wesley7137/quantum · Datasets at Hugging Face

text stringlengths 0 8.13M
3/2 1/2 1/2
→ →
90P1/2) transition, with the atoms being prepared in the correct initial state by classical
microwave fields. The advantage to working with a one-photon transition is the higher
coupling strength, and the availability of proven cavity designs. The advantage offered
by a two-photon transition is the potential for lower decoherence induced by stray fields
[46]. Relative shifts of the energy levels induced by external electric or magnetic fields
are reduced due to the common quantum numbers (except n) of the two states, and the
use of m = 0 to m = 0 transitions, possible for a two-photon transition, can further
reduce relative shifts.
The two photon micromaser has been demonstrated [39] operating just short of
the one-atom-at-a-time regime, and the experiment is made easier by moving to high-
n Rydberg transitions. Two factors significantly improve the ability to create a two
4
photon maser: atom-field coupling strength scales as n , thus an n = 90 state is coupled
25 times more strongly than the n = 40 states used in previous two-photon maser
experiments [39] and the transition frequency is also significantly reduced making the
cavity decay time 6 times longer for the same cavity Q-factor. Moreover although they
aremorecloselyseparatedinenergy, Rydbergatomswithn > 90canbestate-sensitively
detected using tunnelling field ionisation, which has been demonstrated with quantum
efficiencies above 80%, and with an ionisation efficiency above 98% [41].
In addition to the fabrication of the cavities themselves, tuning of the resonant
frequencies of the cavities, on an individual basis, is required. For full flexibility, fast
switching of the frequencies (to turn cavities on or off) is desirable. A general method
Quantum Computing Using Crossed Atomic Beams 10
for such switching is to tune the resonant frequencies of the cavities. This can be
achieved for microfabricated cavities by an array of piezoelectric elements mounted to
the computational wafer. By changing applied electric potentials on each piezoelectric
element, andthus theforceappliedtoeachcavity, thephysical dimensions ofthecavities
can be varied, and with them their resonant frequencies. This method is known to work
well for larger microwave cavities, and should allow fast (kilohertz speeds) switching of
all the cavity elements on the chip.
5. Performance and decoherence
Potential sources of decoherence include the decay lifetime of the microwave cavities,
variationof atomicvelocities, andthe accuracy of the two-atomoverlap in thecollisional
cavities.
The fidelity of the three-atom entangled state from the micromaser will be affected
by the uncertainty in the atomic velocities, and therefore interaction times. A velocity
resolution of 0.5% has been achieved in similar experiments [36]. This limits the fidelity
of the three-atom entangled states generated by the system to approximately 99.5%.
Velocity selection uncertainties have a larger effect on the collisional entanglement
process, as they affect not just the transit time of the atoms through the cavity, but
also their arrival times, altering the two-atom overlap time. The arrival times of atoms
are jittered further due to the mechanism by which the single atom sources operate. A
velocity-selected pulse ofatomsenters thesourcecavity, andeachatomhasaprobability
P 0.9 of emitting a photon into the cavity mode and emerging in the correct atomic
e
≃
state for the subsequent microwave fields. Once this has occurred, the cavity photon
blocks the occurrence of further emission events. The time from the start of the atomic
pulse to the emission event is then 1.1 atom-transit times along the short axis of the
source cavity – about 0.01 µs – with a standard deviation of around 0.01 µs. In the
collisional cavity, the atoms travel along the long axes of the cavity, and so 0.01 µs
corresponds to 1% of the atomic overlap time. This is expected to limit the collisional
entanglement fidelity to about 99%, while the differing transit times of the two atoms
will contribute to dephasing at below the 1% level.
Othercontributionstodephasing comefromstray, fluctuatingelectricandmagnetic
fields in the apparatus altering the energies of the atomic states. These fields come from
contact potentials due to deposition of atomic vapours on the surfaces of the apparatus,
andthegrainboundariesintheniobiumusedtoconstruct themicrowave cavities. These
effects can be minimised by enclosing the atomic paths with superconducting material,
essentially eliminating the stray fields along the beam path, and by preparation and
treatment of the niobium cavities to minimise the effects of grain boundaries.
Extrapolatingfrompreviouslyrealisedmicrowavecavitydesignsandknowndatafor
lower Rydberg states, the interaction time of an atom with the two-photon micromaser
cavity is expected to be on the order of 1 µs, the time in-between atoms to be around
10 µs, and the cavity decay lifetime 10 ms. The loss of phase coherence between two
Quantum Computing Using Crossed Atomic Beams 11
successive atoms caused by the finite cavity lifetime would therefore be just 0.05%.
There are other small uncertainties associated with the operation of the device,
such as the precision of the state rotations, but these can be controlled to a very high
level, below a 0.1% contribution to decoherence, with minimal experimental overhead,
and are purely technologically limited.
It can be seen that the cavity decay will not be the limiting factor on the
performance of the computer, but other errors such as the overlap of atoms in the
collisional entanglement cavity, and small uncertainties in state preparation, mainly
due to the accuracy of the selection of atomic velocities, will limit the performance of
the gate operations.
The accuracy of the velocity selection could be improved past the 0.5% level in
several ways. Firstly, the use of longer selection paths, with fast switching tolerances on
the microwave fields and careful control of field leakage could improve the resolution.
Improved Doppler velocity selection by laser excitation, for example by using selection
on all three excitation steps rather than just one, could narrow the distribution a little
more. More precise velocity selection schemes are also possible.
The timing jitter of the single atom sources could be improved significantly by the
construction of re-entrant microwave cavities with very thin cross-sections, hence low
mode volumes and high coupling strengths. Such cavities could also be expected to
have higher decay rates, which would allow increases in the rate of atom generation,
and hence computational speed.
As a final note, we recognise that scaling the micromaser down to this size and
reaching the level of integration required to build a quantum computer presents a
formidable technological challenge. However all of the required components of such
a system have been previously demonstrated and the techniques for fabricating an
integrated device have also been proven in recent years. If all of these strands can be
brought together, the result will be a quantum computer with the potential to scale to
tens of qubits in the near future, and hundreds or thousands of qubits with refinement
of the operating conditions. The system has the potential to cross the threshold for
fault-tolerant quantum computing [47, 48, 49], and therefore scale to arbitrary size.
We have shown that a scalable cavity QED based quantum computer using some
of the most recent advances in quantum information science is technically possible. It

