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 Size Coupling with environment

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 τ m (with good signal/noise ratio) Energy Relaxation Rate Γ 1 ON Coherence Decay Rate Γ 2 OFF Dead time t d (time to reset device) Fidelity (F = P 00c + P 11c − 1)

16. Charge Qubit – Cooper Pair Box Biased to combat continuous charge Q r 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 Q r 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 Q r 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) >2x10 4 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