GROWTH ESTIMATES FOR DISCRETE QUANTUM GROUPS

Quantum Resource Estimates for Computing Elliptic Curve Discrete Logarithms

We give precise quantum resource estimates for Shor’s algorithm to compute discrete logarithms on elliptic curves over prime fields. The estimates are derived from a simulation of a Toffoli gate network for controlled elliptic curve point addition, implemented within the framework of the quantum computing software tool suite LIQUi|〉. We determine circuit implementations for reversible modular a...

Quasi-Discrete Locally Compact Quantum Groups

Let A be a C *-algebra. Let A ⊗ A be the minimal C *-tensor product of A with itself and let M (A ⊗ A) be the multiplier algebra of A ⊗ A. A comultiplication on A is a non-degenerate *-homomorphism ∆ : A → M (A ⊗ A) satisfying the coassociativity law (∆ ⊗ ι)∆ = (ι ⊗ ∆)∆ where ι is the identity map and where ∆ ⊗ ι and ι ⊗ ∆ are the unique extensions to M (A ⊗ A) of the obvious maps on A ⊗ A. We ...

Paragrassmann Integral, Discrete Systems and Quantum Groups

This report is based on review paper [1]. Some aspects of differential and integral calculi on generalized grassmann (paragrassmann) algebras are considered. The integration over paragrassmann variables is applied to evaluate the partition function for the Z p+1 Potts model on a chain. Finite dimensional paragrassmann representations for GL q (2) are constructed. Generalizations of grassmann al...

Operator Growth Functions of Discrete Groups

A generalizationof the growth functions of nitelygeneratedgroups is introduced, namely the growth functionswith operatorcoeecients g2G gz jgj. The questions of rationality and convergence of such series are discussed. The operator growth functions of surface groups are explicitly computed. The operator geodesic growth functions are also studied.

Structural Properties of Inner Amenable Discrete Groups