Related papers: Optimal correction of independent and correlated e…
Contrary to the assumption that most quantum error-correcting codes (QECC) make, it is expected that phase errors are much more likely than bit errors in physical devices. By employing the entanglement-assisted stabilizer formalism, we…
Quantum error-correcting codes will be the ultimate enabler of a future quantum computing or quantum communication device. This theory forms the cornerstone of practical quantum information theory. We provide several contributions to the…
We investigate the performance of a quantum error-correcting code when pushed beyond its intended capacity to protect information against errors, presenting formulae for the probability of failure when the errors affect more qudits than…
Recent progress in quantum cryptography and quantum computers has given hope to their imminent practical realization. An essential element at the heart of the application of these quantum systems is a quantum error correction scheme. We…
In quantum error correction, it is an important assumption that errors on different qubits are independent. In our previous work [Phys. Rev. A {\bf 92}, 052320 (2015)], the generality of the concatenated five-qubit code has been investgated…
Quantum error correction protects quantum information against environmental noise. When using qubits, a measure of quality of a code is the maximum number of errors that it is able to correct. We show that a suitable notion of ``number of…
In this work we prove that the 5-qubit quantum error correcting code does not fix qubit independent errors, even assuming that the correction circuit does not introduce new errors. We say that a quantum code does not fix a quantum computing…
A quantum error-correcting code is defined to be a unitary mapping (encoding) of k qubits (2-state quantum systems) into a subspace of the quantum state space of n qubits such that if any t of the qubits undergo arbitrary decoherence, not…
Quantum error correction is an essential ingredient for universal quantum computing. Despite tremendous experimental efforts in the study of quantum error correction, to date, there has been no demonstration in the realisation of universal…
Quantum states have high affinity for errors and hence error correction is of utmost importance to realise a quantum computer. Laflamme showed that 5 qubits are necessary to correct a single error on a qubit. In a Pauli error model, four…
We analyze the effect of a quantum error correcting code on the entanglement of encoded logical qubits in the presence of a dephasing interaction with a correlated environment. Such correlated reservoir introduces entanglement between…
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 optimally decoding a quantum error correction code -- that is to find the optimal recovery procedure given the outcomes of partial "check" measurements on the system. In general, this problem is NP-hard. However,…
Certain physical aspects of quantum error correction are discussed for a quantum computer (n-qubit register) in contact with a decohering environment. Under rather plausible assumptions upon the form of the computer-environment interaction,…
We present a semidefinite program optimization approach to quantum error correction that yields codes and recovery procedures that are robust against significant variations in the noise channel. Our approach allows us to optimize the…
Quantum information processing offers dramatic speedups, yet is famously susceptible to decoherence, the process whereby quantum superpositions decay into mutually exclusive classical alternatives, thus robbing quantum computers of their…
We study the performance of common quantum stabilizer codes in the presence of asymmetric and correlated errors. Specifically, we consider the depolarizing noisy quantum memory channel and perform quantum error correction via the five and…
The surface code represents a promising candidate for fault-tolerant quantum computation due to its high error threshold and experimental accessibility with nearest-neighbor interactions. However, current exact surface code threshold…
We identify gauge freedoms in quantum error correction (QEC) codes and introduce strategies for optimal control algorithms to find the gauges which allow the easiest experimental realization. Hereby, the optimal gauge depends on the…
It has recently been shown that there are efficient algorithms for quantum computers to solve certain problems, such as prime factorization, which are intractable to date on classical computers. The chances for practical implementation,…