Related papers: Stabilizer-Code Channel Transforms Beyond Repetiti…
We consider coding schemes for computationally bounded channels, which can introduce an arbitrary set of errors as long as (a) the fraction of errors is bounded with high probability by a parameter $p$ and (b) the process which adds the…
We present a unifying approach to quantum error correcting code design that encompasses additive (stabilizer) codes, as well as all known examples of nonadditive codes with good parameters. We use this framework to generate new codes with…
Preparing arbitrary logical states is a central primitive for universal fault-tolerant quantum computation and the cost of encoded-state preparation contributes directly to the overall resource overhead. This makes the synthesis of…
Stabilizer simulation of Clifford quantum circuits - error-correction circuits, Clifford subroutines, etc. - on classical computers has played a central role in our understanding of circuit performance. The stabilizer description, however,…
Quantum stabilizer codes constructed from sparse matrices have good performance and can be efficiently decoded by belief propagation (BP). A conventional BP decoding algorithm treats binary stabilizer codes as additive codes over GF(4).…
Tailored topological stabilizer codes in two dimensions have been shown to exhibit high storage threshold error rates and improved subthreshold performance under biased Pauli noise. Three-dimensional (3D) topological codes can allow for…
In this paper we estimate the fidelity of stabilizer and CSS codes. First, we derive a lower bound on the fidelity of a stabilizer code via its quantum enumerator. Next, we find the average quantum enumerators of the ensembles of finite…
We propose a method to detect lower bounds to quantum capacities of a noisy quantum communication channel by means of few measurements. The method is easily implementable and does not require any knowledge about the channel. We test its…
In the context of measurement-based quantum computation a way of maintaining the coherence of a graph state is to measure its stabilizer operators. Aside from performing quantum error correction, it is possible to exploit the information…
We construct an explicit quantum coding scheme which achieves a communication rate not less than the coherent information when used to transmit quantum information over a noisy quantum channel. For Pauli and erasure channels we also present…
We consider the fundamental protocol of dense coding of classical information assuming that noise affects both the forward and backward communication lines between Alice and Bob. Assuming that this noise is described by the same quantum…
Stochastic encoders for channel coding and lossy source coding are introduced with a rate close to the fundamental limits, where the only restriction is that the channel input alphabet and the reproduction alphabet of the lossy source code…
Characterizing how quantum error correction circuits behave under realistic hardware noise is essential for testing the premises that enable scalable fault tolerance. Logical error rates conditioned on syndrome outcomes are needed to enable…
Entanglement subject to noise can not be shielded against decaying. But, in case of many noisy channels, the degradation can be partially prevented by using local unitary operations. We consider the effect of local noise on shared quantum…
First, a canonical form for stabilizer parity check matrices of arbitrary size and rank is derived. Next, it is shown that the closely related canonical form of the Clifford group can be computed in time $O(n^3)$ for $n$ qubits, which…
Polarization-adjusted convolutional (PAC) codes were recently proposed and arouse the interest of the channel coding community because they were shown to approach theoretical bounds for the (128,64) code size. In this letter, we propose…
Channel polarization, originally proposed for binary-input channels, is generalized to arbitrary discrete memoryless channels. Specifically, it is shown that when the input alphabet size is a prime number, a similar construction to that for…
Exact quantum codes detecting a prescribed set of Pauli errors are approached through algebraic constructions--stabilizer, codeword-stabilized, permutation-invariant, topological, and related families. Geometrically, exact Pauli detection…
High-fidelity decoding of quantum error correction codes relies on an accurate experimental model of the physical errors occurring in the device. Because error probabilities can depend on the context of the applied operations, the error…
We propose a scalable decoding framework for correcting correlated hook errors in stabilizer measurement circuits. Traditional circuit-level decoding attempts to estimate the precise location of faults by constructing an extended Tanner…