Presentation

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COUPLING SUPERCONDUCTING QUBITS VIA A CAVITY BUS

MAJER ET.AL. NATURE (2007)

OVIDIU COTLET AND LÁSZLÓ SZŐCS

Majer et al. Nature (2007)

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DiVincenzo’s Criteria for Quantum Computing

1. Scalability and well-defined qubits2. Initialization of qubits3. Small decoherence4. 1 and 2 qubit gates5. Measurement

arXiv:cond-mat/9612126

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Motivation

o Previous studies have shown that two nearby qubits can be coupled with local interactions

o Highly desirable to perform gate operations between two distant qubits– How to accomplish?– Use a quantum bus (cavity photons) to

transfer informationo Why use photons?Majer et al. Nature (2007)

Strong coupling limit

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Experiment Goals

o Demonstrate a coherent, nonlocal coupling between two qubits in a transmission line cavity

o Cavity mediates the qubit-qubit interaction via photons

Blais et al. Rhy. Rev. A (2007)

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THEORY

o Begin with the Jaynes Cummings (JC) Hamiltonian

o Eigenstates and eigenenergies readily obtained

o Vacuum Rabi splitting can be observed by moving to a rotating frame and solving the equations of motion

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THEORY

o The solution is , which produces 2 peaks at

o This allows for a measurement of the coupling constant

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Theory

o Consider the strongly dispersive limit, o Using the canonical Schrieffer-Wolf Transformation, eliminate interaction term to 1st order

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THEORY

o That was for 1 qubit. How about 2?o Natural generalization:

o Can easily show that

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THEORY

o Salient features:– No TLS-cavity interaction (no energy is

exchanged) – Cavity frequency shifted by qubit state– Qubit-qubit interaction can be

effectively turned off by making the qubits strongly detuned from one another:

Majer et al. Nature (2007)

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THEORY

o A.C. Stark Shift: rearrange the Hamiltonian

o By applying a strongly detuned drive, we can adjust the number of photons in the cavity, thereby adjusting the qubit transition frequency.

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Experiment Setup

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Strong Qubit-Cavity Coupling

o Demonstrate that each-qubit can be strongly coupled to the cavity

o Use vacuum Rabi splitting to determine the coupling constants

o Ensures that we can go into strongly dispersive limit and that qubit-qubit coupling is big

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Strongly Dispersive Limit

o Cavity shields qubits from the environment.

o Can further isolate qubit by strongly detuning it from the cavity

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Qubit-Qubit Interaction

o Qubits interact by exchanging their excitations through virtual photons in the cavity:

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Single Qubit Control

o Demonstrate fast control of each qubit individually in order to satisfy the 1st part of criteria 4

o Detune the qubits from one another:o Apply a pulse at , then apply a

measurement pulse at to monitor transmission

o From transmission, infer :

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Single Qubit Control

o Response consistent with that of single qubit Rabi oscillation coupling does not affect single qubit operation

o Determine decoherence time to be 78 and 120 ns, which is larger than the coherent manipulation time

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Multiplex Measuremento Use π pulses to put your qubits into desired

states:

o Use probing field resonant with cavity and compare theoretical (via master equation) with actual value

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Coherent State Transfer Between Qubits

o Can transfer the state of one qubit to the other by turning qubit-qubit coupling on and off

o Use off-resonant Stark drive to quickly push qubits into resonance

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Coherent State Transfer

1. Initially qubits are 80 MHz detuned, and are allowed to relax to

2. Apply π pulse to create or 3. Apply Stark pulse to bring qubits into

resonance for some variable time Because not eigenstates of system, we’ll see oscillation

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Coherent State Transfer

o Quarter period of oscillation between qubits is o This is the second part of DiVincenzo’s criterion 4

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Coherent State Transfer

o Observed qubit-qubit oscillation frequency agrees very well with value of J measured from CW spectroscopy

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Summary

o Demonstrated non-local coupling of qubits

o Qubit-qubit interaction is due to the exchange of virtual photons, protecting against cavity induced losses

o Qubits may be manipulated individually and a universal 2 qubit gate can be performed

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Summary

1. Scalability and well-defined qubits2. Initialization of qubits3. Small decoherence4. 1 and 2 qubit gates5. Measurement

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Thank you for your time and attention.

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