The power of one qumode for quantum computation

TL;DR

This paper introduces the 'power of one qumode', a new quantum computational model using a single squeezed state to perform phase estimation, linking resource requirements like squeezing to problem complexity.

Contribution

It presents a novel model based on a single squeezed state for phase estimation, connecting squeezing resources to computational complexity in quantum algorithms.

Findings

Squeezing quantifies resource needs for phase estimation problems.

Exponential squeezing is needed for factoring, while no squeezing suffices for DQC1.

The model bridges resource requirements between different quantum computational tasks.

Abstract

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.