UNIVERSITY OF NOTRE DAME

Xiangning Luo EE 698A

Department of Electrical Engineering, University of Notre Dame

Superconducting Devices for Quantum Computation

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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 ComputationClassical 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

|Ψ(0)> Preparation:

The initial preparation of the state defines a wave function at time t0=0.

|Ψ(1)>

….

|Ψ(n)>

P(Ф)=|<Ф|Ψ(n)>|2

U(t1,t0)

U(t2,t1)

U(tn,tn-1)

0

1

n

State evolution:

Evolved by a sequence of unitary operations

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 =

2/

2/

2/

2/

0

0

2cos

2sin

2sin

2cos

0

0

i

i

i

ii

e

e

e

ee

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 - superconductorsAdvantage of solid state implementations Possibility of a scalable implementation of the qubitsSuperconducting 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 QubitSystem Hamiltonian

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

Energy state of n Cooper pairTunneling term

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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

I. Chiorescu et al., Science 299, 1869 (2003).

Coherent time evolution between two quantum states was observed.

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.

Φ=h/4eclockwise anticlockwise

symmetric superposition

antisymmetric superposition

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The superconducting Flux Qubit

I. Chiorescu et al., Science 299, 1869 (2003).

Qubit energy separation is adjusted by changing the external flux.

Resonant absorption peaks/dips are observed.

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.

Measurements of two energy levels of qubit

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The superconducting Flux Qubit

I. Chiorescu et al., Science 299, 1869 (2003).

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.

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.

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.