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## Quantum Computing with Quantum Dots

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### A quantum computer is any device for computation that makes direct use of ... A qubit can hold a one, a zero, or, crucially, a superposition of these. ... – PowerPoint PPT presentation

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Title: Quantum Computing with Quantum Dots

1
Quantum Computing with Quantum Dots
By Ravichandra reddy ph06m005
2
Plan of talk
• Quantum computer
• Quantum dots
• Computing with dots
• Recent developments

3
Quantum computer
• A quantum computer is any device for computation
that makes direct use of distinctively quantum
mechanical phenomena , such as superposition and
entanglement , to perform operations on data.
• The basic principle
• the quantum properties of particles can be
used to represent and structure data, and that
quantum mechanisms can be devised and built to
perform operations with these data

4
Bits vs Qubits
• The device computes by manipulating those bits
with the help of logic gates
• A qubit can hold a one, a zero, or, crucially, a
superposition of these.
• manipulating those qubits with the help of
quantum logic gates
• A classical computer has a memory made up of bits
, where each bit holds either a one or a zero

5
Bits vs. qubits
• the qubits can be in a superposition of all the
classically allowed states.
• the register is described by a wavefunction
• the phases of the numbers can constructively and
destructively interfere with one another this is
an important feature for quantum algorithms.

6
Bits vs Qubits
• For an n qubit quantum register, recording the
state of the register requires 2n complex numbers
• (the 3-qubit register requires 23 8 numbers).
• Consequently, the number of classical states
encoded in a quantum register grows exponentially
with the number of qubits
• For n300, this is roughly 1090, more states
than there are atoms in the observable universe.

7
Quantum dot
• A quantum dot is a semiconductor nanostructure
that confines the motion of conduction band
electrons , valence band holes , or excitons
(pairs of conduction band electrons and valence
band holes) in all three spatial directions.

8
The confinement can be due to
• gtelectrostatic potentials
• (generated by external electrodes, doping,
strain, impurities),
• gt the presence of an interface between
different semiconductor materials
• gt the presence of the semiconductor surface
(e.g. in the case of a semiconductor
nanocrystal ).
• gt a combination of these.

9
Dimensions
• Small quantum dots, such as colloidal
semiconductor nanocrystals, can be as small as 2
to 10 nanometers, corresponding to 10 to 50 atoms
in diameter and a total of 100 to 100,000 atoms
within the quantum dot volume.
• At 10 nanometers in diameter, nearly 3 million
quantum dots could be lined up end to end and fit
within the width of a human thumb.

10
• quantum wires , which confine the motion of
electrons or holes in two spatial directions and
allow free propagation in the third. 2) quantum
wells, which confine the motion of electrons or
holes in one direction and allow free propagation
in two directions.

11
compared to atoms
• both have a discrete energy spectrum and bind a
small number of electrons.
• In contrast to atoms, the confinement potential
in quantum dots does not necessarily show
spherical symmetry.
• In addition, the confined electrons do not move
in free space but in the semiconductor host
crystal.
• play an important role for all quantum dot
properties.

12
energy scales
• the order of 10 ev in atoms, but only 1 milli
e.v in quantum dots.
• In contrast to atoms, the energy spectrum of a
quantum dot can be engineered by controlling the
geometrical size, shape, and the strength of the
confinement potential.
• it is relatively easy to connect quantum dots by

13
How to find?
• the energy levels can be probed by optical
spectroscopy techniques.
• blue shift due to the confinement compared to the
bulk material .
• quantum dots of the same material, but with
different sizes, can emit light of different
colors.

14
coloration
• The larger the dot, the redder
• The smaller the dot, the bluer
• The coloration is directly related to the energy
levels of the quantum dot.

15
Blue Shift
• the bandgap energy inversely proportional to the
square of the size of the quantum dot.
• Larger quantum dots have more energy levels
which are more closely spaced.
• This allows the quantum dot to absorb photons
containing less energy, i.e. those closer to the
red end of the spectrum.

16
Applications
• sharper density of states
• superior transport and optical properties, and
are being researched for use in diode lasers ,
amplifiers, and biological sensors.
• use in solid-state quantum computation . By
applying small voltages to the leads, one can
control the flow of electrons through the quantum
dot and thereby make precise measurements of the
spin and other properties

17
Applications
• Another cutting edge application of quantum dots
is also being researched as potential artificial
fluorophore for intra-operative detection of
tumors using fluorescence spectroscopy .
• Quantum dots may have the potential to increase
the efficiency and reduce the cost of todays
typical silicon photovoltaic cells .
• 7-fold increase in final output

18
Quantum computer
• A quantum computer is any device for computation
that makes direct use of distinctively quantum
mechanical phenomena , such as superposition and
entanglement , to perform operations on data.

