We use complexity theory to rigorously investigate the difficulty of classically simulating evolution under many-body localized (MBL) Hamiltonians. Using the defining feature that MBL systems have a complete set of quasilocal integrals of motion (LIOMs), we demonstrate a transition in the classical complexity of simulating such systems as a function of evolution time. On one side, we construct a quasipolynomial-time tensor-network-inspired algorithm for strong simulation of 1D MBL systems (i.e., calculating the expectation value of arbitrary products of local observables) evolved for any time polynomial in the system size. On the other side, we prove that even weak simulation, i.e. sampling, becomes formally hard after an exponentially long evolution time, assuming widely believed conjectures in complexity theory. Finally, using the consequences of our classical simulation results, we also show that the quantum circuit complexity for MBL systems is sublinear in evolution time. This result is a counterpart to a recent proof that the complexity of random quantum circuits grows linearly in time.

UR - https://arxiv.org/abs/2205.12967 ER - TY - JOUR T1 - Spectral Form Factor of a Quantum Spin Glass Y1 - 2022 A1 - Winer, Michael A1 - Barney, Richard A1 - Christopher L. Baldwin A1 - Galitski, Victor A1 - Swingle, Brian KW - Disordered Systems and Neural Networks (cond-mat.dis-nn) KW - FOS: Physical sciences KW - High Energy Physics - Theory (hep-th) KW - Statistical Mechanics (cond-mat.stat-mech) KW - Strongly Correlated Electrons (cond-mat.str-el) AB -It is widely expected that systems which fully thermalize are chaotic in the sense of exhibiting random-matrix statistics of their energy level spacings, whereas integrable systems exhibit Poissonian statistics. In this paper, we investigate a third class: spin glasses. These systems are partially chaotic but do not achieve full thermalization due to large free energy barriers. We examine the level spacing statistics of a canonical infinite-range quantum spin glass, the quantum p-spherical model, using an analytic path integral approach. We find statistics consistent with a direct sum of independent random matrices, and show that the number of such matrices is equal to the number of distinct metastable configurations -- the exponential of the spin glass "complexity" as obtained from the quantum Thouless-Anderson-Palmer equations. We also consider the statistical properties of the complexity itself and identify a set of contributions to the path integral which suggest a Poissonian distribution for the number of metastable configurations. Our results show that level spacing statistics can probe the ergodicity-breaking in quantum spin glasses and provide a way to generalize the notion of spin glass complexity beyond models with a semi-classical limit.

UR - https://arxiv.org/abs/2203.12753 U5 - https://doi.org/10.48550/arXiv.2203.12753 ER - TY - JOUR T1 - The Lieb-Robinson light cone for power-law interactions Y1 - 2021 A1 - Minh C. Tran A1 - Andrew Y. Guo A1 - Christopher L. Baldwin A1 - Adam Ehrenberg A1 - Alexey V. Gorshkov A1 - Andrew Lucas AB -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.

UR - https://arxiv.org/abs/2103.15828 ER - TY - JOUR T1 - Singularities in nearly-uniform 1D condensates due to quantum diffusion Y1 - 2021 A1 - Christopher L. Baldwin A1 - P. Bienias A1 - Alexey V. Gorshkov A1 - Michael Gullans A1 - M. Maghrebi AB -Dissipative systems can often exhibit wavelength-dependent loss rates. One prominent example is Rydberg polaritons formed by electromagnetically-induced transparency, which have long been a leading candidate for studying the physics of interacting photons and also hold promise as a platform for quantum information. In this system, dissipation is in the form of quantum diffusion, i.e., proportional to k2 (k being the wavevector) and vanishing at long wavelengths as k→0. Here, we show that one-dimensional condensates subject to this type of loss are unstable to long-wavelength density fluctuations in an unusual manner: after a prolonged period in which the condensate appears to relax to a uniform state, local depleted regions quickly form and spread ballistically throughout the system. We connect this behavior to the leading-order equation for the nearly-uniform condensate -- a dispersive analogue to the Kardar-Parisi-Zhang (KPZ) equation -- which develops singularities in finite time. Furthermore, we show that the wavefronts of the depleted regions are described by purely dissipative solitons within a pair of hydrodynamic equations, with no counterpart in lossless condensates. We close by discussing conditions under which such singularities and the resulting solitons can be physically realized.

