We study classical and quantum LDPC codes of constant rate obtained by the lifted product
construction over non-abelian groups. We show that the obtained families of quantum LDPC …

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 …

The quantum computing devices of today have tens to hundreds of qubits that are highly
susceptible to noise due to unwanted interactions with their environment. The theory of …

Some form of quantum error correction is necessary to produce large-scale fault-tolerant
quantum computers and finds broad relevance in physics. Most studies customarily assume …

A bstract We explicitly construct a class of holographic quantum error correction codes with
non-trivial centers in the code subalgebra. Specifically, we use the Bacon-Shor codes and …

We introduce the hemicubic codes, a family of quantum codes obtained by associating
qubits with the $ p $-faces of the $ n $-cube (for $ n\gt p $) and stabilizer constraints with …

Complexity theory typically focuses on the difficulty of solving computational problems using
classical inputs and outputs, even with a quantum computer. In the quantum world, it is …

In this work, we develop the theory of quasi-exact fault-tolerant quantum (QEQ) computation,
which uses qubits encoded into quasi-exact quantum error-correction codes ('quasi codes') …

We discuss families of approximate quantum error correcting codes which arise as the
nearly-degenerate ground states of certain quantum many-body Hamiltonians composed of …

The quantum PCP conjecture is one of the central open questions in quantum complexity
theory. It asserts that calculating even a rough approximation to the ground energy of a local …