Complexity and simplicity of optimal control theory pulses shaped for controlling vibrational qubits

Abstract

In the context of molecular quantum computation the optimal control theory (OCT) is used to obtain shaped laser pulses for high-fidelity control of vibrational qubits. Optimization is done in time domain and the OCT algorithm varies values of electric field in each time step independently, tuning hundreds of thousands of parameters to find one optimal solution. Such flexibility is not available in experiments, where pulse shaping is done in frequency domain and the number of "tuning knobs" is much smaller. The question of possible experimental interpretations of theoretically found OCT solutions arises. In this work we analyze very accurate optimal pulse that we obtained for implementing quantum gate CNOT for the two-qubit system encoded into the exited vibrational states of thiophosgene molecule. Next, we try to alter this pulse by reducing the number of available frequency channels and intentionally introducing systematic and random errors (in frequency domain, by modifying the values of amplitudes and phases of different frequency components). We conclude that a very limited number of frequency components (only 32 in the model of thiophosgene) are really necessary for accurate control of the vibrational two-qubit system, and such pulses can be readily constructed using OCT. If the amplitude and phase errors of different frequency components do not exceed ±3% of the optimal values, one can still achieve accurate transformations of the vibrational two-qubit system, with gate fidelity of CNOT exceeding 0.99.

On the design of molecular excitonic circuits for quantum computing: the universal quantum gates

“…For the latter, universal gates have been designed and the feasibility of their physical implementation has also been addressed. 33 Despite these previous studies, and our own contribution here, many challenges still remain to be solved before such molecular systems can be utilized for quantum computing.…”

Polarization entanglement of sum-frequency photons: A tool to probe the Markovian limit

“…In principle, this provides a 2 N capacity to store information [5]. Quantum computing stimulates the development of silicon chip technology [6][7][8], the ion trap technique [9], and the engineering of rotational [10][11][12] and/or vibrational packets [13,14]. Furthermore, progress in the preparation of entangled photons [15,16] has stimulated interest in using them as a spectroscopic tool.…”

On readout of vibrational qubits using quantum beats

“…The time grid for propagation was set in the range (−T /2, T /2), while the pulse reaches its peak at t = 0. The time delay between the shaped computation pulse (whose optimal shape was derived previously 42,43 ) and the readout pulse is simply taken into account by the phases of the qubitencoding vibrational eigenstates (their phases evolve freely after the computation pulse is over while the population in each qubit encoding state remains constant).…”

“…1, as our model for a molecular carrier of several qubits. This molecule has already been studied extensively as a platform for qubit manipulation, including such aspects as effects of rotation and laser power on population transfer, 20 optimal shape of high-fidelity computational pulses 42 and their robustness, 43 although readout has not been considered in detail before. Computational states (qubits, or q-words) are encoded in the vibrationally excited states in the ground electronic state of thiophosgene.…”