19
Quantum superposition
• Quantum superposition is the application of the
superposition principle to quantum mechanics.
• The superposition principle is the addition of
the amplitudes of wavefunctions , or state
vectors
• . It occurs when an object simultaneously
"possesses" two or more values for an observable
quantity
• (e.g. the position or energy of a
particle).

20
Quantum entanglement
• is a quantum mechanical phenomenon in which the
quantum states of two or more objects have to be
described with reference to each other, even
though the individual objects may be spatially
separated .
• leads to correlations between observable physical
properties of the systems.

21
Quantum entanglement
• For example, it is possible to prepare two
particles in a single quantum state such that
when one is observed to be spin-up, the other one
will always be observed to be spin-down and vice
versa
• it is impossible to predict , according to
quantum mechanics, which set of measurements will
be observed. As a result, measurements performed
on one system seem to be instantaneously
influencing other systems entangled with it.

22
A fundamental problem
• in quantum physics is the issue of the
decoherence of quantum systems and the transition
between quantum and classical behavior.

23
Quantum decoherence
• quantum decoherence is the mechanism by which
quantum systems interact with their environments
to exhibit probabilistically additive behavior -
a feature of classical physics - and give the
appearance of wavefunction collapse. Decoherence
• quantum decoherence is the mechanism by which
quantum systems interact with their environments
to exhibit probabilistically additive behavior -
a feature of classical physics - and give the
appearance of wavefunction collapse. Decoherence

24
Quantum decoherence
• Decoherence does not provide a mechanism for the
actual wave function collapse rather it provides
a mechanism for the appearance of wavefunction
collapse. The quantum nature of the system is
simply "leaked" into the environment so that a
total superposition of the wavefunction still
exists, but exists beyond the realm of
measurement.
• Decoherence represents a major problem for the
practical realization of quantum computers

25
prime motivations for proposing spin
• that most of what has been probed is the orbital
coherence of electron states, that is, the
preservation of the relative phase of
superpositions of spatial states of the electron
The coherence times seen in these investigations
are almost completely irrelevant to the spin
coherence times which are important in our
quantum computer proposal. There is some relation
between the two if there are strong spin-orbit
effects, but our intention is that conditions and
materials should be chosen such that these
effects are weak.

26
• Under these circumstances the spin coherence
times (the time over which the phase of a
superposition of spin-up and spin-down states is
well-defined) can be completely different from
the charge coherence times (a few nanoseconds),
and in fact it is known that they can be orders
of magnitude longer

27
Upscaling
• For the implementation of realistic calculations
on a quantum computer, a large number of qubits
will be necessary (on the order of 1,00,000.
• can be operated in parallel
• well achievable with spin-based qubits confined
in quantum dots

28
Pulsed Switching
• quantum gate operations will be controlled
through an effective Hamiltonian

which is switched via external control fields

the exchange coupling J is local, it is finite
only for neighboring qubits
29
• the qubits can be moved around in an array of
quantum dots. Thus, a qubit can be transported to
a place where it can be coupled with a desired
second qubit, where single-qubit operations can
be performed, or where it can be measured.

30
Switching Times
• Single qubit operations can be performed
• A spin can be rotated by a relative angle of

a typical switching time for an angle 180 deg ,
a field 1 tesla  , and g eff 1   is 30 pico
sec         .
the total time consumed by an algorithm can
be optimized
31
Error Correction
• One of the main goals in quantum computation is
the realization of a reliable error-correction
scheme , which requires gate operations with an
error rate not larger than one part in 10000
• a larger number of qubits also requires a larger
total number of gate operations to be performed,
in order to implement the error-correction
schemes
• perform these operations in parallel

32
Precision Requirements
• Quantum computation is not only spoiled by
decoherence, but also by a limited precision of
the gates, i.e. by the limited precision of the
Hamiltonian.
• the exchange and Zeeman interaction need to be
controlled again in about one part in 10000

33
Decoherence due to Nuclear Spins
• a serious source of possible qubit errors using
semiconductors such as GaAs is the hyperfine
coupling between electron spin (qubit) and
nuclear spins in the quantum dot
• In GaAs semiconductors, both Ga and As possess a
nuclear spin 3/2 , and no Ga/As isotopes are
available with zero nuclear spin.

