Related papers: Quantum error correction with degenerate codes for…
Quantum technologies have shown immeasurable potential to effectively solve several information processing tasks such as prime number factorization, unstructured database search or complex macromolecule simulation. As a result of such…
Quantum information can be protected from decoherence and other errors, but only if these errors are sufficiently rare. For quantum computation to become a scalable technology, practical schemes for quantum error correction that can…
Degenerate quantum codes are codes that do not reveal the complete error syndrome. Their ability to conceal the complete error syndrome makes them powerful resources in certain quantum information processing tasks. In particular, the most…
The Heisenberg limit provides a quadratic improvement over the standard quantum limit, and is the maximum quantum advantage that quantum sensors could provide over classical methods. This limit remains elusive, however, because of the…
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 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…
To exploit a given physical system for quantum information processing, it is critical to understand the different types of noise affecting quantum control. Distinguishing coherent and incoherent errors is extremely useful as they can be…
Quantum convolutional code was introduced recently as an alternative way to protect vital quantum information. To complete the analysis of quantum convolutional code, I report a way to decode certain quantum convolutional codes based on the…
Errors are inevitable during all kinds quantum informational tasks and quantum error-correcting codes (QECCs) are powerful tools to fight various quantum noises. For standard QECCs physical systems have the same number of energy levels.…
Quantum error correction is a critical component for scaling up quantum computing. Given a quantum code, an optimal decoder maps the measured code violations to the most likely error that occurred, but its cost scales exponentially with the…
Quantum error correction is widely believed to be essential for large-scale quantum computation, but the required qubit overhead remains a central challenge. Quantum low-density parity-check codes can substantially reduce this overhead…
Noise is ubiquitous in quantum systems and is a major obstacle for the advancement of quantum information science. Noise-robust quantum control achieves high-fidelity operations by engineering the evolution path so that first-order noise…
The design of block codes for short information blocks (e.g., a thousand or less information bits) is an open research problem that is gaining relevance thanks to emerging applications in wireless communication networks. In this paper, we…
The parameters of a nondegenerate quantum code must obey the Hamming bound. An important open problem in quantum coding theory is whether or not the parameters of a degenerate quantum code can violate this bound for nondegenerate quantum…
Erasures are the primary type of errors in physical systems dominated by leakage errors. While quantum error correction (QEC) using stabilizer codes can combat erasure errors, it remains unknown which constructions achieve capacity…
This paper aims to give an overview of the current state of fault-tolerant quantum computing, by surveying a number of results in the field. We show that thresholds can be obtained for a simple noise model as first proved in [AB97, Kit97,…
Quantum error correction protocols have been developed to offset the high sensitivity to noise inherent in quantum systems. However, much is still unknown about the behaviour of a quantum error-correcting code under general noise, including…
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 computers and simulators can potentially outperform classical computers in finding ground states of classical and quantum Hamiltonians. However, if this advantage can persist in the presence of noise without error correction remains…
We study the effectiveness of quantum error correction against coherent noise. Coherent errors (for example, unitary noise) can interfere constructively, so that in some cases the average infidelity of a quantum circuit subjected to…