Fault-tolerant Preparation of Stabilizer States for Quantum CSS Codes by Classical Error-Correcting Codes

TL;DR

This paper introduces methods to fault-tolerantly prepare a broad class of CSS stabilizer states for quantum error correction, utilizing classical coding techniques to reduce resource costs and improve error correction frequency.

Contribution

It presents novel distillation protocols for CSS stabilizer states and demonstrates how classical codes can optimize ancilla usage in quantum syndrome extraction.

Findings

Protocols enable fault-tolerant preparation of CSS states

Classical coding reduces ancilla consumption in syndrome extraction

Increased error correction frequency lowers effective error rates

Abstract

Stabilizer states are extensively studied in quantum information theory for their structures based on the Pauli group. Calderbank-Shor-Steane (CSS) stabilizer states are of particular importance in their application to fault-tolerant quantum computation (FTQC). However, how to fault-tolerantly prepare arbitrary CSS stabilizer states for general CSS stabilizer codes is still unknown, and their preparation can be highly costly in computational resources. In this paper, we show how to prepare a large class of CSS stabilizer states useful for FTQC. We propose distillation protocols using syndrome encoding by classical codes or quantum CSS codes. Along the same lines, we show that classical coding techniques can reduce the ancilla consumption in Steane syndrome extraction by using additional transversal controlled-NOT gates and classical computing power. In the scenario of a fixed ancilla consumption rate, we can increase the frequency of quantum error correction and effectively lower the error rate.