Super-Golden-Gates for PU(2)
arXiv:1704.02106 · doi:10.1016/j.aim.2017.06.022
Abstract
To each of the symmetry groups of the Platonic solids we adjoin a carefully designed involution yielding topological generators of PU(2) which have optimal covering properties as well as efficient navigation. These are a consequence of optimal strong approximation for integral quadratic forms associated with certain special quaternion algebras and their arithmetic groups. The generators give super efficient 1-qubit quantum gates and are natural building blocks for the design of universal quantum gates.
References in corpus (2)
Cited by in corpus (24)
- Normal form for single-qutrit Clifford+T operators and synthesis of single-qutrit gates
- Quantum complexity in gravity, quantum field theory, and quantum information science
- Shorter quantum circuits via single-qubit gate approximation
- Number-Theoretic Characterizations of Some Restricted Clifford+T Circuits
- A Family of Quantum Codes with Exotic Transversal Gates
- A family of permutationally invariant quantum codes
- Ramanujan complexes and Golden Gates in PU(3)
- Quantum Codes from Twisted Unitary -groups
- Density theorems for GL(n)
- Complexity of strong approximation on the sphere
- Expansion in simple groups
- Cutoff on Hyperbolic Surfaces
- From Ramanujan Graphs to Ramanujan Complexes
- Cutoff on Graphs and the Sarnak-Xue Density of Eigenvalues
- The Siegel variance formula for quadratic forms
- Optimal Diophantine Exponents for
- How smooth is quantum complexity?
- The exact convergence rate in the ergodic theorem of Lubotzky Phillips Sarnak
- Tessellation codes: encoded quantum gates by geometric rotation
- Measurement-free code-switching for low overhead quantum computation using permutation invariant codes
- -Ramanujan Graphs
- Quantitative equidistribution of angles of multipliers
- Synthesis of Single Qutrit Circuits from Clifford+R
- Gaussian primes in almost all narrow sectors