Related papers: Fidelity Lower Bounds for Stabilizer and CSS Quant…
It is important to study the behavior of a t-error correcting quantum code when the number of errors is greater than t, because it is likely that there are also small errors besides t large correctable errors. We give a lower bound for the…
Two observations are given on the fidelity of schemes for quantum information processing. In the first one, we show that the fidelity of a symplectic (stabilizer) code, if properly defined, exactly equals the `probability' of the…
We show that within any quantum stabilizer code there lurks a classical binary linear code with similar error-correcting capabilities, thereby demonstrating new connections between quantum codes and classical codes. Using this result --…
We analyze the performance of quantum stabilizer codes, one of the most important classes for practical implementations, on both symmetric and asymmetric quantum channels. To this aim, we first derive the weight enumerator (WE) for the…
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…
Certifying the fidelity of a prepared state to a target stabilizer state is a fundamental task in quantum information processing. Ref. [Phys. Rev. A 99, 042337 (2019)] gave the optimal worst-case lower bound from one fixed stabilizer…
We study, by means of the stabilizer formalism, a quantum error correcting code which is alternative to the standard block codes since it embeds a qubit into a qudit. The code exploits the non-commutative geometry of discrete phase space to…
The geometric measure, the logarithmic robustness and the relative entropy of entanglement are proved to be equal for a stabilizer quantum codeword. The entanglement upper and lower bounds are determined with the generators of code. The…
The realization of quantum error correction protocols whose logical error rates are suppressed far below physical error rates relies on an intricate combination: the error-correcting code's efficiency, the syndrome extraction circuit's…
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…
Stabilizer codes are a simple and successful class of quantum error-correcting codes. Yet this success comes in spite of some harsh limitations on the ability of these codes to fault-tolerantly compute. Here we introduce a new metric for…
Controlling operational errors and decoherence is one of the major challenges facing the field of quantum computation and other attempts to create specified many-particle entangled states. The field of quantum error correction has developed…
We present techniques that improve the performance of asymmetric stabilizer codes in the presence of unital channels with unknown parameters. Our method estimates the channel parameters using information recovered from syndrome measurements…
There is currently a significant need for robust and efficient methods for characterizing quantum devices. While there has been significant progress in this direction, there remains a crucial need to precisely determine the strength and…
For a number of quantum channels of interest, phase-flip errors occur far more frequently than bit-flip errors. When transmitting across these asymmetric channels, the decoding error rate can be reduced by tailoring the code used to the…
Stabilizer codes lie at the heart of modern quantum-error-correcting codes (QECC). Of particular importance is a class called Calderbank-Shor-Steane (CSS) codes, which includes many important examples such as toric codes, color codes, and…
In Part II we show that there exist quantum codes whose probability of undetected error falls exponentially with the length of the code and derive bounds on this exponent.The lower (existence) bound for stabilizer codes is proved by a…
We construct a three-dimensional Calderbank-Shor-Steane (CSS) stabilizer code on the Face-Centered Cubic (FCC) lattice. Physical qubits reside on the edges of the lattice (coordination $K=12$); X-stabilizers act on octahedral voids and…
We use affine variety codes and their subfield-subcodes for obtaining quantum stabilizer codes via the CSS code construction. With this procedure, we get codes with good parameters and a code whose parameters exceed the CSS quantum…
The disjointness of a stabilizer code is a quantity used to constrain the level of the logical Clifford hierarchy attainable by transversal gates and constant-depth quantum circuits. We show that for any positive integer constant $c$, the…