Chiral spin liquids and quantum error-correcting codes

One-point Goppa Codes on Some Genus 3 Curves with Applications in Quantum Error-Correcting Codes

We investigate one-point algebraic geometric codes CL(D, G) associated to maximal curves recently characterized by Tafazolian and Torres given by the affine equation yl = f(x), where f(x) is a separable polynomial of degree r relatively prime to l. We mainly focus on the curve y4 = x3 +x and Picard curves given by the equations y3 = x4-x and y3 = x4 -1. As a result, we obtain exact value of min...

Constacyclic Codes over Group Ring (Zq[v])/G

Recently, codes over some special finite rings especially chain rings have been studied. More recently, codes over finite non-chain rings have been also considered. Study on codes over such rings or rings in general is motivated by the existence of some special maps called Gray maps whose images give codes over fields. Quantum error-correcting (QEC) codes play a crucial role in protecting quantum ...

Correcting Quantum Errors In Higher Spin Systems

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 Z 2 ⊗SN . This QECC, which generalizes Shor’s simple majority vote code, is able to correct errors arising from exactly one quantum particle. I also provide a simple encoding ...

Spin glass reflection of the decoding transition for quantum error correcting codes

Chiral spin states and superconductivity.

It is shown that several different order parameters can be used to characterize a type of P and T -violating state for spin systems, that we call chiral spin states. There is a closely related, precise notion of chiral spin liquid states. We construct soluble models, based on P and T symmetric local spin Hamiltonians, with chiral spin ground states. Mean field theories leading to chiral spin li...