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©HITACHI Cambridge Laboratory
Semiconductor Structures for Quantum Information Processing
David Williams
Hitachi Cambridge Laboratory
Lancaster Nanoelectronics Meeting 07.01.03
©HITACHI Cambridge Laboratory
Shazia Yasin Xiulai Xu
Jörg WunderlichDave WilliamsLuke Robinson
Andrew Ramsay Hua Qin
Bernd KaestnerGreg Hutchinson
David HaskoDaniel Gandolfo
Andrew FergusonEmir Emiroglu
Dimitris DovinosPaul Cain Adel Bririd
Haroon Ahmed
©HITACHI Cambridge Laboratory
Nanoelectronics at the Quantum EdgeCoordinator Andrew Briggs
Materials Department Simon BenjaminClarendonRobert TaylorArzhang Ardavan
Microelectronics Research Centre David Hasko
OXFORD UNIVERSITY
Hitachi Cambridge Laboratory David Williams
©HITACHI Cambridge Laboratory
Quantum Information Processing (QIP)
Quantum CryptographyUse the principles of quantum measurement to ensure secure information transfer for key exchange etc.
Requires single photon generation and detection at 1.5µm for fibre-optic transmission.
Quantum ComputationUse quantum entanglement to perform computations such as factoring large numbers and sorting massive databases.
Requires a controllable and measurable two-level system with a high level of coherence.
Recent developments in single-electronics have applications in both fields.
©HITACHI Cambridge Laboratory
Quantum Information Processing (QIP)System Types
Photon sourcesPhoton detectors
Charge qubitsSpin qubits
Magnetic systemsExciton qubitsFlux systems
Materials SystemsNanofabricated semiconductor structures
Self-organised semiconductor dot structuresCarbon nanotubes filled with endohedral fullerenes
Multilayer superconductor structuresMultilayer and nanofabricated magnetic systems
spin splitting ,l ↑
,l ↓
S
T+
1.340 1.345 1.350
1600
1800
2000
2200
Inte
nsity
(a.u
.)
Energy (eV)
©HITACHI Cambridge Laboratory
Quantum Information Processing (QIP)System Types
Photon sourcesPhoton detectors
Charge qubitsSpin qubits
Magnetic systemsExciton qubitsFlux systems
Materials SystemsNanofabricated semiconductor structures
Self-organised semiconductor dot structuresCarbon nanotubes filled with endohedral fullerenes
Multilayer superconductor structuresMultilayer and nanofabricated magnetic systems
spin splitting ,l ↑
,l ↓
S
T+
1.340 1.345 1.350
1600
1800
2000
2200
Inte
nsity
(a.u
.)
Energy (eV)
©HITACHI Cambridge Laboratory
Coulomb Blockade OscillationsSimulations using CAMSET
©HITACHI Cambridge Laboratory
Equivalent Circuit
1
7
6
5
4
R6,C6
R5,C5
R4,C4
R3,C3
CS7
CS6
CS5
CS4
CD7
CD6
CD5
CD4
Word
Source DrainMemory nodeCSN CDN
3
R2,C2
CS3 CD3
2
R1,C1CD2
2 3
0
1
8 9
CG27
CG26
CG25
CG24
CG23
CG22
5
CG17
CG16
CG15
CG14
CG13
CG12
4 10 11
100 nm
50 nm
10 nm
2 nm
5 nm
10 nm
10 nm
10 nm
22 nm
2 nm
2 nm7
6
5
4
3
2
9
8
1110
30 nm
100 nm
60 nm
CS2CG11 CG21
30 nm
10 nm
35 nm
50 nm
5 nm 5 nm
77.5 nm
1
©HITACHI Cambridge Laboratory
Checklist for quantum computation
1. State preparationWe need a system which is manipulable from the outside
2. Evolution without decoherenceThe external interactions must be removedfor the duration of the computation stage
3. MeasurementAfter the evolution, we need to interact with the system once more
©HITACHI Cambridge Laboratory
Trench-isolated Silicon:GermaniumSiGe material
Intrinsic Si
p - type Si0.9Ge0.1
Intrinsic Si
SiO2
Si Substrate
30nm
g1 g3
g2
S D
Vds
Vg1 Vg3
Vg2
(Also plain silicon-on-insulator (SOI))
1. Gate - gate coupling is reduced2. Two-dimensional structures are fabricable
Metal gates can also be added3. A hard-wall confining potential is obtainable
©HITACHI Cambridge Laboratory
Charge and Spin QubitsThe double-dot system may be used as a single charge qubit or a double spin qubit
What is the true potential distribution at any time?
