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Quantum error correction codes (QECCs) play a central role in both quantum communications and quantum computation. Practical quantum error correction codes, such as stabilizer codes, are generally structured to suit a specific use, and…
We show that within any quantum stabilizer code there lurks a classical binary linear code with similar error-correcting capabilities, thereby demonstrating new connections between quantum codes and classical codes. Using this result --…
The realization of quantum error correction protocols whose logical error rates are suppressed far below physical error rates relies on an intricate combination: the error-correcting code's efficiency, the syndrome extraction circuit's…
Quantum stabilizer codes often struggle with syndrome errors due to measurement imperfections. Typically, multiple rounds of syndrome extraction are employed to ensure reliable error information. In this paper, we consider phenomenological…
Continuous-variable quantum computing architectures based upon the Gottesmann-Kitaev-Preskill (GKP) encoding have emerged as a promising candidate because one can achieve fault-tolerance with a probabilistic supply of GKP states and…
In this paper we study evaluation codes arising from plane quotients of the Hermitian curve, defined by affine equations of the form $y^q+y=x^m$, $q$ being a prime power and $m$ a positive integer which divides $q+1$. The dual minimum…
It remains an open question whether LLMs can acquire or generalize genuinely new reasoning strategies, beyond the sharpened skills encoded in their parameters during pre-training or post-training. To attempt to answer this debate, we…
Dimensionality reduction on quadratic manifolds augments linear approximations with quadratic correction terms. Previous works rely on linear approximations given by projections onto the first few leading principal components of the…
Concatenating bosonic error-correcting codes with qubit codes can substantially boost the error-correcting power of the original qubit codes. It is not clear how to concatenate optimally, given there are several bosonic codes and…
Relative entropy coding (REC) algorithms encode a sample from a target distribution $Q$ using a proposal distribution $P$ using as few bits as possible. Unlike entropy coding, REC does not assume discrete distributions or require…
We propose a systematic procedure for the construction of graphs associated with binary quantum stabilizer codes. The procedure is characterized by means of the following three step process. First, the stabilizer code is realized as a…
Amongst quantum error-correcting codes the surface code has remained of particular promise as it has local and very low-weight checks, even despite only encoding a single logical qubit no matter the lattice size. In this work we discuss new…
Test-time scaling methods have seen a rapid increase in popularity for its computational efficiency and parameter-independent training to improve reasoning performance on Large Language Models. One such method is called budget forcing, a…
Tensor network codes enable structured construction and manipulation of stabilizer codes out of small seed codes. Here, we apply reinforcement learning to tensor network code geometries and demonstrate how optimal stabilizer codes can be…
Quantum information is fragile and must be protected by a quantum error-correcting code for large-scale practical applications. Recently, highly efficient quantum codes have been discovered which require a high degree of spatial…
The repetition code is an important primitive for the techniques of quantum error correction. Here we implement repetition codes of at most $15$ qubits on the $16$ qubit \emph{ibmqx3} device. Each experiment is run for a single round of…
Scalable realisation of quantum computing is reliant on the development of fault tolerant devices. Analysis of quantum error correction protocols typically considers incoherent noise models or noise-free syndrome measurements. While this is…
Beam search is a widely used approximate search strategy for neural network decoders, and it generally outperforms simple greedy decoding on tasks like machine translation. However, this improvement comes at substantial computational cost.…
We introduce a new class of evaluation linear codes by evaluating polynomials at the roots of a suitable trace function. We give conditions for self-orthogonality of these codes and their subfield-subcodes with respect to the Hermitian…
Practical large-scale quantum computation requires both efficient error correction and robust implementation of logical operations. Three-dimensional (3D) color codes are a promising candidate for fault-tolerant quantum computation due to…