Superconducting Qubits

Kyle GartonPhysics C191Fall 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

•Photons•Nuclear Spins

•Ions•Semiconductor Spins

•Quantum Dots•Superconducting Circuits

SizeCoupling with environment

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

•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