لغز الكم: كيف تجمع القياسات الحالات المعقدة سريع

الملخص الأصلي

كما كتبه المؤلفون، بالإنجليزية arXiv:2608.08821v1

Quantum circuits with measurements and unitary feedback (MF) can prepare long-range entangled states in constant depth, but a systematic construction of the MF preparation circuit for a given target state remains underexplored. We develop such a scheme for one-dimensional states, based on the notion of pushable defects: virtual-bond operators of a matrix product state that can be pushed through the tensor at the price of a physical feedback unitary. We show that the set of pushable defects, together with their pushing relations classifies finite-depth MF-preparable states and dictates their preparation circuits. To each class of the target state $$|A\rangle$$, we associate a state $$|B\rangle$$ from which $$|A\rangle$$ can be prepared using a 1-round MF circuit; in particular, $$|A\rangle$$ is preparable from a product state using a circuit with 1 round of MF whenever $$|B\rangle$$ is preparable by a finite-depth local unitary (FDLU) circuit. For a general target state, the scheme is obtained by iterating this procedure until the associated state is FDLU-preparable. For open-boundary matrix product states, the scheme is complete: it constructs a preparation circuit whenever finite-depth MF preparation with left-conditioned feedback corrections is possible. Pushable defects and pushing relations thus emerge as a unifying principle for quantum state preparation via measurements and feedback. This characterization further reveals an intrinsic connection between MF circuits and non-invertible symmetries: states with certain classes of pushing relations are related to a product state by Tambara-Yamagami duality operators, or by continuous cosine symmetry operators with fusion rules $$L_{\alpha} L_{\alpha'} = L_{\alpha+\alpha'} + L_{\alpha-\alpha'}$$, together with their generalizations up to (not necessarily transversal) gates.