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Mid‑Circuit Measurements Unlock Quantum Advantage in Shallow Circuits

Mid-circuit measurements are a powerful tool for state preparation, and they have generated considerable excitement in condensed matter physics due to their rich and surprising effects. In contrast, their usefulness for #quantumcomputation remains comparatively less well understood. In this work, we demonstrate that #midcircuitmeasurementscan enable genuine quantum advantages even in shallow quantum circuits. https://t.co/zH1JbGjPfd Concretely, 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. Warm thanks to Chenfeng Cao for this wonderfully fruitful and inspiring collaboration.