Related papers: Superselection Rules, Quantum Error Correction, an…
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…
Quantum error correction is required to compensate for the fragility of the state of a quantum computer. We report the first experimental implementations of quantum error correction and confirm the expected state stabilization. In NMR…
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.…
I consider the theory of quantum error correcting code (QECC) where each quantum particle has more than two possible eigenstates. In this higher spin system, I report an explicit QECC that is related to the symmetry group ${\Bbb…
The most general method for encoding quantum information is not to encode the information into a subspace of a Hilbert space, but to encode information into a subsystem of a Hilbert space. Recently this notion has led to a more general…
High-rate quantum error correcting codes mitigate the imposing scale of fault-tolerant quantum computers but require efficient generation of non-local, many-body entanglement. We provide a linear-optical architecture with these properties,…
We present a method of concatenated quantum error correction in which improved classical processing is used with existing quantum codes and fault-tolerant circuits to more reliably correct errors. Rather than correcting each level of a…
We prove an accuracy threshold theorem for fault-tolerant quantum computation based on error detection and postselection. Our proof provides a rigorous foundation for the scheme suggested by Knill, in which preparation circuits for ancilla…
We show that superselection rules do not enhance the information-theoretic security of quantum cryptographic protocols. Our analysis employs two quite different methods. The first method uses the concept of a reference system -- in a world…
We generalize the construction of quantum error-correcting codes from GF(4)-linear codes by Calderbank et al. to p^m-state systems. Then we show how to determine the error from a syndrome. Finally we discuss a systematic construction of…
Robust quantum computation requires encoding delicate quantum information into degrees of freedom that are hard for the environment to change. Quantum encodings have been demonstrated in many physical systems by observing and correcting…
We describe a quantum error correction scheme aimed at protecting a flow of quantum information over long distance communication. It is largely inspired by the theory of classical convolutional codes which are used in similar circumstances…
The quantum error correction theory is as a rule formulated in a rather convoluted way, in comparison to classical algebraic theory. This work revisits the error correction in a noisy quantum channel so as to make it intelligible to…
The process of dynamical decoherence may cause apparent superselection rules, which are sometimes called `environmentally induced' or `soft'. A natural question is whether such dynamical processes are eventually also responsible for at…
This report surveys quantum error-correcting codes. As Preskill claimed, 21st century would be the golden age of quantum error correction. Quantum channels behave differently from classical channels, so researchers face difficulties in…
It is conjectured that quantum computers are able to solve certain problems more quickly than any deterministic or probabilistic computer. A quantum computer exploits the rules of quantum mechanics to speed up computations. However, it is a…
Quantum information theory has shown strong connections with classical statistical physics. For example, quantum error correcting codes like the surface and the color code present a tolerance to qubit loss that is related to the classical…
It is important to protect quantum information against decoherence and operational errors, and quantum error-correcting (QEC) codes are the keys to solving this problem. Of course, just the existence of codes is not efficient. It is…
Quantum error correction was invented to allow for fault-tolerant quantum computation. Systems with topological order turned out to give a natural physical realization of quantum error correcting codes (QECC) in their groundspaces. More…
Error-correction process has to be carried out periodically to prevent accumulation of errors in fault-tolerant quantum computation. It is believed that the best choice to get maximum threshold value is carrying out an error-correction…