Superconducting Qubits
Kyle Garton
Physics C191
Fall 2009
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)
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
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
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)
Superconducting Quantum
Interference Device (SQUID)
Qubit Options
Size
Coupling with
environment
• Photons
• Nuclear Spins
• Ions
• Semiconductor Spins
• Quantum Dots
• Superconducting Circuits
Superconducting Circuits
• Strong coupling to environment – short
coherence times
• Strong qubit-qubit coupling – fast gates
Superconducting Circuits
• Easy electrical access
• Easily engineered with capacitors, inductors,
Josephson junctions
• Easy to fabricate and integrate
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
Quantum Characteristics
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
Types of Superconducting Qubits
• Charge Qubit – Cooper Pair Box
• Flux Qubit – RF-SQUID
• Phase Qubit – Current Biased Junction
Readout
•
•
•
•
Switch reading ON and OFF
Controls Coupling
Doesn’t Contribute Noise (ON or OFF)
Strong read and repeat rather than weak
continuous measurements
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)
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
Charge Qubit – Cooper Pair Box
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
Flux Qubit – RF-SQUID
Phase Qubit - Current Biased Junction
• Current controlled to combat
continuous charge Qr
• Differences in current
determines energy state
Phase Qubit – Current Biased Junction
Circuit Example
Qubit Interaction
• Easily fabricate transmission lines and inductors
to couple qubits
• Can be coupled at macroscopic distances
Fabrication
• Use existing microfabrication techniques from
IC industry
• Electron beam lithography for charge and flux
qubits
• Optical lithography for phase qubits
Accomplishments
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•
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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…
Future
• Active area of research
• Need to simultaneously optimize parameters
• New materials to improve properties
• Engineering better circuits to handle noise
• Local RF pulsing