34
Two-Qubit Gates--Coupled Quantum Dots
• multi-(qu)bit gate allows calculations through
combination of several (qu)bits.
• two-qubit gates are (in combination with
single-qubit operations) sufficient for quantum
computation --they form a universal set
• combined action of the Coulomb interaction and
the Pauli exclusion principle

35
• . Two coupled electrons in absence of a magnetic
field have a spin-singlet ground state, while the
first excited state in the presence of strong
Coulomb repulsion is a spin triplet. Higher
excited states are separated from these two
lowest states by an energy gap, given either by
the Coulomb repulsion or the single-particle
confinement.

36
a universal quantum gate.
H(t) is Heisenberg spin Hamiltonian , J(t) is
the exchange coupling between the two spins .
U is a swap operator ( time evolution of J(t)
after a pulse )
37
• it can be used, together with single-qubit
rotations, to assemble any quantum algorithm
• combination of swap'' operator and
single-qubit operations , applied in the
sequence gives universal gate XOR

38
• reduce the study of general quantum computation
to the study of single-spin rotations (see Sec.
) and the exchange mechanism, in particular how
J(t) can be controlled experimentally. The
central idea is that J(t) can be switched by
raising or lowering the tunneling barrier between
the dots.

39
Laterally Coupled Dots
• consider a system of two coupled quantum dots in
a two-dimensional electron gas (2DEG), containing
one (excess) electron each, as described in Sec.
. The dots are arranged in a plane, at a
sufficiently small distance , such that the
electrons can tunnel between the dots (for a
lowered barrier) and an exchange interaction
between the two spins is produced. We model this
system of coupled dots with the Hamiltonian

40
• for small quantum dots, say 2a 40 nm , we need
to consider the bare Coulomb interaction
• Separated dots ( agtgtbhor magnaton) are thus
modeled as two harmonic wells with frequency .
This is motivated by the experimental evidence
that the low-energy spectrum of single dots is
well described by a parabolic confinement
potential

41
Vertically Coupled Dots
• Such a setup of the dots has been produced in
multilayer self-assembled quantum dots (SAD)  as
well as in etched mesa heterostructures
• in 3D the exchange interaction is not only
sensitive to the magnitude of the applied fields,
but also to their direction.

42
• Spin Measurements through Spontaneous
Magnetization
• Spin Measurements via the Charge
• Quantum Dot as Spin Filter and Read-Out/Memory
Device
• Optical Measurements

43
through Spontaneous Magnetization
• One scheme for reading out the spin of an
electron on a quantum dot is implemented by
tunneling of this electron into a supercooled
paramagnetic dot . There the spin induces a
magnetization nucleation from the paramagnetic
metastable phase into a ferromagnetic domain,
whose magnetization direction is along the
measured spin direction and which can be measured
by conventional means.

44
via the Charge
• While spins have the intrinsic advantage of long
decoherence times, it is very hard to measure a
single spin directly via its magnetic moment.
• yielding a potentially 100 reliable measurement
requires a switchable spin-filter'' tunnel
barrier which allows only, say, spin-up but no
spin-down electrons to tunnel.

45
Optical Measurements
• Measurements of the Faraday rotation originating
from a pair of coupled electrons would allow us
to distinguish between spin singlet and triplet
In the singlet state (, no magnetic moment) there
is no Faraday rotation, whereas in the triplet
state () the polarization of linearly polarized
light is rotated slightly due to the presence of
the magnetic moment.

46
References
• M. A. Reed, J. N. Randall, R. J. Aggarwal, R. J.
Matyi, T. M. Moore, and A. E. Wetsel, Observation
of discrete electronic states in a
zero-dimensional semiconductor nanostructure,
Phys. Rev. Lett. 60, 535 (1988).
• M. A. Reed, Quantum Dots, Scientific American
268, Number 1, 118, 1993.

47
• Guido Burkard , Hans-Andreas Engel, and Daniel
LossDepartment of Physics and Astronomy,
University of Basel, Klingelbergstrasse 82,
CH-4056 Basel, Switzerland
• Published in  Fortschritte der Physik 48
(Special Issue on Experimental Proposals for
Quantum Computation),  pp. 965-886 (2000).
• wikipedia

48
• Thank u !

49
• Http//theorie5.physick.unibas.ch/qcomp/qcomp.html