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European Quantum Electronics Conference (EQEC)

Molecular quantum computing applying optimal control theory: quantum gates and algorithms

Carmen M. Tesch, Regina de Vivie‐Riedle

Published Jan 1, 2003• 0 citations
Publisher

Abstract

A molecular approach to quantum computing is demonstrated. The vibrational normal modes of molecules in an ensemble are used to encode qubit systems. In each mode a certain degree of excitation is referred to as |0>, another degree of excitation in the same mode is referred to as |1/spl rarr/. For the realization of quantum gates within and between the qubits, single shaped femtosecond laser pulses in the IR-regime is applied.

DOI
10.1109/eqec.2003.1314244

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The Journal of Chemical Physics•Feb 14, 2008•38 citations
A molecular approach to quantum computing is demonstrated. The vibrational normal modes of molecules in an ensemble are used to encode qubit systems. In each mode a certain degree of excitation is referred to as |0>, another degree of excitation in the same mode is referred to as |1/spl rarr/. For the realization of quantum gates within and between the qubits, single shaped femtosecond laser pulses in the IR-regime is applied.
A new physical implementation for quantum computation is proposed. The vibrational modes of molecules are used to encode qubit systems. Global quantum logic gates are realized using shaped femtosecond laser pulses which are calculated applying optimal control theory. The scaling of the system is favorable; sources for decoherence can be eliminated. A complete set of one- and two-quantum gates is presented for a specific molecule. Detailed analysis regarding experimental realization shows that the structural resolution of today's pulse shapers is easily sufficient for pulse formation.
The phase of quantum gates is one key issue for the implementation of quantum algorithms. In this paper we first investigate the phase evolution of global molecular quantum gates, which are realized by optimally shaped femtosecond laser pulses. The specific laser fields are calculated using the multitarget optimal control algorithm, our modification of the optimal control theory relevant for application in quantum computing. As qubit system we use vibrational modes of polyatomic molecules, here the two IR-active modes of acetylene. Exemplarily, we present our results for a Pi gate, which shows a strong dependence on the phase, leading to a significant decrease in quantum yield. To correct for this unwanted behavior we include pressure on the quantum phase in our multitarget approach. In addition the accuracy of these phase corrected global quantum gates is enhanced. Furthermore we could show that in our molecular approach phase corrected quantum gates and basis set independence are directly linked. Basis set independence is also another property highly required for the performance of quantum algorithms. By realizing the Deutsch-Jozsa algorithm in our two qubit molecular model system, we demonstrate the good performance of our phase corrected and basis set independent quantum gates.
Elementary quantum gates have been constructed using molecular vibrational and rotational modes to encode two qubits and implement the Deutsch–Jozsa algorithm. The molecular system chosen was 12C16O. Several phase-correct global quantum gates were constructed using optimal control theory (OCT). The gate fidelity was more than 90%. On implementing the Deutsch–Jozsa algorithm combining these elementary gates, a fidelity greater than 96.11% was obtained, which indicates that vibrational and rotational qubits are promising for performing quantum algorithms.
We explore how the globality of quantum logic operations is ensured in the context of optimal control theory when qubits are encoded in vibrational eigenstates of different normal modes and specially shaped laser fields act as quantum logic operations. In a two-qubit model system, transition mechanisms for optimized laser fields generating single qubit flips, local NOT and global NOT and controlled-NOT (CNOT) gates are investigated and compared. We evaluate the participation of vibrational eigenstates beyond the qubit basis in the global gate mechanisms and how different features of CNOT and NOT gates relate to the characteristics of the vibrational manifold. When a non-qubit normal mode interacting via anharmonic resonances is introduced, neither the global gate mechanisms nor the optimized laser fields show a significant increase in complexity. Similar features of the global quantum gates in both model systems indicate a generality of the deduced principles. Finally, a primary concept for a realization of global quantum gates in an actual experiment referring to state-of-the-art techniques is presented. The possible reconstruction of optimized laser fields with sequences of simple Gaussian subpulses is demonstrated and some critical parameters are deduced.
Within the context of vibrational molecular quantum computing, we investigate the implementation of a full addition of two binary digits and a carry that provides the sum and the carry out. Four qubits are necessary and they are encoded into four different normal vibrational modes of a molecule. We choose the bromoacetyl chloride molecule because it possesses four bright infrared active modes. The ground and first excited states of each mode form the one-qubit computational basis set. Two approaches are proposed for the realization of the full addition. In the first one, we optimize a pulse that implements directly the entire addition by a single unitary transformation. In the second one, we decompose the full addition in elementary quantum gates, following a scheme proposed by Vedral et al. [Phys. Rev. A 54, 147 (1996)]. Four elementary quantum gates are necessary, two two-qubit CNOT gates (controlled NOT) and two three-qubit TOFFOLI gates (controlled-controlled NOT). All the logic operations consist in one-qubit flip. The logic implementation is therefore quasiclassical and the readout is based on a population analysis of the vibrational modes that does not take the phases into account. The fields are optimized by the multitarget extension of the optimal control theory involving all the transformations among the 2(4) qubit states. A single cycle of addition without considering the preparation or the measure or copy of the result can be carried out in a very competitive time, on a picosecond time scale.