UR - https://arxiv.org/abs/2103.06293 ER - TY - JOUR T1 - Distinct Critical Behaviors from the Same State in Quantum Spin and Population Dynamics Perspectives Y1 - 2020 A1 - Christopher L. Baldwin A1 - S. Shivam A1 - S. L. Sondhi A1 - M. Kardar AB -There is a deep connection between the ground states of transverse-field spin systems and the late-time distributions of evolving viral populations -- within simple models, both are obtained from the principal eigenvector of the same matrix. However, that vector is the wavefunction amplitude in the quantum spin model, whereas it is the probability itself in the population model. We show that this seemingly minor difference has significant consequences: phase transitions which are discontinuous in the spin system become continuous when viewed through the population perspective, and transitions which are continuous become governed by new critical exponents. We introduce a more general class of models which encompasses both cases, and that can be solved exactly in a mean-field limit. Numerical results are also presented for a number of one-dimensional chains with power-law interactions. We see that well-worn spin models of quantum statistical mechanics can contain unexpected new physics and insights when treated as population-dynamical models and beyond, motivating further studies.

UR - https://arxiv.org/abs/2009.05064 ER - TY - JOUR T1 - Optimal Protocols in Quantum Annealing and QAOA Problems Y1 - 2020 A1 - Lucas T. Brady A1 - Christopher L. Baldwin A1 - Aniruddha Bapat A1 - Yaroslav Kharkov A1 - Alexey V. Gorshkov AB -Quantum 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.

UR - https://arxiv.org/abs/2003.08952 ER - TY - JOUR T1 - Spin-Mediated Mott Excitons Y1 - 2020 A1 - T. -S. Huang A1 - Christopher L. Baldwin A1 - M. Hafezi A1 - V. Galitski AB -Motivated by recent experiments on Mott insulators, in both iridates and ultracold atoms, we theoretically study the effects of magnetic order on the Mott-Hubbard excitons. In particular, we focus on spin-mediated doublon-holon pairing in Hubbard materials. We use several complementary theoretical techniques: mean-field theory to describe the spin degrees of freedom, the self-consistent Born approximation to characterize individual charge excitations across the Hubbard gap, and the Bethe-Salpeter equation to identify bound states of doublons and holons. The binding energy of the Hubbard exciton is found to increase with increasing the N{é}el order parameter, while the exciton mass decreases. We observe that these trends rely significantly on the retardation of the effective interaction, and require consideration of multiple effects from changing the magnetic order. Our results are consistent with the key qualitative trends observed in recent experiments on iridates. Moreover, the findings could have direct implications on ultracold atom Mott insulators, where the Hubbard model is the exact description of the system and the microscopic degrees of freedom can be directly accessed.

UR - https://arxiv.org/abs/2004.10825 ER - TY - JOUR T1 - Studying viral populations with tools from quantum spin chains Y1 - 2020 A1 - Saumya Shivam A1 - Christopher L. Baldwin A1 - John Barton A1 - Mehran Kardar A1 - S. L. Sondhi AB -We 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.

UR - https://arxiv.org/abs/2003.10668 ER - TY - JOUR T1 - Quantum Approximate Optimization with a Trapped-Ion Quantum Simulator Y1 - 2019 A1 - G. Pagano A1 - A. Bapat A1 - P. Becker A1 - K. S. Collins A1 - A. De A1 - P. W. Hess A1 - H. B. Kaplan A1 - A. Kyprianidis A1 - W. L. Tan A1 - Christopher L. Baldwin A1 - L. T. Brady A1 - A. Deshpande A1 - F. Liu A1 - S. Jordan A1 - Alexey V. Gorshkov A1 - C. Monroe AB -Quantum computers and simulators may offer significant advantages over their classical counterparts, providing insights into quantum many-body systems and possibly solving exponentially hard problems, such as optimization and satisfiability. Here we report the first implementation of a shallow-depth Quantum Approximate Optimization Algorithm (QAOA) using an analog quantum simulator to estimate the ground state energy of the transverse field Ising model with tunable long-range interactions. First, we exhaustively search the variational control parameters to approximate the ground state energy with up to 40 trapped-ion qubits. We then interface the quantum simulator with a classical algorithm to more efficiently find the optimal set of parameters that minimizes the resulting energy of the system. We finally sample from the full probability distribution of the QAOA output with single-shot and efficient measurements of every qubit.

UR - https://arxiv.org/abs/1906.02700 ER - TY - JOUR T1 - Quenched vs Annealed: Glassiness from SK to SYK Y1 - 2019 A1 - Christopher L. Baldwin A1 - Brian Swingle AB -We 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.

UR - https://arxiv.org/abs/1911.11865 ER -