Results 861 - 870 of 24440
We describe how to construct emergent strong higher-form symmetries in mixed quantum states that act unitarily on Hilbert space. Our construction uses (quasi-)local recovery channels from quantum error correction to some nearby simple (stabilizer or more general commuting projector) model. We show that when the recovery is done in an appropriate (deterministic) manner, the resulting operators continue to be unitary. When applied to operators acting on topologically non-trivial sub-manifolds (loops, surfaces), the resulting unitaries inherit the logical algebra of the fixed point model. More generally, the unitarity of the emergent symmetries allows one to define emergent excitations whose statistics follow those of the fixed point limit.
The study of entanglement in many-body quantum systems has provided connections between physical properties and the computational resources required for tensor network calculations. In this talk, I will construct rigorous upper bounds on half-system entanglement entropies of states with fixed energy expectation values. These upper bounds are expressed in terms of thermal entropies of subsystems. For frustration-free systems this result shows that, when zero-temperature thermal entropies are proportional to subsystem surface areas, ground states are area-law entangled. In more general systems, and at subextensive energies, the behavior of the specific heat at low temperatures controls the scaling of entanglement with system size. For large classes of systems with conventional thermodynamic properties, I will show that the upper bounds are optimal up to subleading corrections.
Preparing low-energy states of many-body Hamiltonians is a central challenge in quantum computing, quantum complexity, and condensed matter physics. Existing approaches often get trapped in suboptimal states such as high-energy eigenstates or, more generally, low-variance states that resist further energy reduction. In this work, we explore a different perspective: instead of optimizing with respect to a single Hamiltonian, we leverage the fact that many systems admit families of Hamiltonians that share similar low-energy subspaces but differ at higher energies. We show that this redundancy can be turned into an algorithmic resource by establishing an energy-based uncertainty principle, which implies that these Hamiltonians cannot simultaneously admit low-variance states at higher energies. This suggests a simple strategy of alternating energy-lowering steps across such Hamiltonians to destabilize trapped states and enable continued descent. We investigate this approach numerically on models including the 1D AKLT chain and Heisenberg models on general graphs, and observe consistent improvements over standard methods. We also introduce a sparse variant where the uncertainty principle strengthens to yield quadratically larger variance at higher energies, leading to possibly more pronounced energy reduction. Overall, this work suggests a range of open questions at the interface of random matrix theory, local Hamiltonians and state preparation, aimed at understanding when such approaches are practical and how they can be analyzed rigorously.
Abstract not available.
Abstract not available.