Transcript Superconducting Devices for Quantum Computation Xiangning Luo EE 698A Department of Electrical Engineering, University of Notre Dame UNIVERSITY OF NOTRE DAME.

Superconducting Devices for Quantum
Computation
Xiangning Luo
EE 698A
Department of Electrical Engineering, University of Notre Dame
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Outline of Presentation
 Introduction to quantum computation
 Superconducting qubit devices
 Josephson charge qubit
 Qubits based on the flux degree of freedom
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Quantum Computation
Classical Computation:
Classical logic bit: “0” and “1”
Quantum Computation:
Quantum bit, “Qubit”, can be manipulated using the rules of quantum physics
Orthogonal quantum states |0> , |1> and their superposition |Ψ> = c0|0> + c1|1>
A Quantum state of M bits is a superposition of 2M states.
The quantum computation is a parallel computation in which all 2M basis
vectors are acted upon at the same time.
If one wanted to simulate a quantum computer using a classical
computer one would need to multiply together 2M dimensional unitary
matrices, to simulate each step.
A quantum computer can factorize a 250-digit number in seconds while
an ordinary computer will take 800 000 years!
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Quantum Computation
0
|Ψ(0)>
U(t1,t0)
1
Preparation:
The initial preparation of the state defines a
wave function at time t0=0.
|Ψ(1)>
U(t2,t1)
….
State evolution:
Evolved by a sequence of unitary operations
U(tn,tn-1)
n
|Ψ(n)>
P(Ф)=|<Ф|Ψ(n)>|2
Measurement:
Quantum measurement is projective.
Collapsed by measurement of the state
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Quantum Logic Gates
Question: How to implement a general unitary operator?
Answer: Introduce a complete set of logic gates.
Any possible operation on an qubit register can be represented in
terms of a suitable sequence of actions of such elementary logic gates
It is proved that an arbitrary 2x2 unitary matrix may be decomposed as
U=
i / 2

e
ei 
 0
 
0  cos 2
i / 2  
e   sin 
 2

 sin  e i / 2
2
   0
cos 
2
0 
i / 2 
e 
where α,β,ν, and δ are real-valued.
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Superconducting Qubit Devices
Any quantum mechanically coherent system could be used to
implement the ideas of quantum computation.
- single photons
- nuclear spins
- trapped ions
- superconductors
Advantage of solid state implementations
Possibility of a scalable implementation of the qubits
Superconducting devices
The minimum levels of decoherence among solid state
implementations.
A promising implementation of qubit.
two kinds of qubit devices either based on charge or flux degrees of
freedom.
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The Cooper Pair Box Qubit
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The Cooper Pair Box Qubit
System Hamiltonian
Tunneling term
Energy state of n Cooper pair
A sudden square pulse is applied to the gate Vg
The square gate pulse lasts for some time ∆t
Vg returns to zero
The probability that the state does not return to the ground state
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The Cooper Pair Box Qubit
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The Cooper Pair Box Qubit
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The Cooper Pair Box Qubit
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The superconducting Flux Qubit
Coherent time evolution between two quantum states was observed.
antisymmetric superposition
symmetric superposition
clockwise
Φ=h/4e
anticlockwise
Flux qubit consists of 3 Josephson junctions arranged in a superconducting loop.
Two states carrying opposite persistent currents are used to represent |0> and |1>.
External flux near half Φ0=h/2e is applied.
A SQIUD is attached directly.
MW line provides microwave current bursts inducing oscillating magnetic fields.
Current line provides the measuring pulse and voltage line allows the readout of the
switching pulse.
I. Chiorescu et al., Science 299, 1869 (2003).
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The superconducting Flux Qubit
Measurements of two energy levels of qubit
Qubit energy separation is adjusted by
changing the external flux.
Resonant absorption
observed.
peaks/dips
are
Dots are measured peak/dip positions
obtained by varying frequency of MW
pulse.
The continuous line is a numerical fit
giving an energy gap ∆ = 3.4 GHz in
agreement of numerical simulations.
I. Chiorescu et al., Science 299, 1869 (2003).
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The superconducting Flux Qubit
Different MW pulse sequences are used to
induce coherent quantum dynamics of the
qubit in the time domain.
Rabi oscillations - when the MW frequency
equals the energy difference of the qubit,
the qubit oscillates between the ground
state and the excited state.
Resonant MW pulse of variable length with
frequency F = E10 is applied.
MW F = 6.6GHz
MW power 0dbm, -6dbm, and -12dbm
Linear dependence of the Rabi
frequency on the MW amplitude, a key
signature of the Rabi process.
Decay times up to ~150 ns results in
hundreds of coherent oscillations.
The pulse length defines the relative
occupancy of the ground state and the
excited state.
The switching probability is obtained by
repeating the whole sequence of
reequilibration, microwave control pulses,
and readout typically 5000 times.
I. Chiorescu et al., Science 299, 1869 (2003).
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