Related papers: Phases of decodability in the surface code with un…
Ergodic quantum many-body systems undergoing unitary dynamics evolve towards increasingly entangled states characterized by an extensive scaling of entanglement entropy with system volume. At the other extreme, quantum systems repeatedly…
In this work, we develop a reduced complexity maximum likelihood (ML) decoder for quantum low-density parity-check (QLDPC) codes over erasures. Our decoder combines classical inactivation decoding, which integrates peeling with symbolic…
Surface codes are one of the most important topological stabilizer codes in the theory of quantum error correction. In this paper, we provide an efficient way to obtain surface codes through Measurement-based quantum computation (MBQC)…
Undersampled inverse problems occur everywhere in the sciences including medical imaging, radar, astronomy etc., yielding underdetermined linear or non-linear reconstruction problems. There are now a myriad of techniques to design decoders…
Quantum information theory and strongly correlated electron systems share a common theme of macroscopic quantum entanglement. In both topological error correction codes and theories of quantum materials (spin liquid, heavy fermion and…
We study exact decoding for the toric code and for planar and rotated surface codes under the standard independent \(X/Z\) noise model, focusing on Separate Minimum Weight (SMW) decoding and Separate Most Likely Coset (SMLC) decoding. For…
We analyze the dynamics of entanglement entropy in a generic quantum many-body open system from the perspective of quantum information and error corrections. We introduce a random unitary circuit model with intermittent projective…
We consider the problem of a generic stabilizer Hamiltonian under local, incoherent Pauli errors. Using two different approaches -- (i) Haah's polynomial formalism arXiv:1204.1063 and (ii) the homological perspective on CSS codes -- we…
We study how heralded qubit losses during the preparation of a two-dimensional cluster state, a universal resource state for one-way quantum computation, affect its computational power. Above the percolation threshold we present a…
The scaling law, a cornerstone of Large Language Model (LLM) development, predicts improvements in model performance with increasing computational resources. Yet, while empirically validated, its theoretical underpinnings remain poorly…
A set of linearly constrained permutation matrices are proposed for constructing a class of permutation codes. Making use of linear constraints imposed on the permutation matrices, we can formulate a minimum Euclidian distance decoding…
The surface code is a promising candidate for fault-tolerant quantum computation and has been implemented in many quantum hardware platforms. In this work, we propose a new non-local unitary circuit to encode a surface code state based on a…
To improve the efficiency of the encoding and the decoding is the important problem in the quantum error correction. In a preceding work, a general algorithm for decoding the stabilizer code is shown. This paper will show an decoding which…
We consider the problem of calculating the logical error probability for a stabilizer quantum code subject to random Pauli errors. To access the regime of large code distances where logical errors are extremely unlikely we adopt the…
Machine learning has the potential to become an important tool in quantum error correction as it allows the decoder to adapt to the error distribution of a quantum chip. An additional motivation for using neural networks is the fact that…
This paper investigates the problem of variable-length lossy source coding allowing a positive excess distortion probability and an overflow probability of codeword lengths. Novel one-shot achievability and converse bounds of the optimal…
A new class of folded subspace codes for noncoherent network coding is presented. The codes can correct insertions and deletions beyond the unique decoding radius for any code rate $R\in[0,1]$. An efficient interpolation-based decoding…
The surface code is a many-body quantum system, and simulating it in generic conditions is computationally hard. While the surface code is believed to have a high threshold, the numerical simulations used to establish this threshold are…
We examine the robustness of a logical qubit in the planar surface code subject to 'measurement-errors', i.e., to local Pauli measurements at known positions. This yields a measurement-only dynamics, which is driven by the competition…
This dissertation focuses on fountain codes under maximum likelihood (ML) decoding. First LT codes are considered under a practical and widely used ML decoding algorithm known as inactivation decoding. Different analysis techniques are…