1. Superconducting Qubits Kyle Garton Physics C191 Fall 2009

2. 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)

3. 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

4. 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

5. 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)

6. Superconducting Quantum Interference Device (SQUID)

7. Qubit Options • Photons • Nuclear Spins • Ions • Semiconductor Spins • Quantum Dots • Superconducting Circuits Coupling with environment Size

8. Superconducting Circuits • Strong coupling to environment – short coherence times • Strong qubit-qubit coupling – fast gates

9. Superconducting Circuits • Easy electrical access • Easily engineered with capacitors, inductors, Josephson junctions • Easy to fabricate and integrate

10. 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

11. Quantum Characteristics

12. 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

13. Types of Superconducting Qubits • Charge Qubit – Cooper Pair Box • Flux Qubit – RF-SQUID • Phase Qubit – Current Biased Junction

14. Readout • Switch reading ON and OFF • Controls Coupling • Doesn’t Contribute Noise (ON or OFF) • Strong read and repeat rather than weak continuous measurements

15. 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)

16. 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

17. Charge Qubit – Cooper Pair Box

18. 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

19. Flux Qubit – RF-SQUID

20. Phase Qubit - Current Biased Junction • Current controlled to combat continuous charge Qr • Differences in current determines energy state

21. Phase Qubit – Current Biased Junction

22. Circuit Example

23. Qubit Interaction • Easily fabricate transmission lines and inductors to couple qubits • Can be coupled at macroscopic distances

24. Fabrication • Use existing microfabrication techniques from IC industry • Electron beam lithography for charge and flux qubits • Optical lithography for phase qubits

25. 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…

26. Future • Active area of research • Need to simultaneously optimize parameters • New materials to improve properties • Engineering better circuits to handle noise • Local RF pulsing