相关论文: Exact and Approximate Performance of Concatenated …

We prove a new version of the quantum threshold theorem that applies to concatenation of a quantum code that corrects only one error, and we use this theorem to derive a rigorous lower bound on the quantum accuracy threshold epsilon_0. Our…

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,…

I make a rough estimate of the accuracy threshold for fault tolerant quantum computing with concatenated codes. First I consider only gate errors and use the depolarizing channel error model. I will follow P.Shor (quant-ph/9505011) for…

The Gottesman-Knill theorem allows for the efficient simulation of stabilizer-based quantum error-correction circuits. Errors in these circuits are commonly modeled as depolarizing channels by using Monte Carlo methods to insert Pauli gates…

In quantum error correction, the description of noise channel cannot be completely accurate, and fluctuation always appears in noise channel. It is found that when fluctuation of physical noise channel is considered, the average effective…

Recent work on approximate quantum error correction (QEC) has opened up the possibility of constructing subspace codes that protect information with high fidelity in scenarios where perfect error correction is impossible. Motivated by this,…

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…

We identify optimal quantum error correction codes for situations that do not admit perfect correction. We provide analytic n-qubit results for standard cases with correlated errors on multiple qubits and demonstrate significant…

Classical simulations of noisy stabilizer circuits are often used to estimate the threshold of a quantum error-correcting code. Physical noise sources are efficiently approximated by random insertions of Pauli operators. For a single qubit,…

We study relaxations of entanglement-assisted quantum channel coding and establish that non-signaling assistance and a natural semi-definite programming relaxation\, -- \,termed meta-converse\, -- \,are equivalent in terms of success…

One of the main problems for the future of practical quantum computing is to stabilize the computation against unwanted interactions with the environment and imperfections in the applied operations. Existing proposals for quantum memories…

It is shown that, if the loss of entanglement along a quantum channel is sufficiently small, then approximate quantum error correction is possible, thereby generalizing what happens for coherent information. Explicit bounds are obtained for…

Typical studies of quantum error correction assume probabilistic Pauli noise, largely because it is relatively easy to analyze and simulate. Consequently, the effective logical noise due to physically realistic coherent errors is relatively…

We compare the effect of single qubit incoherent and coherent errors on the logical error rate of the Steane [[7,1,3]] quantum error correction code by performing an exact full-density-matrix simulation of an error correction step. We find…

We exhibit a simple, systematic procedure for detecting and correcting errors using any of the recently reported quantum error-correcting codes. The procedure is shown explicitly for a code in which one qubit is mapped into five. The…

We study quasi-exact quantum error correcting codes and quantum computation with them. A quasi-exact code is an approximate code such that it contains a finite number of scaling parameters, the tuning of which can flow it to corresponding…

We have previously (quant-ph/9608012) shown that for quantum memories and quantum communication, a state can be transmitted over arbitrary distances with error $\epsilon$ provided each gate has error at most $c\epsilon$. We discuss a…

We study the properties of error correcting codes for noise models in the presence of asymmetries and/or correlations by means of the entanglement fidelity and the code entropy. First, we consider a dephasing Markovian memory channel and…

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…

We derive necessary and sufficient conditions for the approximate correctability of a quantum code, generalizing the Knill-Laflamme conditions for exact error correction. Our measure of success of the recovery operation is the worst-case…