  Although quantum computers are capable of solving problems like factoring
exponentially faster than the best-known classical algorithms, determining the
resources responsible for their computational power remains unclear. An
important class of problems where quantum computers possess an advantage is
phase estimation, which includes applications like factoring. We introduce a
new computational model based on a single squeezed state resource that can
perform phase estimation, which we call the power of one qumode. This model is
inspired by an interesting computational model known as deterministic quantum
computing with one quantum bit (DQC1). Using the power of one qumode, we
identify that the amount of squeezing is sufficient to quantify the resource
requirements of different computational problems based on phase estimation. In
particular, it establishes a quantitative relationship between the resources
required for factoring and DQC1. For example, we find the squeezing required to
factor has an exponential scaling whereas no squeezing (i.e., a coherent state)
is already sufficient to solve the hardest problem in DQC1.
