![]() Therefore, one has to mitigate the resulting noise and decoherence effects to avoid computational errors. However, it is a formidable task to build a quantum computer, since the quantum mechanical systems storing the information unavoidably interact with their environment. A quantum computer exploits the rules of quantum mechanics to speed up computations. For all capacities considered, we find that a large variety of techniques are useful in establishing bounds.It is conjectured that quantum computers are able to solve certain problems more quickly than any deterministic or probabilistic computer. We compare these bounds with the max-Rains information bound, the mutual information bound, and another bound based on approximate covariance. These bounds are based on the squashed entanglement, and they are established by constructing particular squashing channels. We also establish upper bounds on the two-way assisted quantum and private capacities of the GADC. ![]() Our upper bounds on the quantum capacity of the GADC are tighter than the known upper bound reported recently in for the entire parameter range of the GADC, thus reducing the gap between the lower and upper bounds. These bounds are based on data-processing inequalities and the uniform continuity of information-theoretic quantities, as well as other techniques. We then establish several upper bounds on its classical, quantum, and private capacities. We first determine the parameter range for which the GADC is entanglement breaking and the range for which it is anti-degradable. In this work, we provide an information-theoretic study of the GADC. S in the presence of background noise for low-temperature systems. It can be viewed as the qubit analogue of the bosonic thermal channel, and it thus can be used to model lossy processe The generalized amplitude damping channel (GADC) is one of the sources of noise in superconducting-circuit-based quantum computing. The encoding, syndrome measurement, and syndrome recovery operations can all be implemented with Clifford group operations. Both classes are stabilizer codes, and have good fidelity performance with stabilizer recovery operations. These have significantly higher rates with shorter block lengths than corresponding generic quantum error correcting codes. We present two classes of channel-adapted quantum error correcting codes specifically designed for the amplitude damping channel. Using Lagrange duality, we bound the performance of the structured recovery operations and show that they are nearly optimal in many relevant cases. These structured operations are more computationally scalable than the SDP required for computing the optimal we can thus numerically analyze longer codes. We present computational algorithms to generate near-optimal recovery operations structured to begin with a projective syndrome measurement. This is solvable via a semidefinite program (SDP). We present a convex optimization method to determine the optimal (in terms of average entanglement fidelity) recovery operation for a given channel, encoding, and information source. We may choose quantum error correcting codes and recovery operations that specifically target the most likely errors. In physical systems, errors are not likely to be arbitrary rather we will have reasonable models for the structure of quantum decoherence. Typically, QEC is designed with minimal assumptions about the noise process this generic assumption exacts a high cost in efficiency and performancĮ. Quantum error correction (QEC) is an essential concept for any quantum information processing device.
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