Quantum computation and electron spin

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Quantum computation and electron spin

• Ralitsa Dragomirova
• University of Delaware

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Outline

• What is quantum computation

• Quantum qubit
• Advantages of the quantum computer
• Experimental proposals

• All electrical quantum computation

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Quantum computation

• Goal
• to use the quantum nature of matter to
  produce new methods of computation and
• simulation of physical systems
• Advantages
• exponential speedup for factoring algorithms
• quadratic speedup for search algorithms
• simulations of physical systems

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Postulates of quantum mechanics

• At a fixed time t0 the state of a physical system
  is defined by specifying a ket ?(t0)gt
• Every measurable quantity is described by an
  aperator
• The only possible result of the measurement of a
  physical quantity is one of the eigenvalues of
  the corresponding observable
• Whent the physical quantity A is measured on a
  system in the normalized state ?gt, the
  probability P(an) of obtaining a non degenerate
  eigenvalue an of the corresponding observable A
  is

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Bits and qubits

• Bits
• Building blocks of classical computers
• Possible states 0 and 1
• Qubits
• Building blocks of quantum computer
• Basis states 0gt and 1gt
• Possible states ?gt?0gt?1gt

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Single qubit gates

• Classical NOT gate
• Quantum NOT gate
• Z gate
• Phase gate

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Two qubit gates
Classical AND gate irreversible
Quantum CNOT gate
Further differences

• Entanglement
• Quantum paralelism

We can evaluate f(x) for both x0, 1 using single
quantum circuit
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DiVincenzo criteria

• Scalable array of quantum qubits
• Initialization
• Universal set of quantum gates
• Long relevant decoherence times
• Read out the result

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Experimental proposals

• Ion traps
• Nuclear magnetic resonance
• Neutral atoms
• Superconductor microcircuits
• Quantum Hall systems
• Nuclear spin donors in semiconductors
• Electron spins in quantum dots
• Ballistic quantum wires

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Quantum computation with quantum dots

• Single electron spins in quantum dots as qubits
• Magnetic field can be used to perform single spin
  rotations
• Controlled gating of tunneling barrier can be
  used to achieve two qubit gate
• Advantages
• Scalability
• Long decoherence times Tgt50?s in
  one-electron quantum dot

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Quantum computiong with mobile spins manipulated
by electic fields Phys.Rev.B 69,
245422, A. Popescu, R. Ioniciou

• The qubit spin state of an electron moving in
  a 1D quantum wire balistic transport in 1D 5??m
  GAAS/AlGaAS, CNT
• Initialization
• Spin filters
• Spin injection from ferromagnets into
  semiconductors
• Read out
• magnetic resonance force microscopy
• spin filters and SET

0gt spin up 1gtspin down
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Single qubit gates the spin orbit coupling
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Single qubit gates the spin orbit coupling
Particle propagating with kx (ky) wave vector
will induce spin rotation Ry (Rx)
Particle propagating with kx will experience Ry
Rz rotations
?? L500 nm InGaAs/InAlAs
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Two qubit gate the exchange coupling
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Conclusions

• Quantum computation is an exciting new field
• Spintronics devices can be used to construct
  quantum computer

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Voltage contolable number of electrons
Phys. Rev B 67, 161308, 2003
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Voltage controlable number of electrons