We explore possibility of using the vibrational states of a polyatomic molecule for universal quantum computation. In this approach two vibrational eigenstates (typically, the ground and the first excited vibrational states) are used to represent |0› and |1› states of the quantum information unit, qubit. Different qubits are encoded into different normal vibration modes of a molecule and thus remain independent in the absence of external fields. All the quantum logics operations, starting with the simplest one-qubit flips and going to the more complicated multi-qubit gates, can be applied to such a vibrational register using infrared laser pulses carefully prepared (shaped) in order to induce only the desired vibrational transitions while suppressing the interfering ones. Such an optimal pulse shape can be either predicted theoretically using the optimal control theory or derived experimentally using the adaptive learning algorithms.

According to standard convention the first qubit is the *control* qubit and the second qubit is the *target* qubit. If the control qubit is in state |0›, the state of the target qubit remains intact but, if the control qubit is in the state |1›, the target qubit flips. The ground vibrational state, two overtones, and the combination state of the two normal vibration modes in naphthalene molecule (C10H8) are used to represent |00›, |01›, |10› and |11› states of two-qubit system, respectively.

In this project we try to model and understand how the properties of a molecule chosen to represent quantum bits, such as vibrational frequencies and anharmonicities, affect controllability of the qubit by sub-picosecond laser pulses. It appears that transitions to upper vibrational states. e.g., |2›, |3›, |4› etc., tend to interfere with transitions between the qubit states |0› and |1›. Resolving different transitions, suppressing unwanted ones while inducing the desired ones, is crucial for success of the method. The seemingly complicated picture can be rationalized in terms of general analytic relationships between the anharmonicity parameters and the frequencies. For example, for a two-qubit system these expressions represent planes in the three-dimensional anharmonicity parameter space. Only in the vicinity of these planes the interference effects are significant. Results of this work should help to choose a suitable candidate molecule for practical implementation of the quantum register of several vibrational qubits.

- D. Shyshlov, D. Babikov, "Complexity and simplicity of optimal control theory pulses shaped for controlling vibrational qubits", J. Chem. Phys. 137, 194318 (2012).
- L. Wang, D. Babikov, "Adiabetic coherent control in the anharmonic io trap: Proposal for the vibrational two-qubit system". Phys. Rev. A83, 052319 (2011).
- M. Zhao and D. Babikov, "Coherent and optimal control of adiabatic motion of ions in a trap", Phys. Rev. A 77, 012338 (2008).

- M. Zhao and D. Babikov, "Anharmonic properties of the vibrational quantum computer", J. Chem. Phys. 126, 204102 (2007).

- D. Babikov, “Accuracy of gates in a quantum computer based on vibrational eigenstates,”
*J. Chem. Phys.*121, 7577, (2004).

- M. Zhao and D. Babikov, “Phase control in the vibrational qubit”,
*J. Chem. Phys.*125, 24105 (2006).

**Figure 2:** Conditional NOT (CNOT) gate in a typical two-qubit system. a) Optimally shaped 750 fs laser pulse; b)-e) Population transfer between the qubit states during the pulse for four state-to-state transitions:

(Transition 1);

(Transition 2);

(Transition 3);

(Transition 4).