superconducting qubits kyle garton physics c191 fall 2009
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Superconducting Qubits
Kyle GartonPhysics C191Fall 2009
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Superconductivity
•Classically electrons strongly interact with the lattice and dissipate energy (resistance)
•In a superconducting state there is exactly zero resistance
•External magnetic fields are expelled (Meissner Effect)
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Superconductivity
•Fermi energy is the highest energy level occupied at absolute zero
•Bardeen, Cooper, and Schrieffer (BCS 1957) provide for an even lower energy level
•Electrons condense into Cooper pairs and fill these lower states
•These energy levels are below the energy gap that allows for lattice interaction so there is no resistance
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Superconductivity Notes
•Need very low temperatures to achieve superconductivity (Type I)
•Currents can last thousands for billions of years
•Type II (high temperature) superconductors are not explained by BCS theory
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Josephson Junction
•An thin insulating layer sandwiched between superconductors
•Current can still tunnel through thin layers•At a critical current value voltage will
develop across the junction•Voltage oscillates (converting voltage to
frequency)•Can also operate in inverse mode
(converting frequency to voltage)
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Superconducting Quantum Interference Device (SQUID)
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Qubit Options
•Photons•Nuclear Spins
•Ions•Semiconductor Spins
•Quantum Dots•Superconducting Circuits
SizeCoupling with environment
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Superconducting Circuits
•Strong coupling to environment – short coherence times
•Strong qubit-qubit coupling – fast gates
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Superconducting Circuits
•Easy electrical access
•Easily engineered with capacitors, inductors, Josephson junctions
•Easy to fabricate and integrate
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Quantum Characteristics
•How can a macroscopic device exhibit quantum properties?
•LC oscillator circuit is like a quantum harmonic oscillator
•L=3nH, C=10pF → f=1GHz
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Quantum Characteristics
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DiVincenzo criteria
•scalable physically – microfabrication process
•qubits can be initialized to arbitrary values – low temperature
•quantum gates faster than decoherence time - superconductivity
•universal gate set – electrical coupling•qubits can be read easily – electrical lines
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Types of Superconducting Qubits•Charge Qubit – Cooper Pair Box
•Flux Qubit – RF-SQUID
•Phase Qubit – Current Biased Junction
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Readout
•Switch reading ON and OFF•Controls Coupling•Doesn’t Contribute Noise (ON or OFF)•Strong read and repeat rather than weak
continuous measurements
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Readout
•Measurement time τm (with good signal/noise ratio)
•Energy Relaxation Rate Γ1ON
•Coherence Decay Rate Γ2OFF
•Dead time td (time to reset device)
•Fidelity (F = P00c + P11c − 1)
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Charge Qubit – Cooper Pair Box
•Biased to combat continuous charge Qr
•Cooper pairs are trapped in box between capacitor and Josephson junction
•Charge in box correlates to energy states
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Charge Qubit – Cooper Pair Box
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Flux Qubit – RF-SQUID
•Shunted to combat continuous charge Qr
•Current in right loop correlates to energy states
•Can use RF pulses to implement gates
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Flux Qubit – RF-SQUID
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Phase Qubit - Current Biased Junction•Current controlled to
combat continuous charge Qr
•Differences in current determines energy state
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Phase Qubit – Current Biased Junction
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Circuit Example
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Qubit Interaction
•Easily fabricate transmission lines and inductors to couple qubits
•Can be coupled at macroscopic distances
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Fabrication
•Use existing microfabrication techniques from IC industry
•Electron beam lithography for charge and flux qubits
•Optical lithography for phase qubits
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Accomplishments
•Coherence quality (Q=Tω) >2x104 •Read and reset fidelity >95%•All Bloch states addressed (superposition)•RF pulse implements gate•Scalable fabrication
•Not all at the same time…
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Future•Active area of research
•Need to simultaneously optimize parameters
•New materials to improve properties
•Engineering better circuits to handle noise
•Local RF pulsing