Abstract

Quantum advantage schemes probe the boundary between classically simulatable quantum systems and those that computationally go beyond this realm. Here, we introduce a constant-depth measurement-driven approach for efficiently sampling from a broad class of dense instantaneous quantum polynomial-time circuits and associated Hamiltonian phase states, previously requiring polynomial-depth unitary circuits. Leveraging measurement-adaptive fan-out staircases, our "dynamical circuits" circumvent light-cone constraints, enabling global entanglement with flexible auxiliary qubit usage on bounded-degree lattices. Generated Hamiltonian phase states exhibit statistical metrics indistinguishable from those of fully random architectures. Additionally, we demonstrate measurement-driven globally entangled feature maps capable of distinguishing phases of an extended SSH model from random eigenstates using a quantum reservoir-computing benchmark. Technologically, our results harness the power of mid-circuit measurements for realizing quantum advantages on hardware with a favorable topology. Conceptually, we highlight their power in achieving rigorous computational speedups.

Personal information

Chenfeng Cao is a Humboldt Research Fellow in the group of Prof. Jens Eisert at Freie Universität Berlin. He earned his B.S. in Physics from the University of the Chinese Academy of Sciences in 2019 and completed his Ph.D. in Physics at the Hong Kong University of Science and Technology in 2024, under the supervision of Prof. Bei Zeng. From 2023 to 2024, he served as a research consultant at Phasecraft (UK), working with Prof. Ashley Montanaro. Chenfeng’s research spans several theoretical domains in quantum information science, with particular emphasis on near-term quantum algorithms and the computational boundary between classical and quantum computers.

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