Renormalization group and approximate error correction

Approximate Quantum Error Correction

X iv :q ua nt -p h/ 01 12 10 6v 1 1 8 D ec 2 00 1 Approximate quantum error correction Benjamin Schumacher and Michael D. Westmoreland February 1, 2008 Department of Physics, Kenyon College, Gambier, OH 43022 USA Department of Mathematical Sciences, Denison University, Granville, OH 43023 USA Abstract The errors that arise in a quantum channel can be corrected perfectly if and only if the chann...

The Exact Renormalization Group and Approximate Solutions

We investigate the structure of Polchinski’s formulation of the flow equations for the continuum Wilson effective action. Reinterpretations in terms of I.R. cutoff greens functions are given. A promising non-perturbative approximation scheme is derived by carefully taking the sharp cutoff limit and expanding in ‘irrelevancy’ of operators. We illustrate with two simple models of four dimensional...

Approximate Solutions of Exact Renormalization Group Equations

We study exact renormalization group equations in the framework of the effective average action. We present analytical approximate solutions for the scale dependence of the potential in a variety of models. These solutions display a rich spectrum of physical behaviour such as fixed points governing the universal behaviour near second order phase transitions, critical exponents, first order tran...

Entanglement and Approximate Quantum Error Correction

The possibility of performing quantum error correction obviously lies behind and justifies the vast efforts made up to now in order to develop quantum computation techniques, since it allows fault-tolerant computationeven when quantum systems—in fact extremely sensitive to noise—are considered as the basic carriers of information. Besides well-known algebraic conditions for exact quantum error ...

Renormalization Group Renormalization Group