Measurement-driven quantum advantages in shallow circuits

TL;DR

This paper demonstrates that mid-circuit measurements enable efficient sampling and quantum advantages in shallow circuits, surpassing previous depth limitations and supporting quantum speedups on practical hardware.

Contribution

It introduces a measurement-driven approach for shallow quantum circuits that achieves quantum advantage by bypassing depth constraints and enabling complex entanglement.

Findings

Efficient sampling from structured quantum states using shallow circuits.

Measurement-driven feature maps distinguish quantum phases in machine learning.

Demonstrates quantum advantage on hardware with bounded-degree topology.

Abstract

Quantum advantage schemes probe the boundary between classically simulatable and classically intractable quantum dynamics. We explore the impact of mid-circuit measurements on the computational power of quantum circuits. To this effect, we focus on quantum sampling and introduce a constant-depth measurement-driven approach for efficiently sampling from a broad class of commuting diagonal quantum circuits and associated structured phase states, previously requiring polynomial-depth unitary circuits. By interleaving mid-circuit measurements with feed-forward in randomized "fan-out staircases", our dynamical circuits bypass Lieb-Robinson light-cone constraints, enabling global entanglement with flexible auxiliary qubit usage on bounded-degree lattices (e.g., two-dimensional grids). The generated phase states exhibit random-matrix statistics and anti-concentration comparable to fully random architectures. We further demonstrate measurement-driven feature maps that distinguish phases of an extended SSH model from random eigenstates in a quantum machine-learning benchmark (reservoir computing). Technologically, our results harness mid-circuit measurements to realize quantum advantages on bounded-degree hardware with a favorable topology. Conceptually, they provide complexity-theoretic support for quantum speedups by mid-circuit measurements.