1. Josephson Junctions,Josephson Junctions,
What are they?What are they?
- A Superconductor-Insulator-Superconductor device, placed between two electrodes.
-Josephson Effect: the phase of the wavefunction of a superconducting
electron pair separated by an insulator maintains a fixed phase relation.
-This means that we can describe the wavefunction around the loop of a
Superconductor, with only a phase difference due to the presence of the insulating
Gap.
-This is the very basic form of quantum coherence. The wavefunction in one
branch is coherent with the wavefunction of the second branch. Thus if
we manipulate the state it will be continuous across the boundary with a only
phase difference.
2. SuperconductorsSuperconductors
AluminumAluminum 1.2K1.2K
TinTin 3.7K3.7K
MercuryMercury 4.2K4.2K
NiobiumNiobium 9.3K9.3K
Niobium-TinNiobium-Tin 17.9K17.9K
Tl-Ba-Cu-oxideTl-Ba-Cu-oxide 125K125K
A superconductor is a metal that allows a current to pass through it with no loss
due to heat dissipation.
Typical values for the critical temperature range from mK to 100K
MetalMetal Critical T(K)Critical T(K)
Using Superconductors we can preserve a wavefunction
because the fact that the current wavefunction is not
perturbed by its journey through the metal means that it
will stay in a given state.
The current can be seen as a wavefunction, and is thus
A probability distribution of different current values, this
implies that clockwise and counter clockwise. It is this
view of the current that enables us to create qubits from
a simple loop of superconductor.
3. Superconductors II
-When a metal is cooled to the critical temperature, electrons in the metal form Cooper Pairs.
-Cooper Pairs are electrons which exchange phonons and become bound together.
-As long as kT < binding energy, then a current can flow without dissipation.
-The BCS theory of Superconductivity states that bound photons have slightly lower
energy, which prevents lattice collisions and thus eliminates resistance.
-Bound electrons behave like bosons. Their wavefunctions don’t obey
Pauli exclusion rule and thus they can all occupy the same quantum state.
4. Cooper PairsCooper Pairs
-Cooper pairs can tunnel together through the insulating layer of Josephson Junction.
-This process is identical to that of quantum barrier
penetration in quantum mechanics.
-Because of the superconducting nature (no
resistance) and the fact that Cooper pairs
can jointly tunnel through an insulator we can
maintain a quantum current through the Josephson Junction without an applied voltage.
-Thus a Josephson Junction can be used as a very sensitive voltage, current or
flux detector.
-A changing magnetic field induces a current to flow in a ring of metal, this effect
can be used to detect flux quanta. Radio Astronomy uses these devices frequently.
5. Josephson Junction DevicesJosephson Junction Devices
-There are three primary Josephson Junction devices.
-The Cooper Pair box is the most basic device. We can envision it as a
system with easily split levels, and use the degenerate lowest energy levels as a qubit.
-Similarly to the Cooper Pair box we can use inductors to adjust,
a Josephson Junction, until the potential represented by the
potential well is a degenerate double well. We can then use symmetric and anti-
symmetric wavefunctions and their associated eigenvalues as |0> and |1>.
6. Josephson Junction Devices IIJosephson Junction Devices II
A current-biased Josephson Junction employs
creates a “washboard” shaped potential.
Splitting in the wells indicates allows us to use
the lowest two levels as qubit states.
The higher energy state |1> can be detected because the tunneling probability
under a microwave probe will be 500 times as probable to induce a transition.
Creates a detectable voltage by “going downhill.” Thus we can know the state.
7. WhyWhy Josephson Junctions?Josephson Junctions?
Microscopic implementationsMicroscopic implementations::
based on electron spins, nuclei spins, or other microscopicbased on electron spins, nuclei spins, or other microscopic
propertiesproperties
(+)decohere slowly as naturally distinguishable from environment(+)decohere slowly as naturally distinguishable from environment
(+)single ions can be manipulated with high precision(+)single ions can be manipulated with high precision
(-)hard to apply to many qubits(-)hard to apply to many qubits
(-)difficult to implement with devices(-)difficult to implement with devices
Macroscopic Implementations: Solid StateMacroscopic Implementations: Solid State
- Semiconductors: quantum dots, single donor systemsSemiconductors: quantum dots, single donor systems
- Superconductors: Josephson Junctions:Superconductors: Josephson Junctions:
- more success so farmore success so far
- Josephson tunnel junction is “the only non-dissipative, stronglyJosephson tunnel junction is “the only non-dissipative, strongly
non-linear circuit element available at low temperature “non-linear circuit element available at low temperature “
8. Benefits of Josephson JunctionsBenefits of Josephson Junctions
- Low temperatures of superconductorLow temperatures of superconductor::
- no dissipation of energyno dissipation of energyno resistanceno resistanceno electron-electronno electron-electron
interactions(due to energy gap of Cooper pairs)interactions(due to energy gap of Cooper pairs)
- low noise levelslow noise levels
- PrecisePrecise manipulation of qubits possiblemanipulation of qubits possible
- ScalableScalable theoretically for large numbers of qubitstheoretically for large numbers of qubits
