We construct a qubit regularization of the O(3) non-linear sigma model in two and three spatial dimensions using a quantum Hamiltonian with two qubits per lattice site. Using a worldline formulation and worm algorithms, we show that in two spatial dimensions our model has a quantum critical point where the well-known scale-invariant physics of the three-dimensional Wilson-Fisher fixed point is reproduced. In three spatial dimensions, we recover mean-field critical exponents at a similar quantum critical point. These results show that our qubit Hamiltonian is in the same universality class as the traditional classical lattice model close to the critical points. Simple modifications to our model also allow us to study the physics of traditional lattice models with O(2) and Z2 symmetries close to the corresponding critical points.

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We analyze two-derivative two-nucleon interactions in a combined pionless effective field theory and large-Nc expansion. At leading order in the large-Nc expansion, relationships among lowenergy constants emerge. We find these to be consistent with experiment. However, it is critical to correctly address the subtraction-point dependence of the low-energy constants. These results provide additional confidence that the dual-expansion procedure is useful for analyzing low-energy few-body observables.

We formulate the physics of two species of nonrelativistic hard-core bosons with attractive or repulsive delta function interactions on a spacetime lattice in the worldline approach. We show that worm algorithms can efficiently sample the worldline configurations in any fixed particle-number sector if the chemical potential is tuned carefully. Since fermions can be treated as hard-core bosons up to a permutation sign, we apply this approach to study nonrelativistic fermions. The fermion permutation sign is an observable in this approach and can be used to extract energies in each particle-number sector. In one dimension, nonrelativistic fermions can only permute across boundaries, and so our approach does not suffer from sign problems in many cases, unlike the auxiliary field method. Using our approach, we discover limitations of the recently proposed complex Langevin calculations in one spatial dimension for some parameter regimes. In higher dimensions, our method suffers from the usual fermion sign problem. Here we provide evidence that it may be possible to alleviate this problem for few-body physics.