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||Quantum Information Processing : Implementation Adrian Leathers, Benjamin Jacot & Nicolo D’anna
Adrian Leathers, Benjamin Jacot & Nicolò D’Anna
Paper presentation
18.03.17 1
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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)