©HITACHI Cambridge Laboratory
Observation of peak splittingPeak splitting indicates that the presence of an extra charge on one one dot significantly affects the energy of the other dot.Overall period calculated from lithographic structure.
0
0.6
1.2
-0.4 0 0.4
I ds/n
A
Vg2
/V
Simulation
Effective dot size is 30nm - peak splitting is seen at 4.2K instead of previously at 50mK
Cain, Ahmed and Williams APL 78, 3624 (2001)
©HITACHI Cambridge Laboratory
Molecular State @ 4.2K ?
-0.10 -0.05 0.00 0.05 0.100.5
0.6
0.7
0.8
0.9
1.0
1.1
Vg#17 (V)
Vg#1
5 (V
)
0 5 10 15 20 250.5
0.6
0.7
0.8
0.9
1.0
1.1
Vg#1
5 (V
)
Ids (pA)
Tb ~ 4.2 K, measured on 02/08/2002
pA
Vds
Vg#2 Vg#15
Vg#17
Ids
50nm
©HITACHI Cambridge Laboratory
Advantages of the structure for QC1. State preparation
Suitable voltages applied to the contacts and gates can be used to prepare the dots in a known charge state.
2. Evolution without decoherenceA combination of low temperatures and local energy filtering
can be used to maintain coherence for a sufficient time.
3. MeasurementHighly sensitive single-electron electrometers can be integrated
with the dots to perform both control and measurement.
©HITACHI Cambridge Laboratory
Stability Diagram for Two p-Dots•Each region has a different charge state, e.g. (NA, NB)
•Crossing a boundary where the conductance maximaoccur changes the charge state of one dot by ±1
•Crossing a boundary where no maxima occur transfers a charge from one dot to the other only
•For sequential tunnelling, only expect resonances at the triple points.
(NA +1, N
B )
(NA , N
B )
(NA , N
B +1)
(NA +1, N
B -1)
©HITACHI Cambridge Laboratory
n,m
n-1,m+1
n+1,m-1
n-1,m
n-2,m+1
n+2,m-1
n+1,m
n,m+1
Vg2
Vg1
Control of double n-dot states
©HITACHI Cambridge Laboratory
Strategies to Reduce Decoherence1. Improved electromagnetic filtration
2. Decouple control and measurement processes
3. Operate on timescales very much faster than decohering processes
4. Operate in “decoherence-free subspaces”2.
Measurements (and Theory) Needed1. Drive the system to prove that it is an appropriate two-level system (eg Rabi oscillations)
2. Demonstrate that a particular state can be set and maintained
3. Demonstrate a single quantum gate
4. Show how to integrate gates2.
©HITACHI Cambridge Laboratory
Candidate For Charge Qubit
0
0.1
0.2
0.3
0.4
0.5
0.2
0.3
0.4
0.5
0.6
0.7
-1 -0.8 -0.6 -0.4 -0.2 0Vg2
/V∆g2
DS
el1 el2
Electrometers are added which can be biased relative to the dots to perform both control and measurement
Cain, Williams and Ahmed
JAP 92, 346 July 2002
©HITACHI Cambridge Laboratory
Scaling?Driving Electrodes Qubit Structures Output Electrometers Bias Gates
We need to integrate the qubits to make quantum gates, with controlled qubit-qubit interactions, state initialisation, control during processing, and readout.
