Demonstration of Quantum Algorithms with

Cavity Coupled Superconducting Qubits

Chris Myers and Yves Salathé

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Based on paper by L.DiCarlo et al. Nature 2009

Introduction

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Several criteria have to be fulfilled in order to build a

quantum computer (DiVincenzo).

Contents

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Cavity and circuit QED

The transmon qubit

Qubit spectroscopy and operations

The dynamical phase

Implementation of the Grover algorithm

Conclusion

Cavity QED

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Circuit QED

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Cavity QED Circuit QED

Atom Superconducting Qubit

Cavity Transmission Line Resonator

The Transmon Qubit

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• Same Hamiltonian as Cooper Pair Box

• Additional large capacitance

• SQUID allows tuning of

Comparison of Transmon and CPB

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Transmon CPB

• The increase in this ratio makes the transmon less sensitive to charge noise

• Also decreases anharmonicity

Charge Dispersion

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The Device

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Qubit Spectroscopy

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Interesting Points

•I : Flux sweet spot for

both qubits

•II : Avoided crossing

with state outside

computational domain

•III : Transverse

coupling

•IV : Vacuum Rabi

splitting

Single-Qubit Operations

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• Apply microwave pulses through the cavity with frequencies close to either or .

•In the frame of the pulse, the Hamiltonian close to resonance for the corresponding qubit is:

•Rotating wave approximation (see exercise 3):

Towards Two-Qubit Operations: The Dynamical Phase

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• Recall: in general, solutions to the Schrödinger equation have to obey

With .

• The exponent is called dynamical phase.

• Adiabatic evolution means that is constant.

Two-Qubit Operations : Spectroscopy

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Adiabatically tune close to point II and back:

Two-Qubit operations : The C-Phase Gate

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• The avoided crossings include state-dependent dynamical phase.

• This evolution is described by the operator:

with , where is the deviation of

the frequency to its value at point I.

• The ground state does not acquire a dynamical phase.

Implementation of Grover Algorithm

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Grover Algorithm

• Start in Ground State

• Create a maximal superposition of all states

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Grover Algorithm

•Apply the oracle O

•This ‘marks’ the solution by inverting it’s phase

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Grover Algorithm

• Apply 1 qubit rotations

• Now in one of the Bell States

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Grover Algorithm

• Apply the operation

• Undoes entanglement, now in equal superposition state

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Grover Algorithm

• More one qubit rotations produces final state, which is the answer .

• Correct state produced with a fidelity of 85%

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Conclusion

Showed the successful implementation of a two qubit

system, by means of circuit QED.

Implementation shows fulfilment of several of the

DiVincenzo criteria.

The architecture used can be expanded to produce a

system of several qubits.

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Thank you for your attention

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