# Magic State Distillation: Not as Costly as You Think

## TL;DR

This paper shows that magic state distillation can be much less costly than previously thought by optimizing circuit design and encoding strategies, potentially making fault-tolerant quantum computing more practical.

## Contribution

It introduces a new circuit formulation that separates error-detecting qubits, enabling low-distance encoding and reducing resource costs significantly.

## Key findings

- Most logical qubits for distillation can be encoded at low code distance.
- Distillation can cost less than a logical Clifford gate in some cases.
- Resource overhead for magic state distillation is substantially reduced.

## Abstract

Despite significant overhead reductions since its first proposal, magic state distillation is often considered to be a very costly procedure that dominates the resource cost of fault-tolerant quantum computers. The goal of this work is to demonstrate that this is not true. By writing distillation circuits in a form that separates qubits that are capable of error detection from those that are not, most logical qubits used for distillation can be encoded at a very low code distance. This significantly reduces the space-time cost of distillation, as well as the number of qubits. In extreme cases, it can cost less to distill a magic state than to perform a logical Clifford gate on full-distance logical qubits.