3/2 1/2 1/2

→ →

90P1/2) transition, with the atoms being prepared in the correct initial state by classical

microwave fields. The advantage to working with a one-photon transition is the higher

coupling strength, and the availability of proven cavity designs. The advantage offered

by a two-photon transition is the potential for lower decoherence induced by stray fields

[46]. Relative shifts of the energy levels induced by external electric or magnetic fields

are reduced due to the common quantum numbers (except n) of the two states, and the

use of m = 0 to m = 0 transitions, possible for a two-photon transition, can further

reduce relative shifts.

The two photon micromaser has been demonstrated [39] operating just short of

the one-atom-at-a-time regime, and the experiment is made easier by moving to high-

n Rydberg transitions. Two factors significantly improve the ability to create a two

4

photon maser: atom-field coupling strength scales as n , thus an n = 90 state is coupled

25 times more strongly than the n = 40 states used in previous two-photon maser

experiments [39] and the transition frequency is also significantly reduced making the

cavity decay time 6 times longer for the same cavity Q-factor. Moreover although they

aremorecloselyseparatedinenergy, Rydbergatomswithn > 90canbestate-sensitively

detected using tunnelling field ionisation, which has been demonstrated with quantum

efficiencies above 80%, and with an ionisation efficiency above 98% [41].

In addition to the fabrication of the cavities themselves, tuning of the resonant

frequencies of the cavities, on an individual basis, is required. For full flexibility, fast

switching of the frequencies (to turn cavities on or off) is desirable. A general method

Quantum Computing Using Crossed Atomic Beams 10

for such switching is to tune the resonant frequencies of the cavities. This can be

achieved for microfabricated cavities by an array of piezoelectric elements mounted to

the computational wafer. By changing applied electric potentials on each piezoelectric

element, andthus theforceappliedtoeachcavity, thephysical dimensions ofthecavities

can be varied, and with them their resonant frequencies. This method is known to work

well for larger microwave cavities, and should allow fast (kilohertz speeds) switching of

all the cavity elements on the chip.

