articles

We are now looking for a first example code to run our CSS-type simulations with. It shall fulfill the commuting condition and have longer code length than the simple 3-qubit / 11-qubit examples we used until now.

Hypergraph product codes were first introduced by Tillich and Zémor [1] in 2014. They are constructed to fulfill the commuting condition by design. Suppose two classical block codes with parity check matrix H_1 of size m_1 \times n_1 and H_2 of size m_2 \times n_2. From this, two larger parity-check matrices H_X and H_Z are constructed, to account for Z-errors and X-errors, respectively.

One fundamental difference between classical bits and qubits is that qubits can suffer from two independent types of errors: amplitude errors and phase errors. These two error types can occur separately or jointly on a given qubit, and a quantum error correction code needs to account for both.

We extend ldpc_dec to handle these two types of error using two codes of matched properties and two decoder instances. We will first review the prerequisites to handle both kinds of errors, and, in a second step, apply the corresponding principles to qLDPC. In other words, we turn our attention now to real quantum error correction.

In this article, we take a first step from classical LDPC towards qLDPC. We discuss how channel information is fed into the decoder and how this impacts the decoding process. To this end, we first take a more detailed look at decoding for classical LDPC codes and then generalize to qLDPC.

To get started with qLDPC, we need a good decoder as a base. It should be simple and easily extendable. I have written many classical Belief-Propagation (BP) decoders in Matlab, C, and C++. For this task, we write a new one from scratch, and use the Rust programming language.

Quantum error correction (QEC) is one of the key challenges in building a fault-tolerant quantum computer and differs significantly from classical error correction coding. The latter is a well-established scientific field with decades of research, while QEC is very active, pushing forward every day.

I am starting resilient quantum, a website dedicated to two topics.

First, a resource for everyone who wants to get familiar with quantum computing. Check the presentations section to get an introduction on quantum computing basics and algorithms.