Quantum CNOT and CV gates

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Quantum CNOT and CV gates

• Jacob D. Biamonte

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Direction

• Realize CNOT and CV Gates as NMR pulses
• J. Jones, R. Hansen and M. Mosca, Quantum Logic
  Gates and Nuclear Magnetic Resonance Pulse
  Sequences, J.Magn.Resonance 135, pages 353-360,
  (1998), quant-ph/9805070.

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The goal of single qubit gates are to rotate a
vector on the Bloch Sphere
Basic building blocks of all single qubit gates
q
Alternatively the state of a single qubit may be
described in as a density matrix
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Here is how it works
q
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Common Single Operation Gates (our building
blocks)
Basic building blocks of all single qubit gates
These can be used to create the Pauli Spin
Matrices
The phase shift and controlled Phase shift gates
are also important
Controlled Phase gate
Phase gate
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Common Gates that are often needed in quantum
algorithms
Controlled single qubit gates
Controlled Pauli Spin Matrices
si
Other Gates
Hadamard
V Gate
H
How can we build these useful gates from
elementary building blocks?
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Construction of the CNOT Gate
By adjusting the Controlled Phase gate one may
build many uses two qubit gates
Fp
Hadamard
This form allows the construction of many useful
gates
ltgt
Z
H
H
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Construction of the CV Gate
By adjusting the Controlled Phase gate one may
build many uses two qubit gates
Fp/2
Hadamard
This form allows the construction of many useful
gates
ltgt
S
H
H
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Toffoli Gate
Now smaller gates can be used to build larger
gates
?
V
V
V
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Additional information

• A. Barenco, C. Bennett, R. Cleve, D. DiVincenzo,
  N. Margolus, P. Shor. T. Sleator, J. Smolin, and
  H. Weinfurter, Elementary gates of quantum
  computation, Physical Review A, 52(5)3457-3467,
  (1995), quant-ph/9503016.
• J. Jones, R. Hansen and M. Mosca, Quantum Logic
  Gates and Nuclear Magnetic Resonance Pulse
  Sequences, J.Magn.Resonance 135, pages 353-360,
  (1998), quant-ph/9805070.