~~ 奈米電子學期末報告奈米電子學期末報告 ~~Quantum Dot ComputingQuantum Dot Computing

陳奕帆陳奕帆國立台灣大學應用力學研究所國立台灣大學應用力學研究所

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What is Quantum Dot?What is Quantum Dot?

A quantum dot consists of a tiny piece of aluminum sA quantum dot consists of a tiny piece of aluminum separated by an insulator from another piece of alumineparated by an insulator from another piece of aluminum (known as a reservoir)um (known as a reservoir)

All these components are embedded on a computer chAll these components are embedded on a computer chipip

Aluminum kept at .03 degrees above absolute zero, mAluminum kept at .03 degrees above absolute zero, making it a superconductoraking it a superconductor

Two dots have been connected using nanowires, whicTwo dots have been connected using nanowires, which is quite an accomplishment, do to the necessity to loh is quite an accomplishment, do to the necessity to lock out the outside worldck out the outside world

What is Quantum Dot?What is Quantum Dot?

A quantum dot is essentially a pool of electronA quantum dot is essentially a pool of electrons, approximately 180 nanometers wides, approximately 180 nanometers wide

It’s so small that adding a single electron is a sIt’s so small that adding a single electron is a significant changeignificant change

Electrons fill the dot in successive orbitals, muElectrons fill the dot in successive orbitals, much like an atomch 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 ComputingPros and Cons for Quantum Computing

Potential advantages:Potential advantages: ScalabilityScalability Silicon compatibilitySilicon compatibility Microfabrication (and nanofabrication)Microfabrication (and nanofabrication) Possibility of ‘engineering’ structuresPossibility of ‘engineering’ structures Interaction with light (quantum communication)Interaction with light (quantum communication)

Potential disadvantage:Potential disadvantage: Much stronger contact of qubits with environment, Much stronger contact of qubits with environment,

so (usually) much more rapid decoherenceso (usually) much more rapid decoherence

Power of Quantum ComputingPower of Quantum Computing

Quantum information storageQuantum information storage N qubits stores 2N qubits stores 2NN complex numbers complex numbers N unentangled qubit configurations store (2N unentangled qubit configurations store (222))NN

N entangled qubit configurations store (2N entangled qubit configurations store (222)**2)**2NN

Consider information in 94 entangled qubits 2Consider information in 94 entangled qubits 222

*2*294 94 = 8*10= 8*102828

Quantum computersQuantum computers Operate on 2Operate on 2NN variables simultaneously variables simultaneously

Requirements for a QuantumRequirements for a QuantumComputerComputer

Robust representation of quantum informationRobust representation of quantum information– super-coherent qubits– super-coherent qubits

Ability to prepare an initial quantum state –optiAbility to prepare an initial quantum state –optical imprintingcal imprinting

Ability to manipulate quantum state through unAbility to manipulate quantum state through unitary transformations – exchange interaction in itary transformations – exchange interaction in quantum dotsquantum dots

Ability to measure the result - Faraday rotationAbility to measure the result - Faraday rotations in FM semiconductorss in FM semiconductors

How does it work?How does it work?

Voltage is applied to the dot to align the energy levels Voltage is applied to the dot to align the energy levels in both pieces of aluminum to allow a pair of electronin both pieces of aluminum to allow a pair of electrons (known as a Cooper pair) to tunnel back and forths (known as a Cooper pair) to tunnel back and forth

The absence or presence of the Cooper pair in the dot The absence or presence of the Cooper pair in the dot determines whether the dot represents a 0 or 1determines whether the dot represents a 0 or 1

Electrical current is used to measure the dot’s stateElectrical current is used to measure the dot’s state Electrical charge was used previously, but the charges Electrical charge was used previously, but the charges

increased the speed at which the qubit’s coherence is increased the speed at which the qubit’s coherence is lostlost

Quantum State and QubitsQuantum State and Qubits

Quantum state is defined to be a state vector in an N diQuantum state is defined to be a state vector in an N dimensional Hilbert space – a superposition of the basis mensional Hilbert space – a superposition of the basis statesstates