- Efficient use of resourcesEfficient use of resources: circuit implementation using: circuit implementation using
existing integrated circuit fabrication technologyexisting integrated circuit fabrication technology
- Nonlinear Circuit ElementNonlinear Circuit Element
- Needed for quantum signal processingNeeded for quantum signal processing
- ““easy” to analyze electrodynamics of circuiteasy” to analyze electrodynamics of circuit
Current versus flux across
Josephson Junction
9. Circuit Implementation IssuesCircuit Implementation Issues
Electrical measurements of circuit elements:Electrical measurements of circuit elements:
ClassicalClassical Quantum =Quantum =
Numerical valuesNumerical values wavefunctionswavefunctions
-- E.g.E.g. classical capacitor chargeclassical capacitor charge superposition of positive andsuperposition of positive and
negative chargenegative charge
• Need to implement gate operations for transferring qubit
information between junction and circuit via entanglement:
•Read, Write, Control
•But need to avoid introducing too much noise to system,
want to isolate qubits from external electrodynamic
environment
C = 10 pF |C > = a*|0> + b*|1>
10. ProblemsProblems
Intrinsic decoherenceIntrinsic decoherence due todue to
entanglemententanglement
Statistical variations inherent in fabricationStatistical variations inherent in fabrication transitiontransition
frequencies and coupling strength determined and taken intofrequencies and coupling strength determined and taken into
account in algorithmsaccount in algorithms
Noise from environmentNoise from environment causes timecauses time
dependent decoherence and relaxationdependent decoherence and relaxation
relaxation: bloch sphere latitude diffusing, state mixing-relaxation: bloch sphere latitude diffusing, state mixing-∆Θ∆Θ
decoherence: bloch sphere longtitude diffusing, dephasing -decoherence: bloch sphere longtitude diffusing, dephasing -∆Φ∆Φ
Due to irreversible interaction with environment,Due to irreversible interaction with environment,
destroys superposition of statesdestroys superposition of states
-- change capacitor dielectric constant change capacitor dielectric constant
-- low frequency parts of noise causelow frequency parts of noise cause
resonance to wobbleresonance to wobble
diphase oscillation in circuitdiphase oscillation in circuit
-- noise with frequency of transition will causenoise with frequency of transition will cause
transition between statestransition between states energy relaxationenergy relaxation
11. More ProblemsMore Problems
Unwanted transitions possibleUnwanted transitions possible
Can engineer energy difference between states to avoid thisCan engineer energy difference between states to avoid this
Spurious resonance states:Spurious resonance states:
Example: spurious microwave resonators inside Josephson tunnelExample: spurious microwave resonators inside Josephson tunnel
barrier coupling destroys coherence by decreasing amplitude ofbarrier coupling destroys coherence by decreasing amplitude of
oscillationsoscillations
Measurement CrosstalkMeasurement Crosstalk: entanglement of different: entanglement of different
qubitsqubits
Measuring 1 qubit affects state of other qubitsMeasuring 1 qubit affects state of other qubits
solve with single shot measurement of all qubitssolve with single shot measurement of all qubits
2 qubits done, but multiple will be a challenge2 qubits done, but multiple will be a challenge
12. Current Research inCurrent Research in
Superconducting QubitsSuperconducting Qubits
•Identification and reduction of sources ofIdentification and reduction of sources of
decoherencedecoherence
•Improved performance of qubitImproved performance of qubit
manipulationmanipulation
13. Decoherence In Josephson PhaseDecoherence In Josephson Phase
Qubits from Junction ResonatorsQubits from Junction Resonators
• Microscopic two-level systems (resonators)Microscopic two-level systems (resonators)
found within tunnel barriersfound within tunnel barriers
• Affect oscillation amplitude rather than timingAffect oscillation amplitude rather than timing
14. Decoherence In Josephson PhaseDecoherence In Josephson Phase
Qubits from Junction ResonatorsQubits from Junction Resonators
15. Simultaneous State Measurement ofSimultaneous State Measurement of
Coupled Josephson Phase QubitsCoupled Josephson Phase Qubits
• Previous studies rely on separate measurementsPrevious studies rely on separate measurements
of each qubitof each qubit
• Need simultaneous measurement to establishNeed simultaneous measurement to establish
entanglemententanglement
• Crosstalk necessitates faster measurementCrosstalk necessitates faster measurement
schemesschemes
16. Simultaneous State Measurement ofSimultaneous State Measurement of
Coupled Josephson Phase QubitsCoupled Josephson Phase Qubits
17. Faster Qubit Measurement SchemeFaster Qubit Measurement Scheme
• Allows for study of 2-qubit dynamicsAllows for study of 2-qubit dynamics
• ~2-4ns measurement scheme is an order of~2-4ns measurement scheme is an order of
magnitude faster than previous onesmagnitude faster than previous ones
• Short bias current pulse reduces well depthShort bias current pulse reduces well depth
19. Superconducting TetrahedralSuperconducting Tetrahedral
Quantum BitsQuantum Bits
• Enhanced quantum fluctuations allow junctionsEnhanced quantum fluctuations allow junctions
of higher capacitancesof higher capacitances
• Quadratic susceptibility to flux, charge noiseQuadratic susceptibility to flux, charge noise
• Variety of manipulation schemes using magneticVariety of manipulation schemes using magnetic
or electric biasor electric bias
