Quantum CNOT and CV gates Jacob D Biamonte
Quantum CNOT and CV gates Jacob D. Biamonte
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.
The goal of single qubit gates are to rotate a vector on the Bloch Sphere q Alternatively the state of a single qubit may be described in as a density matrix: Basic building blocks of all single qubit gates:
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: X Z Y The phase shift and controlled Phase shift gates are also important: Controlled Phase gate: S Phase gate: e-iφ
? ? Common Gates that are often needed in quantum algorithms: Controlled single qubit gates: R(θ) Controlled Pauli Spin Matrices: σi Other Gates: H Hadamard H V Gate: V V How can we build these useful gates from elementary building blocks? ? ?
Construction of the CNOT Gate: By adjusting the Controlled Phase gate one may build many uses two qubit gates: Φ=π Z e-iφ Hadamard: This form allows the construction of many useful gates: <=> H Z H
Construction of the CV Gate: By adjusting the Controlled Phase gate one may build many uses two qubit gates: Φ=π/2 S e-iφ Hadamard: This form allows the construction of many useful gates: <=> V H S H
Toffoli Gate: Now smaller gates can be used to build larger gates: V V+ V
Additional information: • • A. Barenco, C. Bennett, R. Cleve, D. Di. Vincenzo, N. Margolus, P. Shor. T. Sleator, J. Smolin, and H. Weinfurter, Elementary gates of quantum computation, Physical Review A, 52(5): 3457 -3467, (1995), quantph/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.
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