Quantifying scrambling in quantum neural networks

Abstract

We quantify the role of scrambling in quantum machine learning. We characterize a quantum neural network’s (QNNs) error in terms of the network’s scrambling properties via the out-of-time-ordered correlator (OTOC). A network can be trained by minimizing a loss function. We show that the loss function can be bounded by the OTOC. We prove that the gradient of the loss function can be bounded by the gradient of the OTOC. This demonstrates that the OTOC landscape regulates the trainability of a QNN. We show numerically that this landscape is flat for maximally scrambling QNNs, which can pose a challenge to training. Our results pave the way for the exploration of quantum chaos in quantum neural networks.

Barren plateaus from learning scramblers with local cost functions

“…These results also extend to learning scramblers [12][13][14][15][16], unitaries which spread local information. This is complemented by an amalgam of results connecting scrambling and QML [17][18][19]. These barren plateaus inhibit learning the dynamics of chaotic quantum systems such as the mixed-field Ising model [20,21], the kicked Dicke model [22][23][24], the non-integrable Bose-Hubbard model [25], the SYK model [26,27], and even black holes [28][29][30], the fastest scramblers known in nature.…”

Information scrambling and entanglement in quantum approximate optimization algorithm circuits

“…( 17) is much lower, but its tripartite information is smaller than that of Eq. (16). To this extent, we need further studies to well-define the relation between complexity C, success rate R, and tripartite information I 3 in a general context.…”

“…In last decades, studies of this physical process mostly focus on the area of black hole information and quantum gravity [10,11]. Recently, more and more works turn their attention to information scrambling in quantum circuits, which pave the way to applications involving benchmarking noise [12], recovering lost information [13], characterizing performance of quantum neural networks [14][15][16], unifying chaos and random circuits [17,18], and so on [19,20]. In addition, the process of information scrambling is observed experimentally on superconducting quantum processors [21,22].…”

Resource theory of quantum scrambling

“…Scrambling has flourished by connecting diverse areas, including quantum many-body physics ( 3 – 5 ), black hole physics ( 7 – 12 ), and quantum information ( 7 ). It has become a prevalent ingredient in many information processing problems found in quantum machine learning ( 13 – 17 ), shadow tomography with classical shadows ( 18 – 23 ), quantum error correction ( 24 , 25 ), encryption ( 26 ), and emergent quantum state designs ( 27 ). For instance, scrambling dynamics is used in ref.…”