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Research used to hold a sacred place in human society. As we are all seeing firsthand, research is being automated by machines at a rapid pace. I will share some recent experiences and discuss what will remain valuable, what we should do differently, and what research will look like. I don't know the answers, so this will be more of a discussion.

Estimating the ground-state energy of quantum many-body systems is a leading application of quantum computing. For general Hamiltonians, however, the problem is QMA-complete and is therefore unlikely to admit an efficient quantum algorithm. This motivates the search for natural classes of Hamiltonians whose ground-energy problem lies in BQP but is not known to lie in BPP.

In this talk, we identify quantum impurity Hamiltonians as one such class. These Hamiltonians are central to dynamical mean-field theory (DMFT), widely regarded as a gold-standard framework for studying strongly interacting quantum systems. Specifically, by explicitly constructing a guiding state, we give a polynomial-time quantum algorithm that estimates the ground-state energy of quantum impurity Hamiltonians to any inverse polynomial precision. Previously, the best unconditional upper bounds were a quasi-polynomial-time classical algorithm and containment of the corresponding decision problem in QCMA [Bravyi&Gosset arxiv:1609.00735].

Pseudoentangled states are quantum states whose entanglement structure is computationally hard to determine. In particular, given copies of such states, or in some cases even the circuits preparing them, no polynomial-time quantum algorithm can estimate their entanglement entropy across a specified cut. In this talk, I'll discuss a recent result showing that pseudoentangled states can be constructed by 2D-local constant-depth circuits. This gives a strong separation with respect to pseudoerandom states, which cannot be constructed from local constant-depth circuits, and strengthens previous results on the hardness of learning the entanglement structure of local Hamiltonian ground-states.

I will also discuss the backstory for this result, in particular how I used AI tools in order to improve upon my original construction and write the paper.

Based on: https://arxiv.org/abs/2605.31448

No abstract available.

The quantum PCP conjecture is one of the major open problems in quantum complexity theory. It has resisted attack in part because many primitives used in the proof of the classical PCP theorem, such as locality-preserving gap amplification and alphabet reduction, have no obvious quantum analogues due to quantum no-cloning. Locality-preserving gap amplification is a procedure that takes as input a local Hamiltonian problem instance and produces a new instance with a larger promise gap, without increasing the locality of the Hamiltonian, and instead moderately increasing its local qudit dimension. Obtaining this kind of control over the locality during gap amplification is critical to the success of every known strategy for proving the classical PCP theorem. Here, we put forth the first known viable template for quantum locality-preserving gap amplification, and we prove that our procedure amplifies combinatorial gap. Our work introduces a new framework for reasoning about quantum gap amplification in terms of fault-tolerant computation, and illuminates a route toward importing one of the central structural ingredients in classical PCPs into the quantum setting.