# Universal quantum computing with thermal state bosonic systems

## TL;DR

This paper introduces a simplified mixed-state encoding for bosonic systems that enables deterministic initialization and logical operations using only continuous-variable interactions, potentially broadening quantum computing hardware options.

## Contribution

The authors propose a new MSE scheme that encodes each qubit in a single mixed-state bosonic mode with deterministic initialization, avoiding previous operational drawbacks.

## Key findings

- Deterministic logical state initialization from thermal equilibrium.
- Logical operations performed solely with continuous-variable interactions.
- Enhanced noise tolerance without ground state cooling requirements.

## Abstract

Recent development of mixed-state encoding (MSE) allows pure-state logical information to be encoded by a bosonic (continuous-variable) system in mixed physical state. Despite interest due to its counter-intuitiveness, the utility of the current MSE scheme is limited due to several operational drawbacks, namely redundant information carrier, probabilistic initialisation, and requirement of discrete-variable measurement. In this work, we present a simplified MSE that does not suffer from any of these drawbacks. Specifically, our protocol encodes each qubit by only one mixed-state bosonic mode, and the logical basis can be deterministically initialised from thermal equilibrium. All logical operations of this encoding can be performed with continuous-variable interaction and measurement only. Without the necessity of ground state cooling, our proposal could broaden the set of candidate systems for implementing quantum computers, and reduce the reliance on demanding refrigerating facility for current quantum computing architectures. Additionally, our protocol can enhance the noise tolerance of logical qubit even if the system can be efficiently cooled.