Preparing random states and benchmarking with many-body quantum chaos

The Complexity of Learning (Pseudo)random Dynamics of Black Holes and Other Chaotic Systems

“…Thus while for highly complex processes E and a wide range of states ρ, the learning algorithm of [52] is able to predict many ("bounded-degree") observables, we give evidence against the ability of any efficient learning algorithm to predict for every observable. 21 [19] and [52] together with this article illustrate that a complexity cutoff for semiclassical gravity would simultaneously permit accurate computations of the expectation values of general classes of observables, while forbidding the predictions of arbitrary, high complexity observables when the system is chaotic. This together supports the hypothesis of a complexity cutoff: the former permits the validity of semiclassical gravity predictions in the cases where it is expected to be accurate; the latter is precisely where semiclassical gravity fails to match the actual evolution of the system even approximately, e.g.…”

“…[1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]). One such instance includes the dynamics of a large set of chaotic systems -notably including black holes -which are generally well-modeled by highly complex (or apparently complex) unitary time evolution [20][21][22][23][24][25]. Another such instance includes recent work [2,19] on the black hole information paradox [26], which has leveraged high complexity unitary dynamics to show that the tension between semiclassical effective field theory and quantum gravity in an old black hole can be relaxed by limiting the regime of validity of the former using complexity.…”

“…Therefore, once we prove the hardness of learning for random unitaries and states, we relax the restriction to pseudorandom unitaries and states. This is motivated by the connection between pseudorandom states and chaotic systems [22] (see also [56] and [21]) and the expectation that black holes are maximally chaotic systems [44,57]. 16 We note that measures of chaos can even be directly related to relaxations of Haar randomness: [23] shows a (tight) quantitative relationship between out-of-time-order correlators and k-designs, which, like the pseudorandom notions [58] that we use, capture some but not all of the properties of Haar random unitaries.…”

Generation of Pseudo-Random Quantum States on Actual Quantum Processors

“…Unlike simpler states such as W and GHZ, for which the entanglement content is essentially independent of the dimension of the system, for random states, the average multipartite entanglement is an extensive quantity. Moreover, random states are relevant in the study of the complexity of quantum circuits [ 17 ] and black holes [ 18 ] and for benchmarking quantum hardware [ 9 , 19 ].…”

Generation of Pseudo-Random Quantum States on Actual Quantum Processors

“…Unlike simpler states like W and GHZ, for which the entanglement content is essentially independent of the dimension of the system, for random states the average multipartite entanglement is an extensive quantity. Moreover, random states are relevant in the study of the complexity of quantum circuits [16] and black holes [17] and for benchmarking quantum hardware [9,18].…”