5. Performance and decoherence

Potential sources of decoherence include the decay lifetime of the microwave cavities,

variationof atomicvelocities, andthe accuracy of the two-atomoverlap in thecollisional

cavities.

The fidelity of the three-atom entangled state from the micromaser will be affected

by the uncertainty in the atomic velocities, and therefore interaction times. A velocity

resolution of 0.5% has been achieved in similar experiments [36]. This limits the fidelity

of the three-atom entangled states generated by the system to approximately 99.5%.

Velocity selection uncertainties have a larger effect on the collisional entanglement

process, as they affect not just the transit time of the atoms through the cavity, but

also their arrival times, altering the two-atom overlap time. The arrival times of atoms

are jittered further due to the mechanism by which the single atom sources operate. A

velocity-selected pulse ofatomsenters thesourcecavity, andeachatomhasaprobability

P 0.9 of emitting a photon into the cavity mode and emerging in the correct atomic

e

≃

state for the subsequent microwave fields. Once this has occurred, the cavity photon

blocks the occurrence of further emission events. The time from the start of the atomic

pulse to the emission event is then 1.1 atom-transit times along the short axis of the

source cavity – about 0.01 µs – with a standard deviation of around 0.01 µs. In the

collisional cavity, the atoms travel along the long axes of the cavity, and so 0.01 µs

corresponds to 1% of the atomic overlap time. This is expected to limit the collisional

entanglement fidelity to about 99%, while the differing transit times of the two atoms

will contribute to dephasing at below the 1% level.

Othercontributionstodephasing comefromstray, fluctuatingelectricandmagnetic

fields in the apparatus altering the energies of the atomic states. These fields come from

contact potentials due to deposition of atomic vapours on the surfaces of the apparatus,

andthegrainboundariesintheniobiumusedtoconstruct themicrowave cavities. These

effects can be minimised by enclosing the atomic paths with superconducting material,

essentially eliminating the stray fields along the beam path, and by preparation and

treatment of the niobium cavities to minimise the effects of grain boundaries.

Extrapolatingfrompreviouslyrealisedmicrowavecavitydesignsandknowndatafor

lower Rydberg states, the interaction time of an atom with the two-photon micromaser

cavity is expected to be on the order of 1 µs, the time in-between atoms to be around

10 µs, and the cavity decay lifetime 10 ms. The loss of phase coherence between two

Quantum Computing Using Crossed Atomic Beams 11

successive atoms caused by the finite cavity lifetime would therefore be just 0.05%.

There are other small uncertainties associated with the operation of the device,

such as the precision of the state rotations, but these can be controlled to a very high

level, below a 0.1% contribution to decoherence, with minimal experimental overhead,

and are purely technologically limited.

It can be seen that the cavity decay will not be the limiting factor on the

performance of the computer, but other errors such as the overlap of atoms in the

collisional entanglement cavity, and small uncertainties in state preparation, mainly

due to the accuracy of the selection of atomic velocities, will limit the performance of

the gate operations.

The accuracy of the velocity selection could be improved past the 0.5% level in

several ways. Firstly, the use of longer selection paths, with fast switching tolerances on

the microwave fields and careful control of field leakage could improve the resolution.

Improved Doppler velocity selection by laser excitation, for example by using selection

on all three excitation steps rather than just one, could narrow the distribution a little

more. More precise velocity selection schemes are also possible.

The timing jitter of the single atom sources could be improved significantly by the

construction of re-entrant microwave cavities with very thin cross-sections, hence low

mode volumes and high coupling strengths. Such cavities could also be expected to

have higher decay rates, which would allow increases in the rate of atom generation,

and hence computational speed.

As a final note, we recognise that scaling the micromaser down to this size and

reaching the level of integration required to build a quantum computer presents a

formidable technological challenge. However all of the required components of such

a system have been previously demonstrated and the techniques for fabricating an

integrated device have also been proven in recent years. If all of these strands can be

brought together, the result will be a quantum computer with the potential to scale to

tens of qubits in the near future, and hundreds or thousands of qubits with refinement

of the operating conditions. The system has the potential to cross the threshold for

fault-tolerant quantum computing [47, 48, 49], and therefore scale to arbitrary size.

We have shown that a scalable cavity QED based quantum computer using some

of the most recent advances in quantum information science is technically possible. It