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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 weizen@ms4.hinet.net 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)
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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 weizen@ms4.hinet.net 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: • 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 QuantumComputer • 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
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
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 • – 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
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
Solid State Quantum Computers • Precise placement of dopants • Precise alignment of gates • Spin based transistors
Reconfigurable Quantum Computer Showing Transpinor Output Sensor
Pulsed Microwave Field Generated Using a Microstrip Resonator
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)