Hybrid quantum computation – where one makes simultaneous use of continuous and discrete variables at the same time, is a interesting variant of standard quantum computation. In this paper, we proposed a version of hybrid quantum computers that involved a single squeezed state, together with a reservoir of completely mixed states. This is reminiscent of standard DQC1, which involves a single pure qubit together with a completely mixed reservoir.

What is particular interesting here is that this model gives us a nice way to compare different algorithms by how much squeezing they demand. Computing the normalised trace of a exponentially large matrix (standard DQC1), for example, requires only coherent states – no squeezing is required regardless of the size of the matrix. To factor, however, we need squeezing (as measured by how many factors less noisy it is compared to a vacuum state) that scales exponentially with number being factored.

- Power of one qumode for quantum computation

*Nana Liu, Jayne Thompson, Christian Weedbrook, Seth Lloyd, Vlatko Vedral, Mile Gu, and Kavan Modi*

Phys. Rev. A**93**, 052304 – Published 3 May 2016