Dominik Kufel

Helia Kamal, Dominik Kufel, DinhDuy Vu et al.

A recent article [Phys. Rev. X 15, 011047 (2025)] utilizes group-equivariant convolutional neural networks to study the ground state of the kagome Heisenberg antiferromagnet. On the largest finite-size cluster studied to date ($N=108$), the authors report variational energies significantly lower than other numerical methods, including state-of-the-art density matrix renormalization group (DMRG) calculations. In contrast to previous results suggesting a possible spin-liquid ground state, the authors observe a spinon pair-density-wave ground state. We find that: (i) the reported low energies are artifacts of broken ergodicity in the Metropolis--Hastings sampling, since the single-spin-flip update rule utilized by the authors effectively freezes the Markov chains; and (ii) when ergodic sampling is enforced via spin-exchange updates, the neural network converges to energies significantly higher than existing DMRG results, calling the paper's claims into question.

Thomas Schuster, Dominik Kufel, Norman Y. Yao et al.

We prove that recognizing the phase of matter of an unknown quantum state is quantum computationally hard. More specifically, we show that the quantum computational time of any phase recognition algorithm must grow exponentially in the range of correlations $ξ$ of the unknown state. This exponential growth renders the problem practically infeasible for even moderate correlation ranges, and leads to super-polynomial quantum computational time in the system size $n$ whenever $ξ= ω(\log n)$. Our results apply to a substantial portion of all known phases of matter, including symmetry-breaking phases and symmetry-protected topological phases for any discrete on-site symmetry group in any spatial dimension. To establish this hardness, we extend the study of pseudorandom unitaries (PRUs) to quantum systems with symmetries. We prove that symmetric PRUs exist under standard cryptographic conjectures, and can be constructed in extremely low circuit depths. We also establish hardness for systems with translation invariance and purely classical phases of matter. A key technical limitation is that the locality of the parent Hamiltonians of the states we consider is linear in $ξ$; the complexity of phase recognition for Hamiltonians with constant locality remains an important open question.

Andrea Boskovic, Qinyi Chen, Dominik Kufel et al.

In order for an e-commerce platform to maximize its revenue, it must recommend customers items they are most likely to purchase. However, the company often has business constraints on these items, such as the number of each item in stock. In this work, our goal is to recommend items to users as they arrive on a webpage sequentially, in an online manner, in order to maximize reward for a company, but also satisfy budget constraints. We first approach the simpler online problem in which the customers arrive as a stationary Poisson process, and present an integrated algorithm that performs online optimization and online learning together. We then make the model more complicated but more realistic, treating the arrival processes as non-stationary Poisson processes. To deal with heterogeneous customer arrivals, we propose a time segmentation algorithm that converts a non-stationary problem into a series of stationary problems. Experiments conducted on large-scale synthetic data demonstrate the effectiveness and efficiency of our proposed approaches on solving constrained resource allocation problems.