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~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
[email protected]
TEL: +886-2-33665646
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
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
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
Pros and Cons for Quantum Computing
 Potential advantages:
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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
Power of Quantum Computing
 Quantum information storage
 N qubits stores 2N complex numbers
 N unentangled qubit configurations store (22)N
 N entangled qubit configurations store (22)**2N
 Consider information in 94 entangled qubits
22*294 = 8*1028
 Quantum computers
 Operate on 2N variables simultaneously
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
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
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
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
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
t2 relative to the state at t1 if
| Ψ(t2) ＞=U21 | Ψ(t1) ＞ if
U21 = exp [-2Πi H(t2-t1)/h]
 A quantum algorithm is a product of unitary
transformations
Quantum Computer Figures of Merit
 Timescales
 Decoherence time τd
 –Operation Time τop
 –Number of operations = Nop
 Physical tradeoffs
 Physical isolation ⇒ long decoherence times
 Physical isolation ⇒ long operation times
Time Scales
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
Fabrication of Silicon Q-Dot Array Q-Computer
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
Quantum DRAM
 Storage capacity of quantum memory scales like 2N
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– quantum dot density ~1011/cm2
– With 100 fold redundancy, this gives (210)9 qubits/cm2 ,
– 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
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
Roadmap to quantum computing
A Spin Based Roadmap to Quantum Computing
 Tools - Coherent bulk spin creation, manipulation,
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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
Solid State Quantum Computers
 Precise placement of dopants
 Precise alignment of gates
 Spin based transistors
Coupled Nuclear Spins in Silicon Quantum
Computer
Electron Spin Transistor for Quantum
Computing
Solid State Quantum Computer
Solid State Quantum Computer
Solid State Quantum Computer
Electron Spins Trapped Beneath Coupled
Quantum Dots
Typical Design Parameter
Reconfigurable Quantum Computer Showing
Transpinor Output Sensor
Qubit Addressing
Pulsed Microwave Field Generated Using a
Microstrip Resonator
Addressing
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
Reference
 George Bourianoff, Ralph Cavin, Recent progress in
quantum computing and quantum memory.
(www.intel.com/research/silicon)
 NC State University, Nnoscale Quantum Engineering
Group (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)