A quantum double-bracket algorithm for imaginary-time evolution with exponentially shorter depth

Abstract: Imaginary-time evolution (ITE) is a widely used technique for preparing the ground state of a target Hamiltonian. Building on the recently proposed framework of Double-Bracket quantum ITE (DB-QITE), we introduce a probabilistic variant (PDBQITE) that achieves an exponential reduction in circuit depth. Our algorithm requires only a single ancilla qubit and a quantum circuit that consists of one controlled real-time evolution and one mid-circuit measurement per iteration. The trade-off is an exponential decay of the total success probability with the number of iterations, for which we derive an analytical lower bound that is independent of system size. Our numerical simulations show that the per-step success probability remains close to unity, making it realistic to execute many iterations, thus providing a substantial improvement over prior constructions. We show that PDBQITE outperforms the near-term probabilistic algorithm PITE for ground-state preparation of molecular Hamiltonians, and that a hybrid QAOA-PDBQITE scheme achieves higher approximation ratios than QAOA at the same circuit depth on random regular graphs for the MaxCut problem.