We suggest concrete models for self-correcting quantum memory by reporting examples of local stabilizer codes in 3D that have no string logical operators. Previously known local stabilizer codes in 3D all have stringlike logical operators, which make the codes non-self-correcting. We introduce a notion of “logical string segments” to avoid difficulties in defining one-dimensional objects in dis...

In order to use quantum error-correcting codes to improve the performance of a quantum computer, it is necessary to be able to perform operations fault-tolerantly on encoded states. I present a theory of fault-tolerant operations on stabilizer codes based on symmetries of the code stabilizer. This allows a straightforward determination of which operations can be performed fault-tolerantly on a ...

The stabilizer code is the most general algebraic construction of quantum error-correcting codes proposed so far. A stabilizer code can be constructed from a self-orthogonal subspace of a symplectic space over a finite field. We propose a construction method of such a selforthogonal space using an algebraic curve. By using the proposed method we construct an asymptotically good sequence of bina...

We show the equivalence of two approaches to the design of entanglement distillation protocols. The first approach is based on local unitary operations that yield permutations of tensor products of Bell states. The second approach is based on stabilizer codes.

Group Operations Definition. Let G be a group and S a set. An operation of G on S is a rule for combining elements g ∈ G and s ∈ S so that gs ∈ S, such that 1s = s for all s, and (gg’)s = g(g’s) for all g, g’, and s. With this operation, S is called a G-set. Definition. Let s ∈ S, with S a G-set. The orbit of s is the set Os = {s’ ∈ S | s’ = gs for some g ∈ G}. Proposition. S is a union of disj...

We study the nucleation and propagation of the normal zone in large composite superconductors, considering the relatively long time of current redistribution in the stabilizer. We propose a model treating the composite as an effective electrical circuit, which yields two diffusion equations for the electric current and temperature distributions along the conductor. Numerical simulations are per...

We prove that if X is a meromorphic subvariety of a commutative meromorphic group G and X has finite stabilizer, then X is contained in a translate of an algebraic subgroup of G. We give an application with a “diophantine” flavour.

This paper examines the first-best fiscal policy in a stochastic, infinite-horizon representative agent model that exhibits consumption-enhanced as well as wealth-enhanced social status in the household utility. We show that the first-best labor tax rate is a positive constant that is used to correct negative consumption externalities. The first-best capital tax rate is also positive in order t...