circuit quantum electrodynamics - ncku
TRANSCRIPT
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Circuit Quantum Electrodynamicsor
Fundamental Physics with Tiny Pieces of
Cold Metal
Miles Blencowe
Dartmouth College Hanover, New Hampshire, USA
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Support
Experiment: Alex Rimberg (Dartmouth), Eyal Buks
(Technion)
Theory: Andrew Armour (Nottingham, UK), Paul
Nation (RIKEN, Japan)
Funding: National Science Foundation
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I. Circuit Quantum Electrodynamics (cQED)
for Quantum Information Processing
II. cQED and the Quantum-Classical
Correspondence
III. cQED and Analogue Gravity
Outline
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[L DiCarlo et al. Nature 467, 574-578 (2010)]
Four-qubit cQED processor
I. Circuit Quantum Electrodynamics (cQED)
for Quantum Information Processing
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Goal of this first lecture is to understand the physics behind
the cQED scheme for quantum computing.
A classical computer is…
Binary data (…10110111…) encoded in state of a physical
system, for example, as presence (“1”) or absence (“0”) of
electrical charge in a capacitor.
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A quantum computer is…
Superposition principle � quantum bit, or “qubit”:
Unitary operator
Encode qubit in two-level quantum system. Examples:
•Spin ‘down’ and spin ‘up’ states of electron
•Clockwise and anticlockwise electrical currents of
superconducting ring
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Will now analyze following, simpler cQED device
[A. Wallraff et al., Nature 431, 162 (2004);
A. Blais et al., Phys. Rev. A 69, 062320 (2004)]
Coplanar waveguide-CPW (niobium)
Cooper pair box qubit (aluminium)
Control/measurement line
Electron microscope image
Centre conductor of CPW
Ground plane of CPW
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Derive Hamiltonian for Cooper pair box (CPB) qubit -
coplanar waveguide (CPW) resonator system
Use Kirchhoff’s laws:
•Voltages add up to zero
around a closed loop
•Total current entering a
junction equals total exiting a
junction
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Consider first, isolated CPW resonator without the CPB qubit
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Now include Cooper pair box (CPB)
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Now quantize (we are nearly there!)
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Actual CPB qubit slightly more complicated
•Tuning the qubit into resonance with the cavity mode (by varying�ext) and applying microwave pulse allows qubit state
preparation.
•Tuning the qubit away from resonance with the cavity mode
(dispersive limit) allows a measurement of the qubit state (shifts
the cavity mode frequency).
Gives (external magnetic flux) tunable Josephson
energy
For the details, see the original theory and experiment papers:[A. Blais et al., Phys. Rev. A 69, 062320 (2004); A. Wallraff et al., Nature 431, 162 (2004)]
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cQED milestones for quantum information processing
•The “Transmon” [J. Koch et al., Phys. Rev. A 76, 042319 (2007)]
•Coupling superconducting qubits [J. Majer et al., Nature 449, 443
(2007); M. Sillanpaa et al., Nature 449, 438 (2007)]
•Synthesizing arbitrary quantum states in a superconducting
resonator [M. Hofheinz et al., Nature 459, 546 (2009)]
•Preparation and measurement of three-qubit entanglement [L.
DiCarlo et al., Nature 467, 574 (2010)]
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The “transmon” [J. Koch et al., Phys. Rev. A 76, 042319 (2007); J.
Schreier et al., Phys. Rev. B 77, 180502 (2008)]
Increasing Cg reduces the CPB charging energy and hence
dephasing due to 1/f charge fluctuations. Also, increases g,
the CPB-CPW coupling.
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Coupling qubits [J. Majer et al., Nature 449, 443 (2007); M. Sillanpää etal., Nature 449, 438 (2007)]
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Synthesizing arbitrary microwave resonator quantum states[M. Hofheinz et al., Nature 459, 546 (2009)]
Wigner representation of states: theory (top) versus experiment (bottom)
Superconducting qubit used to both prepare and measure
microwave resonator states
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Preparation and measurement of three-qubit entanglement [L.
DiCarlo et al., Nature 467, 574 (2010)]
Transmon qubit