||Quantum Information Processing : Implementation Adrian Leathers, Benjamin Jacot & Nicolo D’anna

Adrian Leathers, Benjamin Jacot & Nicolò D’Anna

Paper presentation

18.03.17 1

||Quantum Information Processing : Implementation Adrian Leathers, Benjamin Jacot & Nicolo D’anna 18.03.17 2

Overview

• Introduction • Theory

• Setup • Results

• Summary

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Introduction

• Motivation :

• Improve coupling between qubits and make possible longer interaction • Perform quantum gates • High selectivity • Reduce losses in the circuit and enhancement of coherent interaction time

• Achivements (at the time of publication Sep. 2007) :

• Single quantum bit (qubit) operation • Coupling mechanism are restricted to local interations and couple only nearest-neighbour qubits

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Cavity QED with one Superconducting Circuit

Transmon

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Cavity QED with two Superconducting Circuits

• Use Cavity as a Quantum bus to couple 2 distant qubits

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Experimental conditions

• Strong coupling (cavity-qubits) : state decay : cavity decay :

• Strong coupling between qubits

• Dispersive limit, high detuning (cavity-qubit) :

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Effective Hamiltonian in the dispersive limit :

• Transition frequency of the qubits :

• Resonance frequency of the cavity :

• Qubit-state-dependent shift of the cavity frequency :

• Transverse exchange interaction qubit-qubit :

• Detuning cavity-qubit :

• Coupling strength cavity-qubit

Second-order perturbation theory gives the effective Hamiltonian :

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Experimental Setup

CapacitorTransmon

Resonator ( - Cavity)

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Calibration Measurements, Vacuum Rabi splitting

Vacuum Rabi Splitting

• Zero detuning, resonance cavity-qubit

• Width of Splitting = 2g

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Calibration Measurements, Strong coupling

• Qubit-qubit strong coupling: 2J

• Width of avoided crossing = 2J

•

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Calibration Measurements, Dark State

Cavity

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Single qubit control

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Multiplex state readoutSelectivity:

= exited population of addressed qubit

= exited population of unaddressed qubit

= 87%

= 94%

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Coherent state transfer

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Coherent state transfer

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State oscillations

and are not eigenstates of the coupled system; oscillations occur.

Reminder; for a time-independent Hamiltonian:

eigenstates

arbitrary state

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Time evolution

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Quantum gate :

The SWAP gate is the permutation of the two qubits :

Source:Basic Concepts of Quantum Information Processing,David DiVincenzo September 11, 2011

Use of the

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Frequency splitting

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Frequency splitting

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Summary

• Strong coupling limit

• Individual and coherent control of two qubits over a long-range via cavity bus

• Multiplexed control and read out of uncoupled qubits

• Full reconstruction of the density matrix (state tomography)

• Good selectivity ~90%

• Quantum gate :

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Current achievements :

• 2016 :

• Google has built a nine-qubit machine and hopes to scale up to 49 within a year.

• D-Wave announced a quantum computer with more than 2000 qubits. But this machine do not entangle all the qubits, but only with near neighbors and interact to produce not a set of parallel computations, but a single overall quantum state.

( ref: sciencemag.com, Gabriel Popkin, 1 December 2016)