1. ~ 奈米電子學期末報告 ~ Quantum Dot Computing 陳奕帆國立台灣大學應用力學研究所 weizen@ms4.hinet.net TEL: +886-2-33665646

2. What is Quantum Dot?  A quantum dot consists of a tiny piece of aluminum separated by an insulator from another piece of aluminum (known as a reservoir)  All these components are embedded on a computer chip  Aluminum kept at.03 degrees above absolute zero, making it a superconductor  Two dots have been connected using nanowires, which is quite an accomplishment, do to the necessity to lock out the outside world

3. What is Quantum Dot?  A quantum dot is essentially a pool of electrons, approximately 180 nanometers wide  It’s so small that adding a single electron is a significant change  Electrons fill the dot in successive orbitals, much like an atom

4. Fundamental Limits to Scaling Electron Based Devices   Fundamental physical analysis suggests that scaling a general, unspecified electronic nano-device will be limited by thermal considerations much like scaled CMOS devices   It also suggests that NO electronic nano-device can perform much better than scaled CMOS   Scaling beyond the end of the CMOS roadmap will require something other than electrons to store finite state e.g. quantum state   Quantum computing will not be limited by the same set of constraints

6. Pros and Cons for Quantum Computing  Potential advantages:  Scalability  Silicon compatibility  Microfabrication (and nanofabrication)  Possibility of ‘engineering’ structures  Interaction with light (quantum communication)  Potential disadvantage:  Much stronger contact of qubits with environment, so (usually) much more rapid decoherence

7. Power of Quantum Computing  Quantum information storage  N qubits stores 2 N complex numbers  N unentangled qubit configurations store (2 2 ) N  N entangled qubit configurations store (2 2 )**2 N  Consider information in 94 entangled qubits 2 2 *2 94 = 8*10 28  Quantum computers  Operate on 2 N variables simultaneously

8. Requirements for a Quantum Computer  Robust representation of quantum information – super-coherent qubits  Ability to prepare an initial quantum state – optical imprinting  Ability to manipulate quantum state through unitary transformations – exchange interaction in quantum dots  Ability to measure the result - Faraday rotations in FM semiconductors

9. How does it work?  Voltage is applied to the dot to align the energy levels in both pieces of aluminum to allow a pair of electrons (known as a Cooper pair) to tunnel back and forth  The absence or presence of the Cooper pair in the dot determines whether the dot represents a 0 or 1  Electrical current is used to measure the dot’s state  Electrical charge was used previously, but the charges increased the speed at which the qubit’s coherence is lost

10. Quantum State and Qubits  Quantum state is defined to be a state vector in an N dimensional Hilbert space – a superposition of the basis states  A qubit is the quantum state of a binary system defined by only 2 basis states | Ψ ＞ = a|0 ＞ +b|1 ＞ where a and b are complex constants, |0 ＞ and |1 ＞ are basis states  A “good” physical realization for qubits has finite number of naturally occurring states –preferably 2

11. Coherence, Decoherence and Quantum Entanglement  Coherence – Maintenance of initial quantum state (superposition)  Decoherence –Loss of initial state  Quantum entanglement-non-local correlation of a distributed quantum system

12. Time evolution and Hamiltonians  The Hamiltonian operator H completely defines  continuous time evolution ih/2Π (d | Ψ ＞ / dt ) = H| Ψ ＞  The unitary operator U defines the state at time t 2 relative to the state at t 1 if | Ψ(t 2 ) ＞ =U 21 | Ψ(t 1 ) ＞ if U 21 = exp [-2Π i H(t 2 -t 1 )/h]  A quantum algorithm is a product of unitary transformations

13. Quantum Computer Figures of Merit   Timescales   Decoherence time τ d   –Operation Time τ op   –Number of operations = N op   Physical tradeoffs   Physical isolation ⇒ long decoherence times   Physical isolation ⇒ long operation times

14. Time Scales

15. Coherence Conserving Qubits  Energetically favored coherent states  Any decoherent process must supply energy to the system  Supercoherent qubits- decoherence rate scales as exp(-KT) when T < Δ ~ 10K when implemented in coupled quantum dot arrays

16. Fabrication of Silicon Q-Dot Array Q-Computer

17. Requirements for a Quantum Memory  Robust representation of quantum information – quantum associative memory  Ability to prepare an initial quantum state – quantum dots  Refresh quantum state to offset decoherence – quantum Zeno effect  Ability to measure the result – optical Faraday rotations

18. Quantum DRAM  Storage capacity of quantum memory scales like 2 N  – quantum dot density ~10 11 /cm 2  – With 100 fold redundancy, this gives (2 10 ) 9 qubits/cm 2,  – More storage than has been or ever could be made  with hard disks.  Issues  – How to refresh a qubit?  Possibly use the quantum Zeno effect

19. Quantum Associative Memory (QUAM)  Associative memories used for storing patterns  Hopfield neural networks have been used to implement classical associative memories  – n neurons can generally store about 0.2*n sets of data  QUAM has scales more efficiently  – Given m binary patterns of length n  – O(mn) operations are required to store data  – O(N)1/2 operations to recall a pattern where  x is the smallest integer such 22x >2m; N= 22x  – 2n+1 qubits are required to store data

20. Roadmap to quantum computing

21. A Spin Based Roadmap to Quantum Computing  Tools - Coherent bulk spin creation, manipulation, storage, transport and metrology  Materials - Optimized ferromagnetic semiconductor material systems  Devices - Spin modulated charge transport, spin based optical modulators, spin based switches  Quantum state devices -manipulation, creation and measurement of quantum state, quantum coherence and single spins  Solid state quantum computers-requires precise alignment and placement of dopants

22. Solid State Quantum Computers  Precise placement of dopants  Precise alignment of gates  Spin based transistors

23. Coupled Nuclear Spins in Silicon Quantum Computer

24. Electron Spin Transistor for Quantum Computing

25. Solid State Quantum Computer

28. Electron Spins Trapped Beneath Coupled Quantum Dots

29. Typical Design Parameter

30. Reconfigurable Quantum Computer Showing Transpinor Output Sensor

31. Qubit Addressing

32. Pulsed Microwave Field Generated Using a Microstrip Resonator

33. Addressing

34. Conclusions  Quantum state devices can potentially provide significant scaling at the end of CMOS roadmap  Research progress is being made in all four elements of quantum computing and quantum memories  Spintronic devices can provide the components of a roadmap to quantum computing

35. Reference  George Bourianoff, Ralph Cavin, Recent progress in quantum computing and quantum memory. (www.intel.com/research/silicon) www.intel.com/research/silicon  NC State University, Nnoscale Quantum Engineering Group (www.ece.ncsu.edu/quanteng/) www.ece.ncsu.edu/quanteng/  K. W. Kim, A. A Kiselev, V. M. Lashkin, W. C. Holton, V. Misra, North Carolina State University (www.ece.ncsu.edu/nano/quantum%20computing/ Quantum%20Computing%20Overview.pdf) www.ece.ncsu.edu/nano/quantum%20computing/