Weight-sharing Transformer quantum states with Suzuki–Trotter decompositions

Transformer quantum states (TQS) achieve competitive accuracy on frustrated spin systems, yet their reliance on increasing the parameter count offers limited systematic control of the accuracy–efficiency trade-off in variational Monte Carlo. We propose a weight-sharing TQS that treats a single encoder block as a short imaginary-time propagator for discrete imaginary-time evolution. Within each block, we embed Suzuki–Trotter decompositions to increase the local approximation order, thereby improving accuracy without adding trainable parameters. In this framework, depth sets the total imaginary time and acts as a learned low-energy projector, providing a tunable accuracy control at fixed parameter count. On the square-lattice $J_1$–$J_2$ Heisenberg model, it attains accuracy comparable to conventional non-weight-sharing TQS while using fewer parameters.