1. Large scale quantum computing in silicon with imprecise qubit couplings ArXiv :1506.04913 (2015)

2. Silicon quantum computing 2010 2015 Single-shot readout of an electron spin in silicon Morello et al., Nature 467, 687 A single-atom electron spin qubit in silicon Pla et al., Nature 489, 541 2012 High-fidelity readout and control of a nuclear spin qubit in silicon Pla et al., Nature 496, 334 2013 Storing quantum information for 30 seconds in a nanoelectronic device 2014 Muhonen et al., Nat. Nanotech. 9, 986 An addressable quantum dot qubit with fault-tolerant control-fidelity Veldhorst et al., Nat. Nanotech. 9, 981 Veldhorst et al., arXiv :1411.5760 To appear in Nature A two-qubit logic gate in silicon SCALING UP!

3. Koiller et al., PRL 88, 027903 (2002) Donor spins in silicon : long memories are hard to couple Valley degeneracy affects exchange spin interactions Pica et al., PRB 89, 235306 (2014)

4. Electron spins in silicon quantum dots : malleable qubits are more fragile Couplings can be engineered Petta et al., Science 309, 2180 (2005) Veldhorst et al., arXiv :1411.5760 (2014)

5. If donors and dots are permanently mixed, donor coherence is lost Coupling «on demand» allows different degrees of freedom to be addressed when convenient Making an useful hybrid oxide - - + Si oxide -- + Si d + Dot voltage DOT DONOR J

6. Highly coherent donors Morley et al., Nature Materials 9, 725 (2010) Wolfowicz et al., Nature Nanotech. 8, 561 (2013) I=9/2 large spin Hilbert space Largest hyperfine coupling – fast (GHz) nuclear spin rotations High fidelity spin rotations A Bi DOT DONOR Clock transition

7. Three qubits Si:Bi clock transitions Bismuth and dot levels can cross at clock transition A DOT Quantum dot

8. Qubit coupling : controlled SWAP Dot-allowed avoided crossing Dot-forbidden crossing J

9. The importance of being adiabatic J CNOT from 3-qubit adiabatic controlled SWAP is more robust «Same» final state population if J is pulsed in μs (Landau-Zener physics)

10. High fidelity donor - dot CNOT “NMR” Global Pulsed ENDOR (CNOT on donor) Δ J 10 mT 10 mV x01x01 x00x00 0x10x1 NMR-controlled swap Dot “ESR” 0xx10xx1x0x1x0x1 x000x000 NMR-controlled swap x00x00 π Phase erasing steps

11. Adiabaticity gives large scale fault - tolerance SiO 2 Si ALD + SiO 2 + + + + + + + + + + + oxide + Si + Exchange couplings vary violently on sub-nm scale

12. Adiabaticity gives large scale fault - tolerance + + + + Uniform local magnetic fields 10 MHz local frequency shifts + + + + Realistic local shifts are < 1 MHz Extreme robustness to locally inhomogeneous magnetic fields

13. Donor - dot scaled architecture J J Adiabatic switching of electrodes is uniform across the array (minimal wiring)

14. One - page surface code Data bits are inspected on a rolling basis by measuring the measurement bits Data qubits Measurement qubits Locally entangled sets of physical qubits host collective logical qubit states Best proven single-qubit error threshold (~1%) Fowler et al., Phys. Rev. A 86, 032324 (2012)

15. Donor - dot surface code Data qubits Quantum Dots Measurement qubits Long coherence donors J J J J

16. CNOT fidelity >99.9% across almost the entire array > 99.5% donor readout fidelity Pla et al., Nature 489, 541 (2012) Watson et al., PRL (2015) A full surface code cycle (10 μs ) 1. The array of interface electron spins is rigidly shifted to neighbouring dots CCD gates should allow fast transport ( ~ 100 ps) 2. CNOTs between the donor-dot pairs to address allow entanglement of the MQ and the DQ The other pairs work as defects – uncostrained degrees of freedom 3. After a cycle of four nearest-neighbour movements the initial configuration is achieved 4. Measurement qubits (donors) are measured to check for errors occurred in the data qubits (dots) J J Fault tolerance

17. ArXiv :1506.04913 (2015) ArXiv :1506.04913 (2015) Presented a novel two-qubit gate between long memory donor states and scalable dot spins Adiabatic tuning of the donor-dot exchange interaction allows high fidelity CNOTs across most of the array, in spite of the vast coupling range Presented a fully scaled silicon architecture to implement the best error correction to date All manipulations are global but for easily controlled local voltage pulses – 10 μs / cycle + Si + oxide - - J

18. Further work Further work J Alternatives to electron transport between neighbouring quantum dots Cycle speed currently limited by ability to sweep the magnetic field (heating) – better ideas?

19. Acknowledgements Brendon Lovett University of St Andrews Stephen Lyon Princeton University Ravindra Bhatt Princeton University Thomas Schenkel Berkeley National Laboratory