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Quantum computation holds the promise of solving certain complex problems exponentially faster than classical computers. However, the high prevalent noise in current quantum devices impedes the accurate execution of even basic algorithms.…
We introduce a new weight and corresponding metric over finite extension fields for asymmetric error correction. The weight distinguishes between elements from the base field and the ones outside of it, which is motivated by asymmetric…
We consider the problem of correcting the errors incurred from sending classical or quantum information through a noisy quantum environment by schemes using classical information obtained from a measurement on the environment. We give a…
In this paper, we address the problem of state communication in finite-level quantum systems through noise-affected channels. Our approach is based on a self-consistent theory of decoding inner products associated with the code and error…
Fault tolerant quantum computing methods which work with efficient quantum error correcting codes are discussed. Several new techniques are introduced to restrict accumulation of errors before or during the recovery. Classes of eligible…
A quantum channel models the interaction between the system we are interested in and its environment. Such a model can capture the main features of the interaction but because of the complexity of the environment we can not assume that it…
Recent advancements in quantum computing have enabled practical use of quantum error detecting and correcting codes. However, current architectures and future proposals of quantum computer design suffer from limited qubit counts,…
Most previous efforts of quantum error correction focused on either extending classical error correction schemes to the quantum regime by performing a perfect correction on a subset of errors, or seeking a recovery operation to maximize the…
Variational hybrid quantum-classical optimization represents one of the most promising avenue to show the advantage of nowadays noisy intermediate-scale quantum computers in solving hard problems, such as finding the minimum-energy state of…
Quantum error-correcting codes so far proposed have not worked in the presence of noise which introduces more than one bit of entropy per qubit sent through a quantum channel, nor can any code which identifies the complete error syndrome.…
To run large-scale algorithms on a quantum computer, error-correcting codes must be able to perform a fundamental set of operations, called logic gates, while isolating the encoded information from…
Error-correcting codes are usually envisioned to counter errors by operating unitary corrections depending on the projective measurement results of some syndrome observables. We here propose a way to use them in a more integrated way, where…
Coherent control errors, for which ideal Hamiltonians are perturbed by unknown multiplicative noise terms, are a major obstacle for reliable quantum computing. In this paper, we present a framework for analyzing the robustness of quantum…
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…
In practical communication and computation systems, errors occur predominantly in adjacent positions rather than in a random manner. In this paper, we develop a stabilizer formalism for quantum burst error correction codes (QBECC) to combat…
Quantum error correction is widely thought to be the key to fault-tolerant quantum computation. However, determining the most suited encoding for unknown error channels or specific laboratory setups is highly challenging. Here, we present a…
While quantum algorithms for solving large scale systems of linear equations offer potentially exponential speedups, their application has largely been confined to sparse matrices. This work extends the scope of these algorithms to a broad…
We use density matrix simulations to study the performance of three distance three quantum error correcting codes in the context of the rare-earth-ion-doped crystal (RE) platform for quantum computing. We analyze pseudothresholds for these…
Machine learning has the potential to become an important tool in quantum error correction as it allows the decoder to adapt to the error distribution of a quantum chip. An additional motivation for using neural networks is the fact that…
In recent years quantum error correction(QEC) has become an important part of AdS/CFT. Unfortunately, there are no field-theoretic arguments about why QEC holds in known holographic systems. The purpose of this paper is to fill this gap by…