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We explore what the integrated use of quantum spatial distribution (QSD), or more specifically, superposition of both spin and position states of particles, and gauge symmetry (GS) within stabilizer formalism provides for quantum error…
In this paper we investigate stabilizer quantum error correction codes using controlled phase rotations of strong coherent probe states. We explicitly describe two methods to measure the Pauli operators which generate the stabilizer group…
In this paper we introduce a technique and a tool for formal verification of various quantum information processing protocols. The tool uses stabilizer formalism and is capable of representing concurrent quantum protocol, thus is more…
In this paper, we introduce a new family of stabilizer quantum LDPC codes derived from the classical linear codes $L_k$ and $L_k^{+}$, defined via sub-exceding functions. In previous work, these codes demonstrated strong performance in…
Qudits offer significant advantages over qubit-based architectures, including more efficient gate compilation, reduced resource requirements, improved error-correction primitives, and enhanced capabilities for quantum communication and…
Bosonic codes utilize the infinite-dimensional Hilbert space of harmonic oscillators to encode quantum information, offering a hardware-efficient approach to quantum error correction. Designing these codes requires precise geometric…
Fault-tolerant quantum computation critically depends on architectures uniting high encoding rates with physical implementability. Quantum low-density parity-check (qLDPC) codes, including bivariate bicycle (BB) codes, achieve dramatic…
Quantum computers promise to efficiently solve important problems classical computers never will. However, in order to capitalize on these prospects, a fully automated quantum software stack needs to be developed. This involves a multitude…
Given their potential for fault-tolerant operations, topological quantum states are currently the focus of intense activity. Of particular interest are topological quantum error correction codes, such as the surface and planar stabilizer…
We introduce quantum pin codes: a class of quantum CSS codes. Quantum pin codes are a generalization of quantum color codes and Reed-Muller codes and share a lot of their structure and properties. Pin codes have gauge operators, an…
The article surveys quantum error control, focusing on quantum stabilizer codes, stressing on the how to use classical codes to design good quantum codes. It is to appear as a book chapter in "A Concise Encyclopedia of Coding Theory,"…
The development of quantum codes with good error correction parameters and useful sets of transversal gates is a problem of major interest in quantum error-correction. Abundant prior works have studied transversal gates which are restricted…
Storing quantum information in a quantum error correction code can protect it from errors, but the ability to transform the stored quantum information in a fault tolerant way is equally important. Logical Pauli group operators can be…
Quantum error correction is a crucial technology for fault tolerant quantum computing. On superconducting platforms, hardware defects in large scale quantum processors can disrupt the regular lattice structure of topological codes and…
In practical communication and computation systems, errors occur predominantly in adjacent positions rather than in a random manner. In this paper, we develop a stabilizer formalism for quantum burst error correction codes (QBECC) to combat…
Quantum error correction (QEC) requires the execution of deep quantum circuits with large numbers of physical qubits to protect information against errors. Designing protocols that can reduce gate and space-time overheads of QEC is…
Quantum error correction allows for faulty quantum systems to behave in an effectively error free manner. One important class of techniques for quantum error correction is the class of quantum subsystem codes, which are relevant both to…
Quantum error correction is an essential ingredient in the development of quantum technologies. Its subject is to investigate ways to embed quantum Hilbert spaces into a physical system such that this subspace is robust against small…
Quantum low-density parity-check (qLDPC) codes are promising candidates for fault-tolerant quantum computation due to their high encoding rates and distances. However, implementing logical operations using qLDPC codes presents significant…
Sensitivity to noise makes most of the current quantum computing schemes prone to error and nonscalable, allowing only for small proof-of-principle devices. Topologically-protected quantum computing aims at solving this problem by encoding…