Fire and ice: Partially fault-tolerant quantum computing with selective state filtering

TL;DR

This paper proposes a partially fault-tolerant quantum computing scheme combining two error-correcting codes, demonstrating practical scalability despite certain limitations.

Contribution

It introduces a novel concatenation of the Laflamme and Iceberg codes with selective state filtering, balancing error correction and resource efficiency.

Findings

Scheme is reliable at realistic noise rates

Resource efficiency is achieved despite non-fault-tolerance

Provides a practical approach toward scalable quantum computing

Abstract

We develop an error-corrected quantum computation scheme based on concatenating the five-qubit Laflamme code onto the four-qubit Iceberg code. The approach skates a thin line: it is explicitly not fault tolerant, risking higher logical error rates, and it relies on selective filtering to prepare encoded states for error correction, risking significant overhead. Yet, at realistic simulated noise rates, the scheme is reliable and resource efficient. It forges a practical path toward scalable quantum computation.