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arXiv:0711.1425 · Physical Review A

NOT gate in acis-transphotoisomerization model

Mamadou Ndong, L. Bomble, Dominique Sugny, Yves Justum, Michèle Desouter-Lecomte

Published Oct 30, 2007• 24 citations
arXivHTMLPDF

Abstract

We numerically study the implementation of a NOT gate by laser pulses in a model molecular system presenting two electronic surfaces coupled by nonadiabatic interactions. The two states of the bit are the fundamental states of the cis-trans isomers of the molecule. The gate is classical in the sense that it involves a one-qubit flip so that the encoding of the outputs is based on population analysis which does not take the phases into account. This gate can also be viewed as a double photoswitch process with the property that the same electric field controls the two isomerizations. As an example, we consider one-dimensional cuts in a model of the retinal in rhodopsin already proposed in the literature. The laser pulses are computed by the multitarget optimal control theory with chirped pulses as trial fields. Very high fidelities are obtained. We also examine the stability of the control when the system is coupled to a bath of oscillators modeled by an ohmic spectral density. The bath correlation time scale being smaller than the pulse duration, the dynamics is carried out in the Markovian approximation

DOI
10.1103/physreva.76.043424

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We numerically study the implementation of a NOT gate by laser pulses in a model molecular system presenting two electronic surfaces coupled by nonadiabatic interactions. The two states of the bit are the fundamental states of the cis-trans isomers of the molecule. The gate is classical in the sense that it involves a one-qubit flip so that the encoding of the outputs is based on population analysis which does not take the phases into account. This gate can also be viewed as a double photoswitch process with the property that the same electric field controls the two isomerizations. As an example, we consider one-dimensional cuts in a model of the retinal in rhodopsin already proposed in the literature. The laser pulses are computed by the multitarget optimal control theory with chirped pulses as trial fields. Very high fidelities are obtained. We also examine the stability of the control when the system is coupled to a bath of oscillators modeled by an ohmic spectral density. The bath correlation time scale being smaller than the pulse duration, the dynamics is carried out in the Markovian approximation
Implementation of quantum controlled-NOT (CNOT) gates in realistic molecular systems is studied using stimulated Raman adiabatic passage (STIRAP) techniques optimized in the time domain by genetic algorithms or coupled with optimal control theory. In the first case, with an adiabatic solution (a series of STIRAP processes) as starting point, we optimize in the time domain different parameters of the pulses to obtain a high fidelity in two realistic cases under consideration. A two-qubit CNOT gate constructed from different assignments in rovibrational states is considered in diatomic (NaCs) or polyatomic (SCCl2)({\text{SCCl}}_{2})(SCCl2​) molecules. The difficulty of encoding logical states in pure rotational states with STIRAP processes is illustrated. In such circumstances, the gate can be implemented by optimal control theory and the STIRAP sequence can then be used as an interesting trial field. We discuss the relative merits of the two methods for rovibrational computing (structure of the control field, duration of the control, and efficiency of the optimization).
The optical switching of molecular ensembles in a dissipative environment is a subject of various fields of chemical physics and physical chemistry. Here we try to switch arrays of molecules from a stable collective ground state to a state in which all molecules have been transferred to another stable higher-energy configuration. In our model switching proceeds through electronically excited intermediates which are coherently coupled to each other through dipolar interactions, and which decay incoherently within a finite lifetime by coupling to a dissipative environment. The model is quite general, but parameters are chosen to roughly resemble the all-trans $\ensuremath{\rightarrow}$ all-cis isomerization of an array of azobenzene molecules on a surface. Using analytical and optimal control pulses and the concept of ``laser distillation,'' we demonstrate that for various aggregates (dimers up to hexamers), controlled and complete switching should be possible.
We study the possibility of implementing a two-qubit controlled-NOT gate operation in a structure consisting of two semiconductor double quantum dots placed in a high- Q optical microcavity and governed by a resonant laser field. The effect of relaxation processes on the dynamics of the two-electron system is discussed. The dissipation rates allowing quantum error correction algorithms to be used are determined. The existing additional excitation channel (laser pulse) is shown to weaken the effect of the nonideality of the cavity on the evolution of the states. Optimal electron coupling coefficients in the quantum dots with control fields are fitted, in which the controlled qubit is switched with the highest probability and the gate implementation takes several hundreds of picoseconds.
Physical implementation of quantum gates acting on qubits does not achieve a perfect fidelity of 1. The actual output qubit may not match the targeted output of the desired gate. According to theoretical estimates, intrinsic gate fidelities >99.99% are necessary so that error correction codes can be used to achieve perfect fidelity. Here we test what fidelity can be accomplished for a CNOT gate executed by a shaped ultrafast laser pulse interacting with vibrational states of the molecule SCCl(2). This molecule has been used as a test system for low-fidelity calculations before. To make our test more stringent, we include vibrational levels that do not encode the desired qubits but are close enough in energy to interfere with population transfer by the laser pulse. We use two complementary approaches: optimal control theory determines what the best possible pulse can do; a more constrained physical model calculates what an experiment likely can do. Optimal control theory finds pulses with fidelity >0.9999, in excess of the quantum error correction threshold with 8 × 10(4) iterations. On the other hand, the physical model achieves only 0.9992 after 8 × 10(4) iterations. Both calculations converge as an inverse power law toward unit fidelity after >10(2) iterations/generations. In principle, the fidelities necessary for quantum error correction are reachable with qubits encoded by molecular vibrations. In practice, it will be challenging with current laboratory instrumentation because of slow convergence past fidelities of 0.99.
The quantum Deutsch-Jozsa algorithm is implemented by using vibrational modes of a two-dimensional double well. The laser fields realizing the different gates (NOT, CNOT, and HADAMARD) on the two-qubit space are computed by the multitarget optimal control theory. The stability of the performance index is checked by coupling the system to an environment. Firstly, the two-dimensional subspace is coupled to a small number Nb of oscillators in order to simulate intramolecular vibrational energy redistribution. The complete (2+Nb)D problem is solved by the coupled harmonic adiabatic channel method which allows including coupled modes up to Nb=5. Secondly, the computational subspace is coupled to a continuous bath of oscillators in order to simulate a confined environment expected to be favorable to achieve molecular computing, for instance, molecules confined in matrices or in a fullerene. The spectral density of the bath is approximated by an Ohmic law with a cutoff for some hundreds of cm(-1). The time scale of the bath dynamics (of the order of 10 fs) is then smaller than the relaxation time and the controlled dynamics (2 ps) so that Markovian dissipative dynamics is used.
Implementation of quantum gates are important for quantum computations in physical system made of polar molecules. We investigate the feasibility of implementing gates based on pendular states of the molecular system by two different quantum optical control methods. Firstly, the Multi-Target optimal control theory and the Multi-Constraint optimal control theory are described for optimizing control fields and accomplish the optimization of quantum gates. Numerical results show that the controlled NOT gate (CNOT) can be realized under the control of above methods with high fidelities (0.975 and 0.999) respectively. In addition, in order to examine the dependence of the fidelity on energy difference in the same molecular system, the SWAP gate in the molecular system is also optimized with high fidelity (0.999) by the Multi-Constraint optimal control theory with the zero-area and constant-fluence constraints.