  Nonreversible Markov chains can outperform reversible chains in the Markov
chain Monte Carlo method. Lifting is a versatile approach to introducing net
stochastic flow in state space and constructing a nonreversible Markov chain.
We present here an application of the lifting technique to the directed-worm
algorithm. The transition probability of the worm update is optimized using the
geometric allocation approach; the worm backscattering probability is
minimized, and the stochastic flow breaking the detailed balance is maximized.
We demonstrate the performance improvement over the previous worm and cluster
algorithms for the four-dimensional hypercubic lattice Ising model. The
sampling efficiency of the present algorithm is approximately 80, 5, and 1.7
times as high as those of the standard worm algorithm, the Wolff cluster
algorithm, and the previous lifted worm algorithm, respectively. We estimate
the dynamic critical exponent of the hypercubic lattice Ising model to be $z
\approx 0$ in the worm and the Wolff cluster updates. The lifted version of the
directed-worm algorithm can be applied to a variety of quantum systems as well
as classical systems.
