Related papers: Local Dimension Invariant Qudit Stabilizer Codes
Quantum error correction (QEC) plays a critical role in preventing information loss in quantum systems and provides a framework for reliable quantum computation. Identifying quantum codes with nice code parameters for physically motivated…
Fault-tolerant quantum computation allows quantum computations to be carried out while resisting unwanted noise. Several error-correcting codes have been developed to achieve this task, but none alone are capable of universal quantum…
Quantum error correcting (QEC) stabilizer codes enable protection of quantum information against errors during storage and processing. Simulation of noisy QEC codes is used to identify the noise parameters necessary for advantageous…
Instead of a quantum computer where the fundamental units are 2-dimensional qubits, we can consider a quantum computer made up of d-dimensional systems. There is a straightforward generalization of the class of stabilizer codes to…
Simulating open quantum systems on quantum computers presents a fundamental challenge: open quantum dynamics are intrinsically nonunitary, whereas quantum computers operate through unitary evolution. Conventional approaches overcome this…
The presence of noise in quantum computers hinders their effective operation. Even though quantum error correction can theoretically remedy this problem, its practical realization is still a challenge. Testing and benchmarking noisy,…
Is the notion of a quantum computer resilient to thermal noise unphysical? We address this question from a constructive perspective and show that local quantum Hamiltonian models provide self-correcting quantum computers. To this end, we…
It is shown that the noise process in quantum computation can be described by spatially correlated decoherence and dissipation. We demonstrate that the conventional quantum error correcting codes correcting for single-qubit errors are…
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 quantum error correction provides a scheme by which the effects…
We introduce a class of cyclic quantum codes, basing the construction not on the simplicity of the stabilizers, but rather on the simplicity of preparation of a code state (at least in the absence of noise). We show how certain known codes,…
Fault-tolerant quantum computation demands extremely low logical error rates, yet superconducting qubit arrays are subject to radiation-induced correlated noise arising from cosmic-ray muon-generated quasiparticles. The quasiparticle…
Quantum error correction requires the use of error syndromes derived from measurements that may be unreliable. Recently, quantum data-syndrome (QDS) codes have been proposed as a possible approach to protect against both data and syndrome…
Quantum error correction and the use of quantum error correction codes is likely to be essential for the realisation of practical quantum computing. Because the error models of quantum devices vary widely, quantum codes which are tailored…
Quantum computers have steadily improved over the last decade, but developing fault-tolerant quantum computing (FTQC) techniques, required for useful, universal computation remains an ongoing effort. Key elements of FTQC such as…
We investigate stabilizer codes with carrier qudits of equal dimension $D$, an arbitrary integer greater than 1. We prove that there is a direct relation between the dimension of a qudit stabilizer code and the size of its corresponding…
Quantum computers have now appeared in our society and are utilized for the investigation of science and engineering. At present, they have been built as intermediate-size computers containing about fifty qubits and are weak against noise…
We discuss stabilizer quantum-error correction codes implemented in a single multi-level qudit to avoid resource escalation typical of multi-qubit codes. These codes can be customized to the specific physical errors on the qudit,…
We present a fault-tolerant universal quantum computing architecture based on a code concatenation of biased-noise qubits and the parity architecture. The parity architecture can be understood as an LDPC code tailored specifically to obtain…
Good quantum codes, such as quantum MDS codes, are typically nondegenerate, meaning that errors of small weight require active error-correction, which is--paradoxically--itself prone to errors. Decoherence free subspaces, on the other hand,…
We apply quantum Construction X on quasi-cyclic codes with large Hermitian hulls over $\mathbb{F}_4$ and $\mathbb{F}_9$ to derive good qubit and qutrit stabilizer codes, respectively. In several occasions we obtain quantum codes with…