We present lrux, a JAX-based software package for fast low-rank updates of determinants and Pfaffians, targeting the dominant computational bottleneck in various quantum Monte Carlo (QMC) algorithms. The package implements efficient low-rank updates that reduce the cost of successive wavefunction evaluations from
O(n3) to
O(n2k) when the update rank
k is smaller than the dimension
n of matrices. Both determinant and Pfaffian updates are supported, together with delayed-update strategies that trade floating-point operations for reduced memory traffic on modern accelerators. lrux natively integrates with JAX transformations such as JIT compilation, vectorization, and automatic differentiation, and supports both real and complex data types. Benchmarks on GPUs demonstrate up to
1000× speedup at large matrix sizes. lrux enables scalable, high-performance evaluation of antisymmetric wavefunctions and is designed as a drop-in component for a wide range of QMC workflows. lrux is available at https://github.com/ChenAo-Phys/lrux.
We propose a novel algorithm for calculating the ground-state energy of quantum many-body systems by combining auxiliary-field quantum Monte Carlo (AFQMC) with tensor-train sketching. In AFQMC, a good trial wavefunction to guide the random walk is crucial for improving the sampling efficiency and controlling the sign problem. Our proposed method iterates between determining a new trial wavefunction in the form of a tensor train, derived from the current walkers, and using this updated trial wavefunction to anchor the next phase of AFQMC. Numerical results demonstrate that the algorithm is highly accurate for large spin systems. The overlap between the estimated trial wavefunction and the ground-state wavefunction also achieves high fidelity. We additionally provide a convergence analysis, highlighting how an effective trial wavefunction can reduce the variance in the AFQMC energy estimation. From a complementary perspective, our algorithm also extends the reach of tensor-train methods for studying quantum many-body systems.
The fixed-node diffusion quantum Monte Carlo (DMC) method is the most accurate method known for calculating the energies of large many-particle quantum systems. The key element of the method is the development of accurate trial many-body wavefunctions which control the statistical efficiency of the calculations and the accuracy obtained. Accurate wavefunctions can be obtained by building correlation effects on top of mean field descriptions such as density functional theory. The wavefunctions can be improved by introducing multi-determinants, pairing functions, and backflow transformations. The calculations are expensive, but the method scales well with system size and calculations on 1000 particles are possible. Some recent applications of the DMC method to atoms, molecules and solids will be presented.