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Quantum Computing Using Harmonic Oscillators in the MicromaserPowerPoint Presentation

Quantum Computing Using Harmonic Oscillators in the Micromaser

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Quantum Computing Using Harmonic Oscillators in the Micromaser

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Quantum Computing Using Harmonic Oscillators in the Micromaser

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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

- Qudit = d-dimensional system
- computational basis:
- qubit: {|0, |1}
- qudit: {|s: s = 0, 1, ... , d-1}

- computational basis:
- Dimensions of Hilbert Space
- qubit 2n
- qudit dn

- d Continuous Variable computation

}

for n quantum systems

- 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

- Position and Momentum of a particle

- USUM|a, b |a, (a+b) mod d “addition modulo-d”
- e.g. for d = 4; |a = |3; |b = |1
USUM|3, 1d=4 |3, (3+1) mod 4 = |3, 0

- 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

- 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

- 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

Coherent State

Fock State

Phase State

Approximate

Phase State

Coherent State

Fock State

n = photon number in cavity field

g= atom-field coupling

tint = interaction time

Trapping occurs when:

- Pump parameter
- Nex = effective pump rate

- 1 spread in n is maximised
tune tint and Nex to produce phase state

- Orthogonal, non-degenerate modes in a multimode cavity
- Number (Fock) State
- Phase State |
- These are conjugate like x, p

- 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)

- 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

- 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

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

?

- 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

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

Whispering Gallery Mode

Quantum

Dot

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

- 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.