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Having protected quantum information is essential to perform quantum computations. One possibility is to reduce the number of particles needing to be protected from noise and instead use systems with more states, so called qudit quantum…
Quantum error correction plays an important role in fault-tolerant quantum information processing. It is usually difficult to experimentally realize quantum error correction, as it requires multiple qubits and quantum gates with high…
Quantum error correction plays a critical role in enabling fault-tolerant quantum computing by protecting fragile quantum information from noise. While general-purpose quantum error correction codes are designed to address a wide range of…
Quantum error correction (QEC) aims to mitigate the loss of quantum information to the environment, which is a critical requirement for practical quantum computing. Existing QEC implementations heavily rely on measurement-based feedback,…
Quantum computing has emerged as a promising alternative for solving combinatorial optimization problems. The standard approach for encoding optimization problems on quantum processing units (QPUs) involves transforming them into their…
Quantum error correction codes (QECC) are a key component for realizing the potential of quantum computing. QECC, as its classical counterpart (ECC), enables the reduction of error rates, by distributing quantum logical information across…
The integration of quantum error correction codes and homomorphic encryption schemes is essential for achieving fault-tolerant secure cloud quantum computing. However, owing to the significant overheads associated with these schemes, their…
I develop methods for analyzing quantum error-correcting codes, and use these methods to construct an infinite class of codes saturating the quantum Hamming bound. These codes encode $k=n-j-2$ qubits in $n=2^j$ qubits and correct $t=1$…
The code that combines channel estimation and error protection has received general attention recently, and has been considered a promising methodology to compensate multi-path fading effect. It has been shown by simulations that such code…
Fault-tolerant quantum computation (FTQC) is expected to address a wide range of computational problems. To realize large-scale FTQC, it is essential to encode logical qubits using quantum error-correcting codes. High-rate concatenated…
The noise model of deletions poses significant challenges in coding theory, with basic questions like the capacity of the binary deletion channel still being open. In this paper, we study the harder model of worst-case deletions, with a…
With the advent of physical qubits exhibiting strong noise bias, it becomes increasingly relevant to identify which quantum gates can be efficiently implemented on error-correcting codes designed to address a single dominant error type.…
Bosonic quantum error correcting codes are primarily designed to protect against single-photon loss. To correct for this type of error, one can encode the logical qubit in code spaces with a definite photon parity, such as cat codes or…
Up to now every good quantum error-correcting code discovered has had the structure of an eigenspace of an Abelian group generated by tensor products of Pauli matrices; such codes are known as stabilizer or additive codes. In this letter we…
Entanglement-assisted quantum error correcting codes (EAQECCs) play a significant role in protecting quantum information from decoherence and quantum noise. Recently, constructing entanglement-assisted quantum maximum distance separable…
We describe the theory of quantum convolutional error correcting codes. These codes are aimed at protecting a flow of quantum information over long distance communication. They are largely inspired by their classical analogs which are used…
The design of block codes for short information blocks (e.g., a thousand or less information bits) is an open research problem that is gaining relevance thanks to emerging applications in wireless communication networks. In this paper, we…
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…
The complexity of the error correction circuitry forces us to design quantum error correction codes capable of correcting a single error per error correction cycle. Yet, time-correlated error are common for physical implementations of…
Quantum error correction is widely thought to be the key to fault-tolerant quantum computation. However, determining the most suited encoding for unknown error channels or specific laboratory setups is highly challenging. Here, we present a…