On Bloch-type functions with Hadamard gaps

We give some sufficient and necessary conditions for an analytic function f on the unit ball B with Hadamard gaps, that is, for ,∞ as well as to the corresponding little space. A remark on analytic functions with Hadamard gaps on mixed norm space on the unit disk is also given

On Bloch-Type Functions with Hadamard Gaps

We give some sufficient and necessary conditions for an analytic function f on the unit ball B with Hadamard gaps, that is, for f(z)=∑k=1∞Pnk(z) (the homogeneous polynomial expansion of f) satisfying nk+1/nk≥λ>1 for all k∈ℕ, to belong to the space ℬpα(B)={f|sup0<r<1(1−r2)α\|ℛfr\|p<∞,f∈H(B)}, p=1,2,∞ as well as to the corresponding little space. A remark on analytic functions with Hadamard gaps on mixed norm space on the unit disk is also given

Layered architecture for quantum computing

We develop a layered quantum computer architecture, which is a systematic framework for tackling the individual challenges of developing a quantum computer while constructing a cohesive device design. We discuss many of the prominent techniques for implementing circuit-model quantum computing and introduce several new methods, with an emphasis on employing surface code quantum error correction. In doing so, we propose a new quantum computer architecture based on optical control of quantum dots. The timescales of physical hardware operations and logical, error-corrected quantum gates differ by several orders of magnitude. By dividing functionality into layers, we can design and analyze subsystems independently, demonstrating the value of our layered architectural approach. Using this concrete hardware platform, we provide resource analysis for executing fault-tolerant quantum algorithms for integer factoring and quantum simulation, finding that the quantum dot architecture we study could solve such problems on the timescale of days.Comment: 27 pages, 20 figure