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Adaptive quantum circuits, which combine local unitary gates, midcircuit measurements, and feedforward operations, have recently emerged as a promising avenue for efficient state preparation, particularly on near-term quantum devices limited to shallow-depth circuits. Matrix product states (MPS) comprise a significant class of many-body entangled states, efficiently describing the ground states of one-dimensional gapped local Hamiltonians and finding applications in a number of recent quantum algorithms. Recently, it has been shown that the Affleck-Kennedy-Lieb-Tasaki state—a paradigmatic example of an MPS—can be exactly prepared with an adaptive quantum circuit of constant depth, an impossible feat with local unitary gates alone due to its nonzero correlation length [Smith , PRX Quantum 4, 020315 (2023)]. In this work, we broaden the scope of this approach and demonstrate that a diverse class of MPS can be exactly prepared using constant-depth adaptive quantum circuits, outperforming theoretically optimal preparation with unitary circuits. We show that this class includes short- and long-ranged entangled MPS, symmetry-protected topological (SPT) and symmetry-broken states, MPS with finite Abelian, non-Abelian, and continuous symmetries, resource states for MBQC, and families of states with tunable correlation length. Moreover, we illustrate the utility of our framework for designing constant-depth sampling protocols, such as for random MPS or for generating MPS in a particular SPT phase. We present sufficient conditions for particular MPS to be preparable in constant time, with global on-site symmetry playing a pivotal role. Altogether, this work demonstrates the immense promise of adaptive quantum circuits for efficiently preparing many-body entangled states and provides explicit algorithms that outperform known protocols to prepare an essential class of states. 

Quantum many-body scar states are highly excited eigenstates of many-body systems that exhibit atypical entanglement and correlation properties relative to typical eigenstates at the same energy density. Scar states also give rise to infinitely long-lived coherent dynamics when the system is prepared in a special initial state having finite overlap with them. Many models with exact scar states have been constructed, but the fate of scarred eigenstates and dynamics when these models are perturbed is difficult to study with classical computational techniques. In this work, we propose state preparation protocols that enable the use of quantum computers to study this question. We present protocols both for individual scar states in a particular model, as well as superpositions of them that give rise to coherent dynamics. For superpositions of scar states, we present both a system-size-linear depth unitary and a finite-depth nonunitary state preparation protocol, the latter of which uses measurement and postselection to reduce the circuit depth. For individual scarred eigenstates, we formulate an exact state preparation approach based on matrix product states that yields quasipolynomial-depth circuits, as well as a variational approach with a polynomial-depth ansatz circuit. We also provide proof of principle state-preparation demonstrations on superconducting quantum hardware. 

Abstract Three recent publications on BEND3 firmly establish its role as a novel sequence‐specific transcription factor that is essential for PRC2 recruitment and maintenance of pluripotency. Here, we briefly review our current understanding of the BEND3‐PRC2 axis in the regulation of pluripotency and also explore the possibility of a similar connection in cancer. 

BEN domain–containing proteins are emerging rapidly as an important class of factors involved in modulating gene expression, yet the molecular basis of how they regulate chromatin function and transcription remains to be established. BEND3 is a quadruple BEN domain–containing protein that associates with heterochromatin and functions as a transcriptional repressor. We find that BEND3 is highly expressed in pluripotent cells, and the induction of differentiation results in the down-regulation of BEND3. The removal of BEND3 from pluripotent cells results in cells exhibiting upregulation of the differentiation-inducing gene expression signature. We find that BEND3 binds to the promoters of differentiation-associated factors and key cell cycle regulators, including CDKN1A , encoding the cell cycle inhibitor p21, and represses the expression of differentiation-associated genes by enhancing H3K27me3 decoration at these promoters. Our results support a model in which transcription repression mediated by BEND3 is essential for normal development and to prevent differentiation.