Measurement-driven quantum advantages in shallow circuits

• URL: http://arxiv.org/abs/2505.04705v1
• Date: Wed, 07 May 2025 18:00:51 GMT
• Title: Measurement-driven quantum advantages in shallow circuits
• Authors: Chenfeng Cao, Jens Eisert,
• Abstract summary: Quantum advantage schemes probe the boundary between classically simulatable quantum systems and those that go beyond this realm.<n>Here, we introduce a constant-depth measurement-driven approach for efficiently sampling from a broad class of dense instantaneous quantum-time circuits.
• Score: 0.3683202928838613
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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