The evolution of entanglement entropy in quantum circuits composed of Haar-random gates and projective measurements shows versatile behavior, with connections to phase transitions and complexity theory. We reformulate the problem in terms of a classical Markov process for the dynamics of bipartition purities and establish a probabilistic cellular-automaton algorithm to compute entanglement entropy in monitored random circuits on arbitrary graphs. In one dimension, we further relate the evolution of the entropy to a simple classical spin model that naturally generalizes a two-dimensional lattice percolation problem. We also establish a Markov model for the evolution of the zeroth Rényi entropy and demonstrate that, in one dimension and in the limit of large local dimension, it coincides with the corresponding second-Rényi-entropy model. Finally, we extend the Markovian description to a more general setting that incorporates continuous-time dynamics, defined by stochastic Hamiltonians and weak local measurements continuously monitoring the system.

%8 4/14/2020 %G eng %U https://arxiv.org/abs/2004.06736 %0 Journal Article %J Phys. Rev. Lett. %D 2020 %T Minimal model for fast scrambling %A Ron Belyansky %A Przemyslaw Bienias %A Yaroslav A. Kharkov %A Alexey V. Gorshkov %A Brian Swingle %XWe study quantum information scrambling in spin models with both long-range all-to-all and short-range interactions. We argue that a simple global, spatially homogeneous interaction together with local chaotic dynamics is sufficient to give rise to fast scrambling, which describes the spread of quantum information over the entire system in a time that is logarithmic in the system size. This is illustrated in two exactly solvable models: (1) a random circuit with Haar random local unitaries and a global interaction and (2) a classical model of globally coupled non-linear oscillators. We use exact numerics to provide further evidence by studying the time evolution of an out-of-time-order correlator and entanglement entropy in spin chains of intermediate sizes. Our results can be verified with state-of-the-art quantum simulators.

%B Phys. Rev. Lett. %V 125 %8 9/22/2020 %G eng %U https://arxiv.org/abs/2005.05362 %N 130601 %R https://doi.org/10.1103/PhysRevLett.125.130601 %0 Journal Article %D 2020 %T Programmable Quantum Annealers as Noisy Gibbs Samplers %A Marc Vuffray %A Carleton Coffrin %A Yaroslav A. Kharkov %A Andrey Y. Lokhov %XDrawing independent samples from high-dimensional probability distributions represents the major computational bottleneck for modern algorithms, including powerful machine learning frameworks such as deep learning. The quest for discovering larger families of distributions for which sampling can be efficiently realized has inspired an exploration beyond established computing methods and turning to novel physical devices that leverage the principles of quantum computation. Quantum annealing embodies a promising computational paradigm that is intimately related to the complexity of energy landscapes in Gibbs distributions, which relate the probabilities of system states to the energies of these states. Here, we study the sampling properties of physical realizations of quantum annealers which are implemented through programmable lattices of superconducting flux qubits. Comprehensive statistical analysis of the data produced by these quantum machines shows that quantum annealers behave as samplers that generate independent configurations from low-temperature noisy Gibbs distributions. We show that the structure of the output distribution probes the intrinsic physical properties of the quantum device such as effective temperature of individual qubits and magnitude of local qubit noise, which result in a non-linear response function and spurious interactions that are absent in the hardware implementation. We anticipate that our methodology will find widespread use in characterization of future generations of quantum annealers and other emerging analog computing devices.

%8 12/16/2020 %G eng %U https://arxiv.org/abs/2012.08827 %0 Journal Article %J Phys. Rev. B %D 2020 %T Quantum Lifshitz criticality in a frustrated two-dimensional XY model %A Yaroslav A. Kharkov %A Jaan Oitmaa %A Oleg P. Sushkov %XAntiferromagnetic quantum spin systems can exhibit a transition between collinear and spiral ground states,

driven by frustration. Classically this is a smooth crossover and the crossover point is termed a Lifshitz point.

Quantum fluctuations change the nature of the transition. In particular, it has been argued previously that in the two-dimensional (2D) case a spin liquid (SL) state is developed in the vicinity of the Lifshitz point, termed a Lifshitz SL. In the present work, using a field theory approach, we solve the Lifshitz quantum phase transition problem for the 2D frustrated XY model. Specifically, we show that, unlike the SU (2) symmetric Lifshitz case, in the XY model, the SL exists only at the critical point. At zero temperature we calculate nonuniversal critical exponents in the Néel and in the spin spiral state and relate these to properties of the SL. We also solve the transition problem at a finite temperature and discuss the role of topological excitations.