©HITACHI Cambridge Laboratory
Closed Double-Dot
VSDVG3
VG2 VG1
8 10-11
1.2 10-10
1.6 10-10
2 10-10
2.4 10-10
-1.5 -1 -0.5 0
SET gate sweep (G1)
Gate Bias (V)
SET
Dra
in C
urre
nt (A
)
measurement anchor point
• Top-down approach• Isolated, scalable charge-state system• Manipulation and measurement through
capacitive coupling• SET current depends on parametron
polarization• Parametron polarization depends on gate
voltages and previous history
©HITACHI Cambridge Laboratory
Tuneable Switching• Observe telegraph-type switching between two states characteristic of
one electron• Rate of switching depends very strongly on upper gate voltage (VG3).
Can continuously tune this rate from stable to higher than sensitivity of measurement apparatus
All measurements taken at 4.2K
©HITACHI Cambridge Laboratory
Manipulation using pulses• Set-Reset operation achieved by selection of appropriate pulse
amplitudes and durations and time delay between far gate and upper gate pulses
• State-switch achieved through tuning upper gate pulse
All at 4.2K
©HITACHI Cambridge Laboratory
Current StatusNanoscale quantum dots and associated infrastructure can be fabricated using electron-beam lithography
We would like to know the potential landscape in more detailThe electron occupancy of an individual quantum dot or a set of quantum dots can be controlled
We need to get a detailed picture of the electron wavefunctionsTunnel barriers can be lowered and raised as required to vary the interaction between dots
We need to know the molecular states, and prove they existThe charge distribution is detectable with electrometers
But is this detection process switchable as required?A device which integrates all of these effects can be used as a single qubit
But for this to be useful we have to integrate the qubits.
©HITACHI Cambridge Laboratory
ConclusionAll the elements for a semiconductor qubit have been demonstrated independently and several have been integrated
Schemes exist for integrating the qubits for making quantum gates
A deeper theoretical understanding of the electron / hole transport behaviour in these systems is needed:
Full dynamical 3-D Poisson solverDetailed theory of electron transport and decoherenceHow to measure / infer the behaviour of closed systems?
(Perform a quantum computation?)
There is much work still to do...
©HITACHI Cambridge Laboratory
Shazia Yasin Xiulai Xu
Jörg Wunderlich Dave WilliamsLuke Robinson
Andrew RamsayHua Qin
Bernd KaestnerGreg Hutchinson
David HaskoDaniel Gandolfo
Andrew FergusonEmir Emiroglu
Dimitris Dovinos Paul CainAdel Bririd
Haroon Ahmed
©HITACHI Cambridge Laboratory
Coherence and Scaleability
In principle, solid-state systems should offer the best chance of making a scaleable quantum computer
However, there are formidable problems ahead
Maintaining coherence for a time sufficient for computation is the largest problem for practical implementations - the very interactions which are useful for control, measurementand scaling provide routes for decoherence
We also need to understand the various decohering processes and determine which are important in particular circumstances.
©HITACHI Cambridge Laboratory
Towards control of coherence
-5 10-11
0
5 10-11
1 10-10
-0.6 -0.4 -0.2 0
I ds/A
Vgs
/V
300uV
200uV
100uV
A gated double quantum dot made from a silicon - silicon germanium heterostructure. When the electronic structure changes from one dot to two in series, the noise is reduced.
Cain, Ahmed, Williams & Bonar APL 77, 3415 (2000)
©HITACHI Cambridge Laboratory
Photon-assisted tunnelling
-0.5
0
0.5
1
1.5
0 0.05 0.1 0.15 0.2 0.25
With no source-drain bias, at 20mK, currents are observed due to electron tunnelling driven by 4.2K black-body radiation