Josephson%20Junction%20Qubits

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Josephson Junction Qubits

• Alex Hegyi
• Justin Ellin
• Andrew Chan

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Classical Resistance (Review)

• Metals
• In a metal, the electrons are shared by atoms in
  a lattice.
• This sea of electrons is free to travel along the
  entire lattice.
• Dissipation
• Caused by inter-electron/ion interactions or
  other atoms, resulting in heat
• (dV) (dI)R, R pL/A (p resistivity, length,
  cross-sectional area)
• P IV
• Prevents indefinite propagation of currents,
  analogous to friction

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Superconductors

• Superconductor Properties
• State characterized by zero (exactly) electrical
  resistance
• Meissner Effect weak external fields only
  penetrate small distances (London skin Depth)
• Type I Superconductivity destroyed abruptly
  when field reaches critical value
• Type II additional critical temperature which
  permits magnetic flux but still no electrical
  resistivity
• Generation of a current to cancel external field

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BSC Theory

• Fermi Energy
• The lowest energy of the highest occupied quantum
  state at absolute zero was considered to be the
  Fermi Energy
• Where N/V is the density of fermions
• This can be derived by considering a
  3-dimensional square box.
• BSC- Bardeen, Cooper, and Schrieffer 1957
• The theory essentially accounts for an energy
  level even below this threshold.
• The gap between this energy level and the fermi
  energy accounts for many of the properties of
  superconductors
• Whereas before the electron could be excited in a
  continuous spectrum of possible energy
  interactions (and interchange/lose energy with
  lattice and other electrons), there is now a
  discrete energy gap.
• The excitations become forbidden and the electron
  sees no obstacles or no resistance! But what
  accounts for this gap?

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Cooper Pairs

• The atoms in a lattice are not fixed
• Free electrons are repulsed from other electrons
  but are able to attract and distort the
  positively charged nucleus. This distortion in
  turn attracts other electrons.
• Coupling (on the order of fractions of an eV)
  usually broken by thermal energy or coulomb
  interaction.
• When the thermal energy is low, T 5K, this
  dominates effectively linking electrons in pairs
  to each other even over large distances .
• The electrons pair up with those of opposite
  spin.
• Exclusion principle no longer applies. All
  electron pairs condense into this bound state
  energy.

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Two Notes on Modern Superconductors

• Current Lifetime occasionally interactions may
  result that do go across the gap.
• Experimentally, currents on superconductors can
  perpetuate for upwards of tens of thousands of
  years.
• Theoretically, could last longer than the known
  age of the universe.
• High Temperature Superconductors superconductors
  that cant be explained by BCS because state
  achieved well above fermi levels
• (Sn5In)Ba4Ca2Cu10Oy superconducting at 200K
  (Dry ice is about this range)
• How do they work?

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Josephson Junction

• Brian David Josephson proposed (1964) sandwiching
  an insulator between two superconductors.
• Provided separation is small, current will tunnel
  through the barrier
• However when the current reaches a certain
  critical value then a voltage will develop across
  the junction which will in turn increase the
  voltage further.
• The frequency of this oscillation is 100 GHz
• Below this critical current, no voltage. Above,
  oscillating voltage.

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Some Uses of Junctions

• SQUIDs (superconducting quantum interference
  devices)
• Precise Measurements
• Voltage to Frequency Converter
• Single-Electron Transistors

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Flux Qubit

• Quantum state is stored in the direction of the
  current
• 0gt is counter-clockwise
• 1gt is clockwise

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Manipulate State

• Requires a constant external magnetic flux
• Flux determines the energy difference between the
  two states
• Apply a microwave pulse
• Causes the flux qubit to oscillate between ground
  state (0gt) and excited state (1gt)

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SQUID

• Superconducting Quantum Interference Device

Critical Current Below Current flows without
voltage Above Oscillating current develops
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Measurement

• Apply a current pulse to SQUID
• Collapses state
• Magnetic flux through flux qubit determines
  critical current of SQUID

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Qubit Interaction

• Entanglement between two qubits is achieved by
  coupling their fluxes
• Superconducting bus
• Transfers a quantum state from one qubit to
  another by sending a single photon along a
  superconducting wire

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Additional DiVincenzo Criteria

• Conversion of stationary, flying qubits
• Optical Microcavities, Cavity QED
• Transmission of flying qubits
• Fiber Optics
• Microwave transmission lines (Circuit QED)way to
  accomplish the above in case of superconducting
  qubits

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Strong Coupling/Cavity QED

• Two-level quantum system coupled to
  electromagnetic cavity
• Strong Coupling characterized as coherent
  exchange of excitation between cavity, quantum
  system
• i.e., coherent conversion between stationary,
  flying qubit
• ModelTwo SHOs connected by weak spring

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Microwave Resonator/Qubit System
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Quantum Communication

• If energy difference between 0gt and 1gt resonant
  with cavity, energy exchanged (Rabi rotation)
• If off-resonant (dispersive) energy not exchanged
• Align qubits along transmission line, tune energy
  difference (using gate bias, flux bias) to
  control interaction with line

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Microwave Resonator/Qubit System