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 Wunderlich
Dave Williams
Luke Robinson
Andrew Ramsay
Hua Qin
Bernd Kaestner
Greg Hutchinson
David Hasko
Daniel Gandolfo
Andrew Ferguson
Emir Emiroglu
Dimitris Dovinos
Paul Cain
Adel Bririd
Haroon Ahmed
©HITACHI Cambridge Laboratory
Nanoelectronics at the Quantum Edge
Coordinator Andrew Briggs
Materials
Department Simon
Benjamin
Clarendon
Robert Taylor
Arzhang Ardavan
Microelectronics
Research Centre
David Hasko
OXFORD
UNIVERSITY
Hitachi Cambridge Laboratory
David Williams
©HITACHI Cambridge Laboratory
Quantum Information Processing (QIP)
Quantum Cryptography
Quantum Computation
Use the principles of quantum
measurement to ensure secure
information transfer for key
exchange etc.
Use quantum entanglement to
perform computations such as
factoring large numbers and
sorting massive databases.
Requires single photon generation
and detection at 1.5µm for fibreoptic transmission.
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)
2200
Intensity (a.u.)
2000
1800
1600
1.340
1.345
Energy (eV)
1.350
System Types
Photon sources
Photon detectors
Charge qubits
Spin qubits
Magnetic systems
Exciton qubits
Flux systems
T+
S
Materials Systems
Nanofabricated semiconductor structures
Self-organised semiconductor dot structures
Carbon nanotubes filled with endohedral fullerenes
Multilayer superconductor structures
Multilayer and nanofabricated magnetic systems
l, ↓
spin splitting
l, ↑
©HITACHI Cambridge Laboratory
Quantum Information Processing (QIP)
2200
Intensity (a.u.)
2000
1800
1600
1.340
1.345
Energy (eV)
1.350
System Types
Photon sources
Photon detectors
Charge qubits
Spin qubits
Magnetic systems
Exciton qubits
Flux systems
T+
S
Materials Systems
Nanofabricated semiconductor structures
Self-organised semiconductor dot structures
Carbon nanotubes filled with endohedral fullerenes
Multilayer superconductor structures
Multilayer and nanofabricated magnetic systems
l, ↓
spin splitting
l, ↑
©HITACHI Cambridge Laboratory
Coulomb Blockade Oscillations
Simulations using CAMSET
©HITACHI Cambridge Laboratory
Equivalent Circuit
30 nm
1
Word
60 nm
C G17
2 nm
7
2 nm
CS7
10 nm
C G16
6
4
C G15
4
10 nm
2
2 nm
10
5 nm
30 nm
100 nm
9
50 nm
R3,C3
100 nm
50 nm
C G23
R2,C2
C D3
C G22
2
C S2
8
R1,C1
C G11
Source
5
C D4
3
C G12
2
11
C G24
C S3
5 nm
1
CD5
4
C G13
8
C G25
R4,C4
C G14
10 nm
C D6
5
C S5
C S4
35 nm
C G26
R5,C5
77.5 nm
3
C D7
6
22 nm
11
10 nm
R6,C6
CS6
5 nm
5
10
C G27
7
10 nm
1
C D2
C G2 1
CSN Memory node CDN
9
Drain
3
0
©HITACHI Cambridge Laboratory
Checklist for quantum computation
1. State preparation
We need a system which is manipulable
from the outside
2. Evolution without decoherence
The external interactions must be removed
for the duration of the computation stage
3. Measurement
After the evolution, we need to interact with
the system once more
©HITACHI Cambridge Laboratory
Trench-isolated Silicon:Germanium
SiGe material
g1
g3
Intrinsic Si
30nm
p - type Si 0.9Ge 0.1
S
D
Intrinsic Si
SiO 2
Vg1
g
2
Vg3
Si Substrate
(Also plain silicon-on-insulator (SOI))
1. Gate - gate coupling is reduced
2. Two-dimensional structures are fabricable
Metal gates can also be added
3. A hard-wall confining potential is obtainable
Vds
Vg2
©HITACHI Cambridge Laboratory
Charge and Spin Qubits
The 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?
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Observation of peak splitting
Peak 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.
Simulation
1.2
ds
I /nA
0.6
0
-0.4
0
0.4
Vg2/V
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 ?
Vg#15
Vg#2
Tb ~ 4.2 K, measured on 02/08/2002
Vds
Ids
pA
50nm
1.1
1.1
1.0
1.0
0.9
0.9
Vg#15 (V)
Vg#15 (V)
Vg#17
0.8
0.8
0.7
0.7
0.6
0.6
0.5
-0.10
0.5
-0.05
0.00
Vg#17 (V)
0.05
0.10
0
5
10
15
20
25
Ids (pA)
©HITACHI Cambridge Laboratory
Advantages of the structure for QC
1. 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 decoherence
A combination of low temperatures and local energy filtering
can be used to maintain coherence for a sufficient time.
3. Measurement
Highly 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)
,N
(N A
)
B
)
+1
B
,N
+1
(N A
,
+1
(N A
)
-1
B
)
NB
•Crossing a boundary where
no maxima occur transfers a
charge from one dot to the
other only
,N
(N A
•Crossing a boundary where
the conductance maxima
occur changes the charge
state of one dot by ±1
•For sequential tunnelling, only
expect resonances at the triple
points.
©HITACHI Cambridge Laboratory
Control of double n-dot states
n-2,m+1
Vg2
n-1,m+1
n-1,m
n,m+1
n,m
n+1,m
n+1,m-1
Vg1
n+2,m-1
©HITACHI Cambridge Laboratory
Strategies to Reduce Decoherence
1. 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) Needed
1. Drive the system to prove that it is an appropriate twolevel 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 gates
2.
©HITACHI Cambridge Laboratory
Candidate For Charge Qubit
el1
S
0.5
0.7
0.4
0.6
0.3
0.5
0.2
0.4
0.1
0.3
el2
D
g2
0
-1
-0.8
∆
-0.6
-0.4
-0.2
Vg2 /V 0
0.2
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
• 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
VG3
VG1
VG2
SET gate sweep (G1)
-10
2.4 10
VSD
SET Drain Current (A)
2 10-10
1.6 10-10
measurement anchor point
1.2 10-10
8 10-11
-1.5
-1
-0.5
0
Gate Bias (V)
©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 Status
Nanoscale quantum dots and associated infrastructure can be
fabricated using electron-beam lithography
We would like to know the potential landscape in more detail
The 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 wavefunctions
Tunnel barriers can be lowered and raised as required to vary
the interaction between dots
We need to know the molecular states, and prove they exist
The 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
Conclusion
All 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 solver
Detailed theory of electron transport and decoherence
How 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 Williams
Luke Robinson
Andrew Ramsay
Hua Qin
Bernd Kaestner
Greg Hutchinson
David Hasko
Daniel Gandolfo
Andrew Ferguson
Emir Emiroglu
Dimitris Dovinos
Paul Cain
Adel 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, measurement
and 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
1 10-10
300uV
-11
5 10
200uV
A
/s
Id
0
-5 10-11
100uV
-0.6
-0.4
V /V
gs
-0.2
0
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
1.5
1
0.5
0
-0.5
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
©HITACHI Cambridge Laboratory