A qubit is the quantum state of a binary system defineA qubit is the quantum state of a binary system defined by only 2 basis statesd by only 2 basis states| Ψ| Ψ ＞＞ = a|0= a|0 ＞＞ +b|1+b|1 ＞ ＞ where a and b are complex cowhere a and b are complex constants, |0nstants, |0 ＞ ＞ and |1and |1 ＞ ＞ are basis statesare basis states

A “good” physical realization for qubits has finite numA “good” physical realization for qubits has finite number of naturally occurring states –preferably 2ber of naturally occurring states –preferably 2

Coherence, Decoherence and Quantum EntangleCoherence, Decoherence and Quantum Entanglementment

Coherence – Maintenance of initial quantum stCoherence – Maintenance of initial quantum state (superposition)ate (superposition)

Decoherence –Loss of initial stateDecoherence –Loss of initial state Quantum entanglement-non-local correlation oQuantum entanglement-non-local correlation o

f a distributed quantum systemf a distributed quantum system

Time evolution and HamiltoniansTime evolution and Hamiltonians

The Hamiltonian operator H completely defineThe Hamiltonian operator H completely definess

continuous time evolutioncontinuous time evolution ih/2Π (d | Ψ ih/2Π (d | Ψ ＞＞ / dt ) = H| Ψ/ dt ) = H| Ψ ＞＞

The unitary operator U defines the state at time The unitary operator U defines the state at time tt2 2 relative to the state at trelative to the state at t11 if if | Ψ(t | Ψ(t22) ) ＞＞ =U=U2121 | Ψ(t | Ψ(t11) ) ＞ ＞ ifif U U2121 = exp [-2Π = exp [-2Πii H(t H(t22-t-t11)/h])/h]

A quantum algorithm is a product of unitary trA quantum algorithm is a product of unitary transformationsansformations

Quantum Computer Figures of MeritQuantum 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 ScalesTime Scales

Coherence Conserving QubitsCoherence Conserving Qubits

Energetically favored coherent statesEnergetically favored coherent states Any decoherent process must supply energy to the Any decoherent process must supply energy to the

systemsystem Supercoherent qubits- decoherence rate scales as eSupercoherent qubits- decoherence rate scales as e

xp(-KT) when T < xp(-KT) when T < ΔΔ ~ 10K when implemented in ~ 10K when implemented in coupled quantum dot arrayscoupled quantum dot arrays

Fabrication of Silicon Q-Dot Array Q-ComputerFabrication of Silicon Q-Dot Array Q-Computer

Requirements for a Quantum MemoryRequirements for a Quantum Memory

Robust representation of quantum informationRobust representation of quantum information– quantum associative memory– quantum associative memory

Ability to prepare an initial quantum stateAbility to prepare an initial quantum state– quantum dots– quantum dots

Refresh quantum state to offset decoherenceRefresh quantum state to offset decoherence– quantum Zeno effect– quantum Zeno effect

Ability to measure the result Ability to measure the result – optical Faraday rotations – optical Faraday rotations

Quantum DRAMQuantum DRAM

Storage capacity of quantum memory scales like 2Storage capacity of quantum memory scales like 2NN

– – quantum dot density ~10quantum dot density ~101111/cm/cm22

– – With 100 fold redundancy, this gives (2With 100 fold redundancy, this gives (21010))9 9 qubits/cmqubits/cm22 , , – – More storage than has been or ever could be madeMore storage than has been or ever could be made with hard disks.with hard disks.

IssuesIssues – – How to refresh a qubit?How to refresh a qubit?

