Researchers propose a way to ease a major obstacle for a widely used simulation technique called Quantum Monte Carlo. The problem, known as the sign problem, makes some quantum many-body simulations grow exponentially hard. The authors show that rotating the local basis of the quantum states reduces the problematic signs in many cases. They benchmark the idea on frustrated Heisenberg antiferromagnets in one dimension and on a two-dimensional “maple-leaf” lattice and report that the improved bases let them reach lower temperatures, comparable to a leading alternative method called numerical linked cluster expansion (NLCE).

The technical idea is simple to state. Quantum Monte Carlo samples many configurations whose statistical weight can be positive or negative. The authors perform local unitary rotations on small clusters of sites (two-site and three-site clusters) to change the representation of the Hamiltonian. They choose the rotations to minimize a cost function called non-stoquasticity, which measures the amount of negative off-diagonal matrix elements in the bond Hamiltonians. This cost can be computed cheaply and without running a full Monte Carlo simulation. In the cases they studied, the local minima of this cost coincide with bases that maximize the average Monte Carlo sign.

At a high level, why this helps is easy to understand. The sign problem appears when the weights sampled by Monte Carlo are not all positive. When that happens the average sign becomes small, and the statistical uncertainty grows exponentially with system size and inverse temperature. Changing the basis changes the matrix elements of the Hamiltonian. By finding bases that reduce negative off-diagonal elements, the method lowers the chance of encountering operator sequences with negative weights. For some known cases, such as fully frustrated ladders, working in a cluster eigenbasis already fixes the sign problem; the authors’ optimization generalizes that idea to search the full space of local rotations.