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Quantum Computing with Quantum Dots


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

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

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

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

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.

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.

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.

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.

  • 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.

  • 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.

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
  • play an important role for all quantum dot

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
    tunnel barriers to conducting leads

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

  • 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.

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.

  • 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

  • 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

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.

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
  • . It occurs when an object simultaneously
    "possesses" two or more values for an observable
  • (e.g. the position or energy of a

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.

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
  • 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.

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

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

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
  • Decoherence represents a major problem for the
    practical realization of quantum computers

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.

  • 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

  • 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

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
  • 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.

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
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
  • perform these operations in parallel

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
  • the exchange and Zeeman interaction need to be
    controlled again in about one part in 10000

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.

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

  • . 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

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 )
  • 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 

  • 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.

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

  • 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

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.

Measuring a Single Spin (Read-Out)
  • Spin Measurements through Spontaneous
  • Spin Measurements via the Charge
  • Quantum Dot as Spin Filter and Read-Out/Memory
  • Optical Measurements

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.

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.

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.

  • 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.

  • 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

  • Thank u !

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