Towards quantum information processing with spins in silicon Thomas Schenkel E O Lawrence Berkeley National Laboratory T Schenkel LBL gov http www ebit lbl gov Thomas Schenkel Accelerator and Fusion Research Division Berkeley Lab Ion Beam Technology Program Path to logic demonstrations with donor electron spin qubits in silicon 1 Develop devices for single spin readout 2 Spin dependent transport in transistors Develop a technique for qubit array formation 3 Single ion implantation with Scanning Probe alignment Process and materials studies for T2 optimization 4 Spin dynamics in pre device structures Demonstration of quantum logic Formulate protocol requires only single spin readout and placement of multiple isotopes into one readout channel theory fabrication measurement collaboration between LBNL UC Berkeley J Bokor B Whaley R deSousa and Princeton University S Lyon A Tyryshkin Thomas Schenkel Accelerator and Fusion Research Division Berkeley Lab Ion Beam Technology Program Wave particle duality of C60 molecules Wave superposition of states in double slits leads to interference Particle interaction of molecules with environment destroys interference decoherence and classical behavior Quantum info processing requires the coherent superposition of N qubits Particle Wave Thomas Schenkel Accelerator and Fusion Research Division 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 needed to beat classical computers and including error correction overhead N 10 000 2 Why in Silicon long coherence times for electron and nuclear spins of donor atoms in a silicon matrix device requirements converting with trends in classical silicon transistor technology 3 Walk through five DiVincenzo criteria for donor electron spins in Silicon Thomas Schenkel Accelerator and Fusion Research Division Berkeley Lab Ion Beam Technology Program Why in solids Scalability Classical transistor scaling and quantum computer development converge Thomas Schenkel Accelerator and Fusion Research Division Berkeley Lab Ion Beam Technology Program Moore s Law Gordon Moore Intel exponentially more cheaper faster and smaller transistors more cheaper As many transistors made each year as raindrops fall on of California more then 10 transistors per ant on the planet Thomas Schenkel Accelerator and Fusion Research Division Berkeley Lab Ion Beam Technology Program Moore s Law of exponential speedup of silicon transistors faster Thomas Schenkel Accelerator and Fusion Research Division Berkeley Lab Ion Beam Technology Program smaller Thomas Schenkel Accelerator and Fusion Research Division Berkeley Lab Ion Beam Technology Program Why silicon vastly abundant semiconductor that is easy to work with SiO2 Si interface has quite low defect density 1010 cm 2eV 1 that s still 1 per 100 nm scale device very high degree of control over electrical properties allows large scale integration most importantly very long coherence times 1 ms because it can be prepared as a nuclear spin free environment pure 28Si compared to other materials with specific advantages III V s e g quantum dots in GaAs direct band gap for opto electronic integration very high quality 2DEGs but short coherence times 1 s due to nuclear spin flips diamond e g NV defects larger band gap for high temperature operation low spin orbit coupling but difficult to make larger wafers hard to dope electrons on liquid helium endohedral C60 Thomas Schenkel Accelerator and Fusion Research Division Berkeley Lab Ion Beam Technology Program Donor electron spin qubits in silicon 31P natural quantum dot Si Ne 3s2 3p2 P Ne 3s2 3p3 3p3 binding energy 45 meV 100 abundant isotope with I 1 2 28Si matrix can be prepared with I 0 Thomas Schenkel Accelerator and Fusion Research Division Berkeley Lab Ion Beam Technology Program Qubit spins of 31P atoms in silicon Long decoherence times nuclear spin 1000 s electron spin tens of ms SiO2 Bohr radius of bound 3p electron of 31P in Si 2 nm m0 h2 0 a0 Si 2 m0 q meff Si o m0 Si 0 53 A meff Si 12 TEM image taken from S Dunham 03 Thomas Schenkel Accelerator and Fusion Research Division Berkeley Lab Ion Beam Technology Program Criteria for physical implementation of a quantum computer DiVincenzo 1 2 3 4 5 6 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 Efficient quantum communication form transmit and convert flying qubits 31P donor spins in silicon natural quantum dots 20 to 200 nm Thomas Schenkel Accelerator and Fusion Research Division Berkeley Lab Ion Beam Technology Program Solid state quantum computer scheme with 31P in 28Si B E Kane Nature 1998 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 Thomas Schenkel Accelerator and Fusion Research Division Berkeley Lab Ion Beam Technology Program Criteria for physical implementation of a quantum computer 1 DiVincenzo Well defined extendible qubit array stable memory Array of single donor atoms P As Sb Bi in a silicon crystal matrix formed by single ion implantation or STM H lithography 2 3 4 5 Initialization in the 000 state polarization at low temperature 0 3 K in strong magnet field 5 T kT g BB Long decoherence time 104 operation time to allow for error correction T2 T1 in pure 28Si 10 s limited by residual 29Si and by gate and interface effects Universal set of gate operations Not ESR rotations need local B or g control CNOT two qubit interaction via J or dipolar coupling or RKKY or e shuttling Read out projective measurement Single shot single spin readout much faster then decoherence time spin to charge conversion spin dependent transport Thomas Schenkel Accelerator and Fusion Research Division Berkeley Lab Ion Beam Technology Program Qubit arrays bottom up STM hydrogen lithography 50 nm 10nm 41nm 65nm J O Brien et al Univ New South Wales Sydney Aharonov Bohm ring of P atoms connected to pre implanted contacts and overgrown with Si on Si 100 TC Shen J Tucker et al 2003