There has been extensive discussion about how many qubits are required for a fault-tolerant quantum computer capable of demonstrating quantum utility. However, we should not overlook the fact that, for now, available quantum computers are not fully error-corrected. How far can we go under these conditions? We present a comprehensive analysis of how deep noisy quantum circuits can be for a broad class of physically reasonable noise channels. The key takeaway—spoiler alert—is that such circuits are logarithmically deep, in a precise average-case sense.

The glass may be seen as half full or half empty: the achievable circuit depth ultimately depends on the exact average gate fidelities. Nonetheless, it is important to recognize that these circuits will effectively be noise-induced shallow circuits, and they will not exhibit barren plateaus during training. I am delighted to share this work, authored together with the wonderful team of Antonio Anna Mele, Armando Angrisani, Soumik Ghosh, Sumeet Khatri, Daniel Stilck França, and Yihui Quek, of the Freie Universität Berlin, Helmholtz-Zentrum Berlin, EPFL, the University of Chicago, the Fraunhofer Heinrich-Hertz-Institut, and the Massachusetts Institute of Technology.

We are delighted to see this work now being published in Nature Physics.