1. Silicon-based Quantum Computation C191 Final Project Presentation Nov 30, 2005 Cheuk Chi Lo Kinyip Phoa Dept. of EECS, UC Berkeley

2. Silicon-based Quantum Computation: Presentation Outline • Introduction • Proposals for Silicon Quantum Computers • Physical Realization: Technology and Challenges • Summary and Conclusions

3. Introduction: Why Silicon? • We know silicon from years of building classical computers • Donor nuclear spins are well-isolated from environment low error rates and long decoherence time • Integration of quantum computer with conventional electronics • Scalability advantages?

4. Introduction: DiVincenzo’s Criteria • Well-defined qubits • Ability to initialize the qubits • Long decoherence time • Manipulation of qubit states • Read-out of qubit states • Scalability (~105 qubits)

5. II. Overview of Silicon Quantum Computation Architectures Silicon Quantum Computer Proposals Shallow Donor Qubits Deep Donor Qubits Silicon-29 Qubits Electron Shuttling Exchange Coupling Magnetic Dipolar Coupling

6. BAC BDC Silicon Shallow Donor Qubits: Qubit Definition and State Manipulation Spin Resonance J-Gate (Exchange Coupling) A-Gate (Hyperfine Interaction) Control gate barrier Silicon-28 Qubit S-Gates(Electron shuttling) magnetic dipolar coupling BE Kane, Nature, 393 14 (1998) AJ Skinner et al, PRL, 90 8 (2003) R de Sousa et al, Phys Rev A, 70 052304 (2004)

7. Summary of Silicon Shallow Donor Qubits • Qubit: donor nuclear spin or hydrogenic qubit (nucleus + electron spins) • Initialization: Recycling of nuclear state read-out + nuclear spin-state flip via interaction with donor electron • Decoherence time: e.g. at 1.5K • nucleus spin T1 > 10 hours • electron spin T1 > 0.3hours • Qubit Manipulation • Single Qubit Manipulation: hyperfine interaction + spin resonance • Multi-qubit Interaction: Exchange coupling, Magnetic dipolar coupling or Electron shuttling • Read-out: Transfer of nucleus spin state to donor electron via hyperfine interaction, then read-out of electron spin state

8. Physical Realization of a Si QC Some common features that must be realized in a shallow donor Si QC are: • Array of single, activated 31P atoms: • Single-spin state read-out: • Integrated control gates • Process Variations

9. Formation of Ordered Donor Arrays “Top-down”  single ion implantation T Schenkel et al, APR, 94(11) 7017 (2003) “Bottom up”  STM based Hydrogen Lithography JL O’Brien et al, Smart Mater. Struct., 11 741 (2002)

10. Spin-State Read-out with SET’s & Fabrication of Control Gates Read-out: Spin state  Charge state (e.g. measurement by SET) Control Gate Challenges: • Qubit-qubit spacing requirements for different coupling mechanisms: • Exchange Coupling: 10-20nm • Magnetic Dipolar Coupling: 30nm • Electron Shuttling: >1m • State-of the art electron beam lithography: • can do ~10nm, but not dense patterns Qubit interaction control gates extremely challenging! • Read-out Challenges: • SET’s are susceptible to 1/f and telegraphic noises (from the random charging and discharging of defect/trap states in the silicon host) • alignment and thermal budget of SET’s with the donor atom sites also present as a fabrication challenge. (UNSW) (L Chang, PhD Thesis, EECS)

11. Process Variations • Process Variations may arise from: • substrate temperature gradient, • uneven reagent use during fabrication, • differences in material thermal expansion • strain induced by the patterning of the substrate (leads to uncertainty in ground state donor electron wavefunction, due to incomplete mixing of states) • Consequences: • Need careful tuning and initialization of qubits • Limit of scalability? • Introduce strain in silicon intentionally? • lifts degeneracy of electronic state  less vulnerable to process variations (IBM)

12. Silicon Deep Donors Proposal Excited State Bi Er Bi Optical Excitation Ground State Bi Er Bi Bi Er Bi AM Stoneham et al, J. Phys.: Condens. Matter, 15 (2003), L447

13. Initialization, Manipulationand Readout? • Initialization by polarized light or injection of polarized electron • both are not very possible under room temperature • Manipulation with microwave pulses • like the work by Charnock et. al. on N-V centers in diamond • Readout optically • detection of photons emitted • potentially require detection of single photon • Disorderness of donor ion • Irreproducibility and difficult to address qubits

14. Decoherence Time andThermal Ionization

15. Summary of Silicon Deep Donor Qubits • Qubit: deep donor (e.g. Bismuth) nuclear spin, proposed to work at room temperature. • Initialization: Optical pumping or injection of polarized electron, questionable in feasibility. • Decoherence time: fraction of nanosecond at room temperature • Qubit Manipulation: via applying intense microwave pulse, like N-V centers in diamond • Read-out: optical readout of photon emitted from transition between two states

16. Silicon-29 Quantum Computer Overview Manipulating qubits by Dysprosium (Dy) magnet Initialize with circularly polarized light NMR-type quantum computer Readout using MRFM CAI TD Ladd et. al. , PRL, 89(1) 017901, 2002

17. Decoherence Times • Long decoherence time (T1 and T2) • Reported T1 as large as 200 hours, measured in dark • Experimentally find T2 as long as 25 seconds • T2 is reduced by the presence of 1/f noise due to the traps at lattice defects and impurities

18. Summary of Silicon NMR quantum computer • Qubit: Chains of silicon-29 isotope for ensemble measurement • Initialization: Optical pumping with circularly polarized light • Decoherence time: measured as long as 200 hours in dark at 77K for T1 but only 25 seconds for T2 • Qubit Manipulation: combination of static magnetic field and RF magnetic field • Read-out: with cantilever, performing MRFM CAI

19. Problem:RF Coil, Dy Magnet & MRFM The deposition method of Dy magnet is not outlined! It won’t be trivial to incorporate The cantilever tip for MRFM is not included in the schematic. How to insert it? TD Ladd et. al. , PRL, 89(1) 017901, 2002

20. Summary and Conclusions • Several proposals for implementing quantum computer in silicon • Shallow donor (phosphorus) qubit • Deep donor (bismuth) qubit • Silicon-29 NMR quantum computer • Difficulties faced in each proposals • Arguments on the feasibility • Most experimental efforts are on shallow donor qubits • Convergence with conventional electronics processing requirements: • Currently: 90nm technology node (~45nm features) • 22nm technology node in 2016! • Strained-silicon: hot topic of research in semiconductor industry • Narrower transistor performance window with ordered dopants • Single-electron transistors and other nanoelectronics (http://www.ITRS.net)

21. Thank You Thank You!