Spacetime duality between sequential and measurement-feedback circuits

• URL: http://arxiv.org/abs/2507.12523v1
• Date: Wed, 16 Jul 2025 18:00:01 GMT
• Title: Spacetime duality between sequential and measurement-feedback circuits
• Authors: Tsung-Cheng Lu, Sarang Gopalakrishnan, Yizhi You,
• Abstract summary: Two approaches for preparing long-range entangled quantum states are (i) linear-depth sequential unitary (SU) circuits, and (ii) constant-depth measurement-feedback (MF) circuits.<n>Here, we establish that a broad class of SU and MF circuits are dual to each other under a spacetime rotation.<n>We investigate this spacetime duality in the preparation of various long-range entangled states, including GHZ states, topologically ordered states, and fractal symmetry-breaking states.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Two prevalent approaches for preparing long-range entangled quantum states are (i) linear-depth sequential unitary (SU) circuits, which apply local unitary gates sequentially, and (ii) constant-depth measurement-feedback (MF) circuits, which employ mid-circuit measurements and conditional feedback based on measurement outcomes. Here, we establish that a broad class of SU and MF circuits are dual to each other under a spacetime rotation. We investigate this spacetime duality in the preparation of various long-range entangled states, including GHZ states, topologically ordered states, and fractal symmetry-breaking states. As an illustration, applying a spacetime rotation to a linear-depth SU circuit that implements a non-invertible Kramers-Wannier duality, originally used to prepare a 1D GHZ state, yields a constant-depth MF circuit that implements a $\mathbb{Z}_2$ symmetry gauging map, which equivalently prepares the GHZ state. Leveraging this duality, we further propose experimental protocols that require only a constant number of qubits to measure unconventional properties of 1D many-body states. These include (i) measurement of disorder operators, which diagnose the absence of spontaneous symmetry breaking, and (ii) postselection-free detection of measurement-induced long-range order, which emerges in certain symmetry-protected topological phases. We also show that measurement-induced long-range order provides a lower bound for strange correlators, which may be of independent interest.

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