Related papers: A note on quantum error correction with continuous…
Quantum error correction is essential for achieving fault-tolerant quantum computation. However, most typical quantum error-correcting codes are designed for generic noise models, which may fail to accurately capture the intricate noise…
To perform reliable quantum computation, quantum error correction is indispensable. In certain cases, continuous covariance symmetry of the physical system can make exact error correction impossible. In this work we study the approximate…
Quantum error correction assisted by entanglement helps to transmit the encoded qudits through quantum channels with some of them being noiseless. Here we consider a more realistic scheme for experiments what we called as partial-noisy…
We present a fault-tolerant [[8, 1, 3]] non-CSS quantum error correcting code and study its logical error rates. We choose the unitary encoding procedure for stabilizer codes given by Gottesman and modify it to suit the setting of a class…
Quantum computers will eventually reach a size at which quantum error correction becomes imperative. Quantum information can be protected from qubit imperfections and flawed control operations by encoding a single logical qubit in multiple…
Covariant codes are quantum codes such that a symmetry transformation on the logical system could be realized by a symmetry transformation on the physical system, usually with limited capability of performing quantum error correction (an…
Continuous quantum error correction has been found to have certain advantages over discrete quantum error correction, such as a reduction in hardware resources and the elimination of error mechanisms introduced by having entangling gates…
The importance of quantum error correction in paving the way to build a practical quantum computer is no longer in doubt. This dissertation makes a threefold contribution to the mathematical theory of quantum error-correcting codes.…
Quantum error correction (QEC) is an essential concept for any quantum information processing device. Typically, QEC is designed with minimal assumptions about the noise process; this generic assumption exacts a high cost in efficiency and…
In many physical systems it is expected that environmental decoherence will exhibit an asymmetry between dephasing and relaxation that may result in qubits experiencing discrete phase errors more frequently than discrete bit errors. In the…
Scalable quantum computing and communication requires the protection of quantum information from the detrimental effects of decoherence and noise. Previous work tackling this problem has relied on the original circuit model for quantum…
We present an efficient approach to continuous-time quantum error correction that extends the low-dimensional quantum filtering methodology developed by van Handel and Mabuchi [quant-ph/0511221 (2005)] to include error recovery operations…
Concatenating quantum error correction codes scales error correction capability by driving logical error rates down double-exponentially across levels. However, the noise structure shifts under concatenation, making it hard to choose an…
We present sparse graph codes appropriate for use in quantum error-correction. Quantum error-correcting codes based on sparse graphs are of interest for three reasons. First, the best codes currently known for classical channels are based…
We describe a qubit encoded in continuous quantum variables of an rf superconducting quantum interference device. Since the number of accessible states in the system is infinite, we may protect its two-dimensional subspace from small errors…
Characterizing and mitigating errors in current noisy intermediate-scale devices is important to improve performance of next generations of quantum hardware. In order to investigate the importance of the different noise mechanisms affecting…
We present a general approach to error detection of bosonic quantum error-correction codes via an adaptive quantum phase estimation algorithm assisted by a single ancilla qubit. The approach is applicable to a broad class of bosonic codes…
We describe a scheme for quantum error correction that employs feedback and weak measurement rather than the standard tools of projective measurement and fast controlled unitary gates. The advantage of this scheme over previous protocols…
In this thesis we examine a variety of techniques for reducing the resources required for fault-tolerant quantum computation. First, we show how to simplify universal encoded computation by using only transversal gates and standard error…
The purpose of this little survey is to give a simple description of the main approaches to quantum error correction and quantum fault-tolerance. Our goal is to convey the necessary intuitions both for the problems and their solutions in…