Quantum^BW Colloquium

A large amount of effort has recently been put into under­stand­ing the barren plateau phenom­e­non. In this perspec­tive talk, we face the increas­ingly loud elephant in the room and ask a question that has been hinted at by many but not explic­itly addressed: Can the struc­ture that allows one to avoid barren plateaus also be lever­aged to efficiently simulate the loss classically?

We present strong evidence that commonly used models with provable absence of barren plateaus are also classi­cally simula­ble, provided that one can collect some classi­cal data from quantum devices during an initial data acqui­si­tion phase. This follows from the obser­va­tion that barren plateaus result from a curse of dimen­sion­al­ity, and that current approaches for solving them end up encod­ing the problem into some small, classi­cally simula­ble, subspaces. This sheds serious doubt on the non-classicality of the infor­ma­tion process­ing capabil­i­ties of param­e­trized quantum circuits for barren plateau-free landscapes and on the possi­bil­ity of super­poly­no­mial advan­tages from running them on quantum hardware. We end by discussing caveats in our arguments, the poten­tial of smart initial­iza­tions, and by highlight­ing new oppor­tu­ni­ties that our perspec­tive raises.

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