Quantum Randomness through Emergent Confinement Mechanism in Measured Tensor Network States

• URL: http://arxiv.org/abs/2504.16995v1
• Date: Wed, 23 Apr 2025 18:00:02 GMT
• Title: Quantum Randomness through Emergent Confinement Mechanism in Measured Tensor Network States
• Authors: Guglielmo Lami, Andrea De Luca, Xhek Turkeshi, Jacopo De Nardis,
• Abstract summary: Large-scale random quantum states are crucial for quantum computing and many-body physics.<n>We present a practical method based on local measurements of random Networks.<n>We show that confinement is a general mechanism underlying random state generation in broader settings.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Randomness is a fundamental aspect of quantum mechanics, arising from the measurement process that collapses superpositions into definite outcomes according to Born's rule. Generating large-scale random quantum states is crucial for quantum computing and many-body physics, yet remains a key challenge. We present a practical method based on local measurements of random Tensor Networks, focusing on random Matrix Product States (MPS) generated by two distinct quantum circuit architectures, both feasible on near-term devices. We certify the emergent quantum randomness using the frame potential and establish a mapping between its behavior and the statistical mechanics of a domain wall particle model. In both architectures, the effect of quantum measurements induces a nontrivial confinement mechanism, where domain walls are either trapped by an external potential or bound in pairs to form meson-like excitations. Our results, supported by both exact analytical calculations and numerical simulations, suggest that confinement is a general mechanism underlying random state generation in broader settings with local measurements, including quantum circuits and chaotic dynamics.

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