  We present an efficient approach for preparing ground states in the context
of strongly interacting local quantum field theories on quantum computers. The
approach produces the vacuum state in a time proportional to the square-root of
the volume, which is a square-root improvement in speed compared to traditional
approaches. The approach exploits a novel method for traversing the path in
parameter space in which the resources scale linearly with a path length
suitably defined in parameter space. Errors due to practical limitations are
controlled and do not exhibit secular growth along the path. The final accuracy
can be arbitrarily improved with an additive cost, which is independent of the
volume and grows slower than logarithmically with the overlap between the state
produced and the exact ground state. We expect that the method could
potentially hold practical value not only within the realm of quantum field
theories but also in addressing other challenges involving long path lengths.
