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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).

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## Superconducting Qubits

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**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)**Qubit Options**• Photons • Nuclear Spins • Ions • Semiconductor Spins • Quantum Dots • Superconducting Circuits Coupling with environment Size**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**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**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**Phase Qubit - Current Biased Junction**• Current controlled to combat continuous charge Qr • Differences in current determines energy state**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

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