The Lieb-Robinson theorem states that information propagates with a finite velocity in quantum systems on a lattice with nearest-neighbor interactions. What are the speed limits on information propagation in quantum systems with power-law interactions, which decay as 1/rα at distance r? Here, we present a definitive answer to this question for all exponents α>2d and all spatial dimensions d. Schematically, information takes time at least rmin{1,α−2d} to propagate a distance~r. As recent state transfer protocols saturate this bound, our work closes a decades-long hunt for optimal Lieb-Robinson bounds on quantum information dynamics with power-law interactions.

%8 3/29/2021 %G eng %U https://arxiv.org/abs/2103.15828 %0 Journal Article %D 2020 %T Optimal Protocols in Quantum Annealing and QAOA Problems %A Lucas T. Brady %A Christopher L. Baldwin %A Aniruddha Bapat %A Yaroslav Kharkov %A Alexey V. Gorshkov %XQuantum Annealing (QA) and the Quantum Approximate Optimization Algorithm (QAOA) are two special cases of the following control problem: apply a combination of two Hamiltonians to minimize the energy of a quantum state. Which is more effective has remained unclear. Here we apply the framework of optimal control theory to show that generically, given a fixed amount of time, the optimal procedure has the pulsed (or "bang-bang") structure of QAOA at the beginning and end but can have a smooth annealing structure in between. This is in contrast to previous works which have suggested that bang-bang (i.e., QAOA) protocols are ideal. Through simulations of various transverse field Ising models, we demonstrate that bang-anneal-bang protocols are more common. The general features identified here provide guideposts for the nascent experimental implementations of quantum optimization algorithms.

%8 3/19/2020 %G eng %U https://arxiv.org/abs/2003.08952 %0 Journal Article %D 2020 %T Studying viral populations with tools from quantum spin chains %A Saumya Shivam %A Christopher L. Baldwin %A John Barton %A Mehran Kardar %A S. L. Sondhi %XWe study Eigen's model of quasi-species, characterized by sequences that replicate with a specified fitness and mutate independently at single sites. The evolution of the population vector in time is then closely related to that of quantum spins in imaginary time. We employ multiple perspectives and tools from interacting quantum systems to examine growth and collapse of realistic viral populations, specifically certain HIV proteins. All approaches used, including the simplest perturbation theory, give consistent results.

%8 3/24/2020 %G eng %U https://arxiv.org/abs/2003.10668 %0 Journal Article %D 2019 %T Quenched vs Annealed: Glassiness from SK to SYK %A Christopher L. Baldwin %A Brian Swingle %XWe show that any SYK-like model with finite-body interactions among \textit{local} degrees of freedom, e.g., bosons or spins, has a fundamental difference from the standard fermionic model: the former fails to be described by an annealed free energy at low temperature. In this respect, such models more closely resemble spin glasses. We demonstrate this by two means: first, a general theorem proving that the annealed free energy is divergent at low temperature in any model with a tensor product Hilbert space; and second, a replica treatment of two prominent examples which exhibit phase transitions from an "annealed" phase to a "non-annealed" phase as a function of temperature. We further show that this effect appears only at O(N)'th order in a 1/N expansion, even though lower-order terms misleadingly seem to converge. Our results prove that the non-bosonic nature of the particles in SYK is an essential ingredient for its physics, highlight connections between local models and spin glasses, and raise important questions as to the role of fermions and/or glassiness in holography.

%8 11/26/2019 %G eng %U https://arxiv.org/abs/1911.11865