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Quantum State Design and Emergent Confinement Mechanism in Measured Tensor Network States
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Quantum State Design and Emergent Confinement Mechanism in Measured Tensor Network States
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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.
Forward citations
Cited by 5 Pith papers
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MPS energy landscapes lack poor local minima because gauge freedom induces effective local overparametrization, proven via invariance under orthogonality center moves and confirmed by numerics on random Hamiltonians.
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Absence of poor local minima in matrix product states
MPS energy landscapes lack poor local minima because gauge freedom induces overparametrization that concentrates local minima near the global minimum, with the local minimum distribution proven invariant under orthogo...
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Lecture notes and accompanying library teach replica tensor network methods to compute circuit-averaged observables in random quantum circuits by mapping them to classical statistical mechanics models.
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