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

2. Silicon-based Quantum Computation: Presentation Outline I. Introduction II. Proposals for Silicon Quantum Computers III. Physical Realization: Technology and Challenges IV. 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 1. Well-defined qubits 2. Ability to initialize the qubits 3. Long decoherence time 4. Manipulation of qubit states 5. Read-out of qubit states 6. Scalability (~10 5 qubits)

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

6. Silicon Shallow Donor Qubits: Qubit Definition and State Manipulation barrier Silicon-28 Control gate A-Gate (Hyperfine Interaction) J-Gate (Exchange Coupling) magnetic dipolar coupling S-Gates (Electron shuttling) B DC B AC 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) Spin Resonance Qubit

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 T 1 > 10 hours electron spin T 1 > 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 31 P atoms: Single-spin state read-out: Integrated control gates Process Variations

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

10. Spin-State Read-out with SET’s & Fabrication of Control Gates Read-out Challenges: i.SET’s are susceptible to 1/f and telegraphic noises (from the random charging and discharging of defect/trap states in the silicon host) ii.alignment and thermal budget of SET’s with the donor atom sites also present as a fabrication challenge. 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! (L Chang, PhD Thesis, EECS) (UNSW)

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

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

13. Initialization, Manipulation and 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 and Thermal 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 NMR-type quantum computer Initialize with circularly polarized light Manipulating qubits by Dysprosium (Dy) magnet Readout using MRFM CAI TD Ladd et. al., PRL, 89(1) 017901, 2002

17. Decoherence Times Long decoherence time (T 1 and T 2 ) Reported T 1 as large as 200 hours, measured in dark Experimentally find T 2 as long as 25 seconds T 2 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 T 1 but only 25 seconds for T 2 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!