Possibly use the quantum Zeno effectPossibly use the quantum Zeno effect

Quantum Associative Memory (QUAM)Quantum Associative Memory (QUAM)

Associative memories used for storing patternsAssociative memories used for storing patterns Hopfield neural networks have been used to implemeHopfield neural networks have been used to impleme

nt classical associative memoriesnt classical associative memories – – n neurons can generally store about 0.2*n sets of datan neurons can generally store about 0.2*n sets of data

QUAM has scales more efficientlyQUAM has scales more efficiently – – Given m binary patterns of length nGiven m binary patterns of length n – – O(mn) operations are required to store dataO(mn) operations are required to store data – – O(N)1/2 operations to recall a pattern whereO(N)1/2 operations to recall a pattern where

x is the smallest integer such 22x >2m; N= 22xx is the smallest integer such 22x >2m; N= 22x

– – 2n+1 qubits are required to store data2n+1 qubits are required to store data

Roadmap to quantum computingRoadmap to quantum computing

A Spin Based Roadmap to Quantum ComputingA Spin Based Roadmap to Quantum Computing

Tools - Coherent bulk spin creation, manipulation, stoTools - Coherent bulk spin creation, manipulation, storage, transport and metrologyrage, transport and metrology

Materials - Optimized ferromagnetic semiconductor Materials - Optimized ferromagnetic semiconductor material systemsmaterial systems

Devices - Spin modulated charge transport, spin baseDevices - Spin modulated charge transport, spin based optical modulators, spin based switchesd optical modulators, spin based switches

Quantum state devices -manipulation, creation and mQuantum state devices -manipulation, creation and measurement of quantum state, quantum coherence and easurement of quantum state, quantum coherence and single spinssingle spins

Solid state quantum computers-requires precise alignSolid state quantum computers-requires precise alignment and placement of dopantsment and placement of dopants

Solid State Quantum ComputersSolid State Quantum Computers

Precise placement of dopantsPrecise placement of dopants Precise alignment of gatesPrecise alignment of gates Spin based transistorsSpin based transistors

Coupled Nuclear Spins in Silicon Quantum Coupled Nuclear Spins in Silicon Quantum ComputerComputer

Electron Spin Transistor for Quantum Electron Spin Transistor for Quantum ComputingComputing

Solid State Quantum ComputerSolid State Quantum Computer

Solid State Quantum ComputerSolid State Quantum Computer

Solid State Quantum ComputerSolid State Quantum Computer

Electron Spins Trapped Beneath Coupled Electron Spins Trapped Beneath Coupled Quantum DotsQuantum Dots

Typical Design ParameterTypical Design Parameter

Reconfigurable Quantum Computer Showing TranspinoReconfigurable Quantum Computer Showing Transpinor Output Sensorr Output Sensor

Qubit AddressingQubit Addressing

Pulsed Microwave Field Generated Using a MicrPulsed Microwave Field Generated Using a Microstrip Resonatorostrip Resonator

AddressingAddressing

ConclusionsConclusions

Quantum state devices can potentially provide Quantum state devices can potentially provide significant scaling at the end of CMOS roadmasignificant scaling at the end of CMOS roadmapp

Research progress is being made in all four eleResearch progress is being made in all four elements of quantum computing and quantum mements of quantum computing and quantum memoriesmories

Spintronic devices can provide the componentSpintronic devices can provide the components of a roadmap to quantum computings of a roadmap to quantum computing

ReferenceReference

George Bourianoff, Ralph Cavin, Recent progress in George Bourianoff, Ralph Cavin, Recent progress in quantum computing and quantum memory. (quantum computing and quantum memory. (www.intel.com/research/siliconwww.intel.com/research/silicon))

NC State University, Nnoscale Quantum Engineering NC State University, Nnoscale Quantum Engineering Group (Group (www.ece.ncsu.edu/quanteng/www.ece.ncsu.edu/quanteng/))

K. W. Kim, A. A Kiselev, V. M. Lashkin, W. C. HoltK. W. Kim, A. A Kiselev, V. M. Lashkin, W. C. Holton, V. Misra, North Carolina State University (on, V. Misra, North Carolina State University (www.ece.ncsu.edu/nano/quantum%20computing/www.ece.ncsu.edu/nano/quantum%20computing/ QuQuantum%20Computing%20Overview.pdfantum%20Computing%20Overview.pdf))