Simulating and predicting dynamics of quantum many-body systems is extremely challenging, even for state-of-the-art computational methods, due to the spread of entanglement across the system. However, in the long-wavelength limit, quantum systems often admit a simplified description, which involves a small set of physical observables and requires only a few parameters such as sound velocity or viscosity. Unveiling the relationship between these hydrodynamic equations and the underlying microscopic theory usually requires a great effort by condensed matter theorists. In the present paper, we develop a new machine-learning framework for automated discovery of effective equations from a limited set of available data, thus bypassing complicated analytical derivations. The data can be generated from numerical simulations or come from experimental quantum simulator platforms. Using integrable models, where direct comparisons can be made, we reproduce previously known hydrodynamic equations, strikingly discover novel equations and provide their derivation whenever possible. We discover new hydrodynamic equations describing dynamics of interacting systems, for which the derivation remains an outstanding challenge. Our approach provides a new interpretable method to study properties of quantum materials and quantum simulators in non-perturbative regimes.

1 aKharkov, Yaroslav1 aShtanko, Oles1 aSeif, Alireza1 aBienias, Przemyslaw1 aVan Regemortel, Mathias1 aHafezi, Mohammad1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/2111.0238501465nas a2200169 4500008004100000245007200041210006900113260001400182520093400196100002301130700002001153700002501173700002101198700002101219700001801240856003701258 2021 eng d00aTight bounds on the convergence of noisy random circuits to uniform0 aTight bounds on the convergence of noisy random circuits to unif c12/1/20213 aWe study the properties of output distributions of noisy, random circuits. We obtain upper and lower bounds on the expected distance of the output distribution from the uniform distribution. These bounds are tight with respect to the dependence on circuit depth. Our proof techniques also allow us to make statements about the presence or absence of anticoncentration for both noisy and noiseless circuits. We uncover a number of interesting consequences for hardness proofs of sampling schemes that aim to show a quantum computational advantage over classical computation. Specifically, we discuss recent barrier results for depth-agnostic and/or noise-agnostic proof techniques. We show that in certain depth regimes, noise-agnostic proof techniques might still work in order to prove an often-conjectured claim in the literature on quantum computational advantage, contrary to what was thought prior to this work.

1 aDeshpande, Abhinav1 aFefferman, Bill1 aGorshkov, Alexey, V.1 aGullans, Michael1 aNiroula, Pradeep1 aShtanko, Oles uhttps://arxiv.org/abs/2112.0071601546nas a2200145 4500008004100000245006600041210006600107260001400173520107500187100001801262700002601280700003201306700002501338856003701363 2020 eng d00aClassical Models of Entanglement in Monitored Random Circuits0 aClassical Models of Entanglement in Monitored Random Circuits c4/14/20203 aThe 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.

1 aShtanko, Oles1 aKharkov, Yaroslav, A.1 aGarcía-Pintos, Luis, Pedro1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/2004.0673601547nas a2200145 4500008004100000245006900041210006900110260001400179520108200193100001801275700002301293700002301316700002501339856003701364 2020 eng d00aLimits on Classical Simulation of Free Fermions with Dissipation0 aLimits on Classical Simulation of Free Fermions with Dissipation c5/21/20203 aFree-fermionic systems are a valuable, but limited, class of many-body problems efficiently simulable on a classical computer. We examine how classical simulability of noninteracting fermions is modified in the presence of Markovian dissipation described by quadratic Lindblad operators, including, for example, incoherent transitions or pair losses. On the one hand, we establish three broad classes of Markovian dynamics that are efficiently simulable classically, by devising efficient algorithms. On the other hand, we demonstrate that, in the worst case, simulating Markovian dynamics with quadratic Lindblad operators is at least as hard as simulating universal quantum circuits. This result is applicable to an experimentally relevant setting in cold atomic systems, where magnetic Feshbach resonances can be used to engineer the desired dissipation. For such systems, our hardness result provides a direct scheme for dissipation-assisted quantum computing with a potential significant advantage in the speed of two-qubit gates and, therefore, in error tolerance.

1 aShtanko, Oles1 aDeshpande, Abhinav1 aJulienne, Paul, S.1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/2005.1084001282nas a2200133 4500008004100000245006000041210006000101260001500161490000800176520088800184100001801072700002101090856003701111 2020 eng d00aUnitary Subharmonic Response and Floquet Majorana Modes0 aUnitary Subharmonic Response and Floquet Majorana Modes c10/13/20200 v1253 aDetection and manipulation of excitations with non-Abelian statistics, such as Majorana fermions, are essential for creating topological quantum computers. To this end, we show the connection between the existence of such localized particles and the phenomenon of unitary subharmonic response (SR) in periodically driven systems. In particular, starting from highly non-equilibrium initial states, the unpaired Majorana modes exhibit spin oscillations with twice the driving period, are localized, and can have exponentially long lifetimes in clean systems. While the lifetime of SR is limited in translationally invariant systems, we show that disorder can be engineered to stabilize the subharmonic response of Majorana modes. A viable observation of this phenomenon can be achieved using modern multi-qubit hardware, such as superconducting circuits and cold atomic systems

1 aShtanko, Oles1 aMovassagh, Ramis uhttps://arxiv.org/abs/1911.05795