Towards Molecular Quantum Computing: Laser Pulse Shaping of Quantum Logic Gates on Diatomic Molecules
The intent of this study is to determine the feasibility of diatomics as molecular quantum computing candidates and shed insight into the use of such experimental laser pulse shaping methods to represent quantum logic gates. Four appropriate rovibrational states of model diatomic molecules are encoded as the qubit states. A set of 2-qubit quantum logic gates (ACNOT, CNOT, NOT, Hadamard) are represented by amplitude and phase shaped laser pulses. The combinations of amplitudes and phases that produce the optimal laser pulse representation, for each quantum logic gate, are determined by a Genetic Algorithm optimization routine. The theoretical laser pulse shaping is analogous to current experimental frequency-domain pulse shaping apparatus with amplitude and phase control at individual frequencies.
A model set of diatomics is sampled in order to determine a relationship between optimal laser pulse shaping and the choice of diatomic molecule. We show that the choice of diatomic molecule greatly influences the ability to produce optimal laser pulse shapes to represent quantum logic gates. Tuneable parameters specific to laser pulse shaping instruments are varied to determine their effect on optimal pulse production. They include varying the number of amplitude and phase components, adjusting the number of frequency components, and altering the frequency width which is synonymous with altering the laser pulse duration. A time domain analytic form of the original frequency domain laser pulse function is derived, providing a useful means to infer the laser pulse dependencies on these parameters. Initially, we show that the appropriate choice of rovibrational state qubits of carbon monoxide (12C16O) and the use of simple shaped binary pulses, 2 amplitude and 2 phase components, can provide significant control for specific quantum gates. Further amplitude variation at each frequency component is shown to be a crucial requirement for optimal laser pulse shaping, whereas phase variation provides minimal contribution. We show that the generation of optimal laser pulse shapes is highly dependent upon the frequency width and increasing the number of frequency components provides incremental improvements to optimal laser pulses.