Verstraete, M. Hastings, J. Cirac
- Physics, Medicine
- Physical review letters
- 30 April 2007

TLDR

Quasiadiabatic continuation of quantum states: The stability of topological ground-state degeneracy and emergent gauge invariance

- M. Hastings, X. Wen
- Physics
- 22 March 2005

We define for quantum many-body systems a quasiadiabatic continuation of quantum states. The continuation is valid when the Hamiltonian has a gap, or else has a sufficiently small low-energy density… Expand

Laplacian growth as one-dimensional turbulence

- M. Hastings, L. Levitov
- Mathematics, Physics
- 3 July 1996

Abstract A new model of Laplacian stochastic growth is formulated using conformal mappings. The model describes two growth regimes, stable and turbulent, separated by a sharp phase transition. The… Expand

Topological quantum order: Stability under local perturbations

- S. Bravyi, M. Hastings, S. Michalakis
- Physics, Mathematics
- 3 January 2010

We study zero-temperature stability of topological phases of matter under weak time-independent perturbations. Our results apply to quantum spin Hamiltonians that can be written as a sum of… Expand

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