Silicon based Quantum Computation Thomas Schenkel E O Lawrence Berkeley National Laboratory T Schenkel LBL gov http www ebit lbl gov Thomas Schenkel Accelerator and Fusion Research Berkeley Lab Ion Beam Technology Program Quantum Computation Superconductors Semiconductor Quantum Dots Quantum Hall NMR in liquids Semiconductor Spins 122Te 31P crystal lattice 31P nano arrays by STM STM integration Ion and Atom Traps in Si single e spin detection 31P nano arrays by Single Ion Implantation SII STM SII integration Centre for QC tech Univ of New South Wales Thomas Schenkel Accelerator and Fusion Research 7 qubit demonstration of Shor s algorithm Chuang et co 01 Berkeley Lab SII Integration 31P15 LBNL Ion Beam Technology Program Quantum Information Science and Technology Roadmap our project is part of a focused effort to reach a quantum computation test bed area by 2012 http qist lanl gov Thomas Schenkel Accelerator and Fusion Research Berkeley Lab Ion Beam Technology Program Why quantum computation with dopant spins in silicon 0 Why Quantum Computation Information storage capacity of N qubits 2N Quantum algorithms promise speedups General paradigm of quantum information theory 1 Why in solids Promise of scalability to large N 1000 But solids are a very noisy environment even at low T 2 Why in Silicon Quantum device requirements are converting with trends in classical silicon transistor technology Strong fundamentals for electron and nuclear spins of 31P atoms in a silicon matrix Thomas Schenkel Accelerator and Fusion Research Berkeley Lab Ion Beam Technology Program Moore s Law Gordon Moore Intel exponentially more cheaper faster and smaller transistors Thomas Schenkel Accelerator and Fusion Research Berkeley Lab Ion Beam Technology Program Moore s Law of exponential speedup of silicon transistors Thomas Schenkel Accelerator and Fusion Research Berkeley Lab Ion Beam Technology Program Thomas Schenkel Accelerator and Fusion Research Berkeley Lab Ion Beam Technology Program Transistors The metal oxide semiconductor field effect transistor MOSFET is the basic switching and amplification device of digital electronics The current between the source and drain electrodes is controlled by the gate voltage When the gate voltage is zero no conduction electrons are present in the channel When the gate is at a positive voltage electrons from the source and drain accumulate in the area of the channel close to the gate As the gate voltage is increased further the number of electrons in the channel increases until saturation is reached With no gate voltage electrons in the channel experience a potential that is higher than the bias potential As the gate voltage increases the potential in the channel gradually lowers and electrons accumulate there Thomas Schenkel Accelerator and Fusion Research Berkeley Lab Ion Beam Technology Program Si Lattice constant 0 5 nm Thomas Schenkel Accelerator and Fusion Research Berkeley Lab Cleavelin TI 03 Ion Beam Technology Program Why silicon vastly abundant semiconductor that is easy to work with and that forms a great interface with a dielectric SiO2 Si interface has very low defect density 1010 cm 2V 1 very high degree of control over electrical properties allows larger scale integration compared to other materials with specific advantages GaAs direct band gap for opto electronic integration but much harder to work with forms poor interface to dielectric no nuclear spin free isotopes diamond larger band gap ideal for high temperature operation but difficult to make larger wafers hard to dope Thomas Schenkel Accelerator and Fusion Research Berkeley Lab Ion Beam Technology Program The 31P qubit in silicon P Ne 3s2 3p3 Si Ne 3s2 3p2 one electron to play with for P in Si Thomas Schenkel Accelerator and Fusion Research Berkeley Lab Ion Beam Technology Program The 31P qubit in silicon 31P is a standard n type dopant in silicon one electron is ionized at room temperature and contributes to electrical conduction but at low temperature 70 K this electron remains bound to the P atom with a binding energy of 45 meV and a Bohr radius of 2 5 nm the spin of this electron in a global magnetic field is a very attractive two level system for quantum information processing e g 0 1 the electron spin decoherence time is quite long 60 ms additionally 31P has a nuclear spin of I 1 2 while the nuclear spin of the silicon matrix can be prepared to be I 0 for isotopically pure 28Si the nuclear spin can be addressed very precisely through hyperfine interaction and nuclear spin decoherence times are very very long hours Thomas Schenkel Accelerator and Fusion Research Berkeley Lab Ion Beam Technology Program Criteria for physical implementation of a quantum computer DiVincenzo 1 2 3 4 5 Well defined extendible qubit array stable memory Initialization in the 000 state Long decoherence time 104 operation time to allow for error correction Universal set of gate operations not cnot Read out Single quantum measurements projective measurement 31P donor spins in silicon natural quantum dots 20 to 200 nm Kane 98 02 nuclear spin in 31P as memory and spin coherent electron transport for two qubit operations gate controlled hyperfine and exchange interactions Yablonovitch 00 e spins and exchange interaction in SixGey heterostructures Thomas Schenkel Accelerator and Fusion Research Berkeley Lab Ion Beam Technology Program Solid state quantum computer scheme with 31P in 28Si Kane 98 31P qubit gate controlled manipulation of single spins nuclear spins store information electron spins transfer information between neighboring qubits J exchange and to nuclear spins A 121 5 neV hyperfine interaction http www lps umd edu issues J oscillations on length scale in Si required control of hyperfine interaction Thomas Schenkel Accelerator and Fusion Research Berkeley Lab Ion Beam Technology Program Thomas Schenkel Accelerator and Fusion Research Berkeley Lab Ion Beam Technology Program quantum information processing in a nutshell entangle ensembles of qubits control prevent interaction with environment limit decoherence run sequences of unitary operations on the ensemble read out the end result in a projective measurement Thomas Schenkel Accelerator and Fusion Research Berkeley Lab Ion Beam Technology Program Necessities for a spin quantum computer 1 Long lived spin states 2 Single spin operations Q NOT controlled spin interactions with an external field 3 Two spin operations Q CNOT controlled interactions between