Quantum computing using harmonic oscillators in the micromaser
This presentation is the property of its rightful owner.
Sponsored Links
1 / 19

Quantum Computing Using Harmonic Oscillators in the Micromaser PowerPoint PPT Presentation


  • 50 Views
  • Uploaded on
  • Presentation posted in: General

Quantum Computing Using Harmonic Oscillators in the Micromaser. Dr. Ben Varcoe, Martin Jones , Gary Wilkes University of Sussex Department of Physics and Astronomy Atomic, Molecular and Optical Physics group. Qubits  Qudits. Qudit = d -dimensional system computational basis:

Download Presentation

Quantum Computing Using Harmonic Oscillators in the Micromaser

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Quantum computing using harmonic oscillators in the micromaser

Quantum Computing Using Harmonic Oscillatorsin the Micromaser

Dr. Ben Varcoe,

Martin Jones, Gary Wilkes

University of Sussex

Department of Physics and Astronomy

Atomic, Molecular and Optical Physics group


Qubits qudits

Qubits  Qudits

  • Qudit = d-dimensional system

    • computational basis:

      • qubit: {|0, |1}

      • qudit: {|s: s = 0, 1, ... , d-1}

  • Dimensions of Hilbert Space

    • qubit  2n

    • qudit  dn

  • d   Continuous Variable computation

}

for n quantum systems


Physical qudits

Physical Qudits

  • Harmonic Oscillators

    • Position and Momentum of a particle

      • Gottesman, Kitaev and Preskill: PRA 64, 012310

    • Amplitude and Phase of a field

      • Bartlett, de Guise and Sanders: PRA 65, 052316


The sum gate

The SUM Gate

  • USUM|a, b  |a, (a+b) mod d “addition modulo-d”

  • e.g. for d = 4; |a = |3; |b = |1

    USUM|3, 1d=4  |3, (3+1) mod 4 = |3, 0


Special case d 2

Special Case: d = 2

  • d = 2

    USUM|00  |00 USUM|01  |01 USUM|10  |11 USUM|11  |10  USUM UCN (for d = 2)

    SUM gate is a generalised CNOT gate


The micromaser

The Micromaser

  • Single atoms and single modes of the field interact via Jaynes-Cummings Hamiltonian

from: http://prola.aps.org/figure/PRA/v46/i1/p567_1/fig1


Micromaser basics

Micromaser Basics

  • Rubidium-85 excitedby three step laser to upper Rydberg level

  • Transition between two levels is resonant with microwave cavity mode

  • Detection of atoms provides information about field


States of interest

States of interest

Coherent State

Fock State

Phase State


States of interest1

States of interest

Approximate

Phase State

Coherent State

Fock State


Trapping states

n = photon number in cavity field

g= atom-field coupling

tint = interaction time

Trapping occurs when:

Trapping States


Generating phase states

Generating Phase States

  • Pump parameter

    • Nex = effective pump rate

  •   1  spread in n is maximised

     tune tint and Nex to produce phase state


Qudits in the micromaser

Qudits in the Micromaser

  • Orthogonal, non-degenerate modes in a multimode cavity

  • Number (Fock) State

  • Phase State |

    • These are conjugate like x, p


Scaling in the micromaser

Scaling in the Micromaser

  • Nex defines maximum Fock state in the phase state superposition; e.g. for Nex = 5:

    | = a|0 + b |1 + c |2 + d |3 + e |4 + f |5

  • So two qudits give dn = 36 states

  • Maximum Nex  1500

    • n = 2  (1500)2 = 2.25 million states!!(compared to 4 for qubits)


Sum gate in the micromaser

SUM Gate in the Micromaser

  • Couple two modes via non-linear Kerr media,

    • e.g. a suitable atom

  • Gives:

  • So if t= -1, interaction is a SUM gate

    • possible in the micromaser (t 1/g)

(n+1)P3/2

(n+1)S1/2

nP3/2


Single qudit operations

Single Qudit Operations

  • Arbitrary unitary transformations by injecting sequences of appropriate atoms

    • linear displacement of cavity mode

    • squeezing of the field state

    • non-linear Kerr transformations

  • Fourier transform converts between Fock and phase eigenstates


Divincenzo criteria

A scalable physical system with well-characterised qudits

The ability to initialise the qudit state

Decoherence times much longer than the quantum gate operation time

A universal set of quantum gates

The ability to measure specific qudits

?

DiVincenzo Criteria


The future

The Future

  • Desktop Micromaser Quantum PCs?

  • Micromaser theory can be used in some quantum dot proposals

    • allows miniaturisation

    • better control over “atoms” (e.g. tint)

    • very strong “atom” – field interaction


Microdisk cavities

Higher frequency (100THz vs. GHz)

lower mode volume (m3 vs. cm3)

More than compensates for reduced lifetime

Single quantum dot

Whispering Gallery Mode

Reduced photon lifetime

Microdisk Cavities

Whispering Gallery Mode

Quantum

Dot

from: http://www.its.caltech.edu/~vahalagr/


Summary

Summary

  • Qudits offer a new and potentially more efficient alternative to qubits.

  • The micromaser is a promising candidate for quantum information applications.

  • Implementation of a qudit QC in the micromaser looks possible.

  • Possibility of future incorporation into solid state architectures.


  • Login