building a quantum information processor using superconducting
TRANSCRIPT
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Building a Quantum Information Processor using Superconducting Circuits
UCSB/NIST TU DelftCEA Saclay Chalmers
Yale/ETHZ NECYale NIST
Chalmers, NEC
Yale/ETHZ NECChalmersJPLYale
YaleETHZ
NISTSanta-BarbaraMaryland
NEC Y l DelftIPHT
NEC YaleNIST
with material from NIST, UCSB,
Berkeley, NEC, NTT, CEA Saclay,
Yale and ETHZ
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Conventional Electronic Circuitsfirst transistor at Bell Labs (1947)basic circuit elements: first transistor at Bell Labs (1947)basic circuit elements:
basis of modern information and communication technology
intel dual core processor (2006)
technology
properties :• classical physics
t h i
2.000.000.000 transistors
• no quantum mechanics• no superposition principle• no quantization of fields
smallest feature size 65 nmclock speed ~ 2 GHzpower consumption 10 W
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Classical and Quantum Electronic Circuit Elements
basic circuit elements: charge on a capacitor:
current or magnetic flux in an inductor:
quantum superposition states:
• charge qg q
• flux
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Constructing Linear Quantum Electronic Circuits
b i i it l t h i LC ill tbasic circuit elements: harmonic LC oscillator: energy:electronic
photon
classical physics:
quantum mechanics:
Review: M. H. Devoret, A. Wallraff and J. M. Martinis, condmat/0411172 (2004)
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Constructing Non-Linear Quantum Electronic Circuits
i it l tcircuit elements:
Josesphson junction:a non-dissipative nonlinear pelement (inductor)
Review: M. H. Devoret, A. Wallraff and J. M. Martinis, condmat/0411172 (2004)
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Constructing Non-Linear Quantum Electronic Circuits
i it l t h i ill t licircuit elements: anharmonic oscillator: non-linear energy level spectrum:
Josesphson junction:a non-dissipative nonlinear pelement (inductor)
electronic
Review: M. H. Devoret, A. Wallraff and J. M. Martinis, condmat/0411172 (2004)
artificial atom
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How to Operate Circuits Quantum Mechanically?
recipe:
• avoid dissipation
• work at low temperatures• work at low temperatures
• isolate quantum circuit from environment
Review: M. H. Devoret, A. Wallraff and J. M. Martinis, condmat/0411172 (2004)
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The challenge:
Generic Quantum Information ProcessorThe challenge:
2-qubit gates:controlled interactionsqubits:
two-level systemsy
single-bit gates readout
• Quantum information processing requires excellent qubits, gates, ...• Conflicting requirements: good isolation from environment while
i t i i d dd bilitM. Nielsen and I. Chuang,
Quantum Computation and Quantum Information (Cambridge, 2000)
maintaining good addressability
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The DiVincenzo Criteria
for Implementing a Quantum Computer in the standard (circuit approach) to quantum information processing (QIP):
#1. A scalable physical system with well-characterized qubits.#2. The ability to initialize the state of the qubits.#3. Long (relative) decoherence times, much longer than the gate-operation time.#4. A universal set of quantum gates.#5. A qubit-specific measurement capability.
plus two criteria requiring the possibility to transmit information:
#6. The ability to interconvert stationary and mobile (or flying) qubits.#7. The ability to faithfully transmit flying qubits between specified locations.
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Outline
• realization of superconducting quantum electronic circuits• the harmonic oscillatorthe harmonic oscillator• the current biased phase qubit• the charge qubit
• controlled qubit/photon interactions• controlled qubit/photon interactions• cavity quantum electrodynamics with circuits
• qubit read-outi l bit t l• single qubit control
• decoherence• two-qubit interactions
• generation of entanglement• realization of quantum algorithms
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Superconducting Harmonic Oscillator
• typical inductor: L 1 nH
a simple electronic circuit:
• typical inductor: L = 1 nH
• a wire in vacuum has inductance ~ 1 nH/mm
• typical capacitor: C = 1 pF
• a capacitor with plate size 10 m x 10 m and dielectric AlOx ( = 10) of thickness 10 nm has
LC
dielectric AlOx ( = 10) of thickness 10 nm has a capacitance C ~ 1 pF
• resonance frequency
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:
parallel LC oscillator circuit: voltage across the oscillator:p g
total energy (Hamiltonian):
with the charge stored on the capacitor
a flux stored in the inductor
i f i i i i i b dproperties of Hamiltonian written in variables and
and are canonical variables
see e.g.: Goldstein, Classical Mechanics, Chapter 8, Hamilton Equations of Motion
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Raising and lowering operators:
in terms of Q and
number operator
with Zc being the characteristic impedance of the oscillatorwith Zc being the characteristic impedance of the oscillator
charge Q and flux operators can be expressed in terms of raising and lowering operatorsoperators:
Exercise: Making use of the commutation relations for the charge and flux operators, sh w that the ha i s illat Ha ilt ia i te s f the aisi g a d l we i g show that the harmonic oscillator Hamiltonian in terms of the raising and lowering operators is identical to the one in terms of charge and flux operators.
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Internal and External Dissipation in an LC Oscillator
internal losses:conductor, dielectric
external losses:radiation, coupling
total losses
impedance
quality factorquality factor
excited state decay rate
problem 2: internal and external dissipation