"quantum codes"

SLIDES Video The construction of low-density parity check (LDPC) quantum codes has some unique challenges in comparison to classical LDPC codes. While there are classical codes with constant encoding rate and linear distance, so-called good codes, no equivalent statement is known for LDPC quantum codes. Even more severely, no LDPC quantum codes with distance larger than polylog(N)sqrt(N) were known to exist for a long time. Hastings-Haah-O’Donnell recently showed that this apparent polylog(N)sqrt(N) distance barrier can be broken [1].

SLIDES VIDEO This work provides the first explicit and non-random family of [[N,K,D]] LDPC quantum codes which encode K∈Θ(N^4/5) logical qubits with distance D∈Ω(N^3/5). The family is constructed by amalgamating classical codes and Ramanujan graphs via an operation called balanced product. Recently, Hastings–Haah–O’Donnell and Panteleev–Kalachev were the first to show that there exist families of LDPC quantum codes which break the polylog(N)√N distance barrier. How-ever, their constructions are based on probabilistic arguments which only guarantee the code parameters with high probability whereas our bounds hold unconditionally.

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Quantum error correction is an indispensable ingredient for scalable quantum computing. In this Perspective we discuss a particular class of quantum codes called low-density parity-check (LDPC) quantum codes. The codes we discuss are alternatives to …

This work provides the first explicit and non-random family of [[N,K,D]] LDPC quantum codes which encode Theta(N^(4/5)) logical qubits with distance Omega(N^(3/5)). The family is constructed by amalgamating classical codes and Ramanujan graphs via an …

We introduce a technique that uses gauge fixing to significantly improve the quantum error correcting performance of subsystem codes. By changing the order in which check operators are measured, valuable additional information can be gained, and we …

We construct and analyze a family of low-density parity check (LDPC) quantum codes with a linear encoding rate, polynomial scaling distance and efficient decoding schemes. The code family is based on tessellations of closed, four-dimensional, …

Quantum error correcting codes protect quantum computation from errors caused by decoherence and other noise. Here we study the problem of designing logical operations for quantum error correcting codes. We present an automated procedure which …

SLIDES A short talk on quantum error correction at the UCLQ Annual Industry Event 2019. It is aimed towards a broad audience and gives a brief overview over the field as well as an outlook towards the coming 10 years.

QuID 2019 was a summer school aimed towards beginning PhD students to learn about several topics in quantum computing. I contributed a series of three lectures on quantum error correction. The course covered the fault-tolerance theorem, Shor’s code, the stabilizer formalism, topological codes and gate constructions for the surface code. SLIDES 1 SLIDES 2 SLIDES 3