Topological Quantum Computing, Apparatus, System and Method

Abstract

A quantum computer, quantum logic circuit, material for forming qubits, and method of operating a quantum computer is described. The material is formed from a quasicrystal or quasicrystalline approximant. In some examples, topological quantum computing is performed based on the quasicrystal or quasicrystalline approximant materials. Quasicrystals and quasicrystalline approximate materials have materials properties that can be adapted to perform quantum computing. In one example, the material is a Tsai-type quasicrystalline approximant with a material structure selected to permit qubits to be generated.

What is claimed is: 
     
         1 . A quantum computer, comprising:
 a fault tolerant topological quantum computer based on qubits in a quasicrystal or quasicrystalline approximant material.   
     
     
         2 . The quantum computer of  claim 1 , wherein the fault tolerant topological computer utilizes a quantum topological spin network formalism (TQFT) based on a quantum code. 
     
     
         3 . The quantum computer of  claim 1 , wherein the qubits are based on entangled spin states in the quasicrystal or quasicrystalline approximant material. 
     
     
         4 . The quantum computer of  claim 1 , wherein the material is a Tsai-type quasicrystalline approximant material. 
     
     
         5 . A topological quantum computing device, comprising:
 a quasicrystal or quasicrystalline approximant material configured to form qubits, wherein each qubit comprises a plurality of quasiparticles of the quasicrystal or quasicrystal approximant material.   
     
     
         6 . The topological quantum computing device of  claim 5 , wherein the quasicrystal or quasicrystalline approximant material is selected to have anyonic properties. 
     
     
         7 . The topological quantum computing device of  claim 5 , wherein the quasicrystal or quasicrystalline approximant material is a spin network. 
     
     
         8 . The topological quantum computing device of  claim 5 , wherein the qubits comprise entangled quantum states of a topological spin network of the quasicrystal or quasicrystalline approximant material. 
     
     
         9 . The topological quantum computing device of  claim 5 , wherein the quasicrystal or a quasicrystalline approximant material comprises ensembles of atoms selected based on an entanglement entropy. 
     
     
         10 . The topological quantum computing device of  claim 5 , wherein the material is a quasicrystalline approximant and ensembles of atoms in the quasicrystalline approximant material comprise guest atomic clusters having a first symmetry within a cage structure having a second symmetry. 
     
     
         11 . The topological quantum computing device of  claim 10 , wherein the material comprises a Tsai-type quasicrystal approximant having a guest atomic cluster within a cage structure. 
     
     
         12 . The topological quantum computing device of  claim 11 , wherein the qubits are a quantum correlated network of fermionic tetrahedral cores across the bulk of the Tsai-type quasicrystalline approximant. 
     
     
         13 . The topological quantum computing device of  claim 5 , wherein each qubit is a quantum superposition of a finite set of energetically allowed molecular dipole spin orientations within the quasicrystal or quasicrystal approximant. 
     
     
         14 . The topological quantum computing device of  claim 5 , wherein each qubit is formed from a plurality of quasiparticles in a quasicrystalline spin network. 
     
     
         15 . The topological quantum computing device of  claim 5 , wherein information in the qubits is encoded in non-local braiding of atomic ensembles of the quasicrystal or quasicrystal approximant. 
     
     
         16 . The topological quantum computing device of  claim 5 , wherein each qubit is a single spin system and a controller selects a duration of a pulse at a resonant frequency to rotate a spin of the qubit to a selected angle. 
     
     
         17 . The topological quantum computing device of  claim 5 , wherein each qubit is a two-spin system and a controller selects a duration of a pulse at a resonant frequency to rotate a spin of the qubit to a selected angle. 
     
     
         18 . A method of performing topological quantum computing, comprising:
 generating a qubit formed from a plurality of quasiparticles of a quasicrystal or quasicrystal approximant material; and   performing a quantum computation using the qubit.   
     
     
         19 . The method of the example of  claim 18 , wherein the qubit is formed from a plurality of quasiparticles in a quasicrystalline spin network. 
     
     
         20 . The method of the example of  claim 18 , wherein information in the qubit is encoded in non-local braiding of atomic ensembles of the quasicrystal or quasicrystal approximant.