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Abstract Twisted bilayer graphene (TBG) has drawn significant interest due to recent experiments which show that TBG can exhibit strongly correlated behavior such as the superconducting and correlated insulator phases. Much of the theoretical work on TBG has been based on analysis of the Bistritzer-MacDonald model which includes a phenomenological parameter to account for lattice relaxation. In this work, we use a newly developed continuum model which systematically accounts for the effects of structural relaxation. In particular, we model structural relaxation by coupling linear elasticity to a stacking energy that penalizes disregistry. We compare the impact of the two relaxation models on the corresponding many-body model by defining an interacting model projected to the flat bands. We perform tests at charge neutrality at both the Hartree-Fock and Coupled Cluster Singles and Doubles (CCSD) level of theory and find the systematic relaxation model gives quantitative differences from the simplified relaxation model. 

Reinforcement learning with neural networks (RLNN) has recently demonstrated great promise for many problems, including some problems in quantum information theory. In this work, we apply reinforcement learning to quantum hypothesis testing, where one designs measurements that can distinguish between multiple quantum states while minimizing the error probability. Although the Helstrom measurement is known to be optimal when there are m=2 states, the general problem of finding a minimal-error measurement is challenging. Additionally, in the case where the candidate states correspond to a quantum system with many qubit subsystems, implementing the optimal measurement on the entire system may be impractical. In this work, we develop locally-adaptive measurement strategies that are experimentally feasible in the sense that only one quantum subsystem is measured in each round. RLNN is used to find the optimal measurement protocol for arbitrary sets of tensor product quantum states. Numerical results for the network performance are shown. In special cases, the neural network testing-policy achieves the same probability of success as the optimal collective measurement. 

Discriminating between quantum states is a fundamental task in quantum information theory. Given two quantum states, ρ+ and ρ− , the Helstrom measurement distinguishes between them with minimal probability of error. However, finding and experimentally implementing the Helstrom measurement can be challenging for quantum states on many qubits. Due to this difficulty, there is a great interest in identifying local measurement schemes which are close to optimal. In the first part of this work, we generalize previous work by Acin et al. (Phys. Rev. A 71, 032338) and show that a locally greedy (LG) scheme using Bayesian updating can optimally distinguish between any two states that can be written as a tensor product of arbitrary pure states. We then show that the same algorithm cannot distinguish tensor products of mixed states with vanishing error probability (even in a large subsystem limit), and introduce a modified locally-greedy (MLG) scheme with strictly better performance. In the second part of this work, we compare these simple local schemes with a general dynamic programming (DP) approach. The DP approach finds the optimal series of local measurements and optimal order of subsystem measurement to distinguish between the two tensor-product states.