Adiabatic quantum computing with phase modulated laser pulses

Abstract

Implementation of quantum logical gates for multilevel systems is demonstrated through decoherence control under the quantum adiabatic method using simple phase modulated laser pulses. We make use of selective population inversion and Hamiltonian evolution with time to achieve such goals robustly instead of the standard unitary transformation language.Use of adiabatic evolution for quantum computation has recently become an attractive approach due to its inherent robustness [1][2][3][4]. In the framework of the adiabatic quantum method, logical implementation of quantum gates uses the language of ground states, spectral gaps and Hamiltonians wherein a quantum gate represents a device which performs a unitary transformation on selected qubits in a fixed period of time. Thus, a computational procedure in the adiabatic quantum computation model is described by the continuous time evolution of a time-dependent Hamiltonian with limited energetic resources-an aspect that is often neglected in the unitary gate language [5].In this letter, we show that an important aspect of the adiabatic quantum computation model lies in addressing an atomic or molecular ensemble and hence in robust implementation. We first demonstrate a simple Hadamard operation with phase modulated laser pulses. Next we show how selective population transfer in a three-level system that has also been demonstrated experimentally [6,7] can be a very useful adiabatic quantum computing logic. Finally, we show that it is possible to decouple states that are parts of the coupled vibrational relaxation tier into simple qubits through control of decoherence through adiabatic coupling. As far as we know, these results are the first realistic demonstration of the possibility of using ensemble states for adiabatic quantum computation in multilevel systems.We apply a linearly polarized laser pulse of the form E(t) = ɛ(t) e i[ωt+φ(t)] to a simple twolevel system with |1〉 → |2〉 transition, where |1〉 and |2〉 represent the ground and excited eigenlevels, respectively, of the field-free Hamiltonian. The laser carrier frequency or the centre frequency for pulsed lasers is ω. We have ɛ(t) and φ(t) as the instantaneous amplitude and phase, respectively. We can define the rate of change of instantaneous phase, , as the frequency sweep. If we expand the instantaneous phase function of E(t) as a Taylor series with constants b n , we have In a recent paper [8], we have proposed the use of simple chirped pulses, which, by contrast, have been produced routinely at very high intensities and at various different wavelengths for many applications, including selective excitation of molecules in coherent control. Establishing this generalization enables us to treat all possible chirped pulse cases by exploring the effects of each of the terms in equation (1) initially for a simple two-level system and then extend it to the multilevel situation for a model five-level system of anthracene molecule, which has been previously investigated with complicated shapedpulses [9,10]. ...

Probing coherence aspects of adiabatic quantum computation and control

“…9,11,32 However, there has been almost no effort to explore the dynamics as one deviates from the pure-state picture though there have been previous attempts that utilized the dressed state formalism. 20 As discussed here, we have elucidated these effects particularly taking advantage of the off-diagonal elements of the density matrix formalism and have shown how the deviation from the two-level character due to the influence of the damping terms compromises the effectiveness of the shaped pulses for either quantum computational applications or coherent control issues.…”

“…Interestingly, such a process essentially is a Hadamard operation in quantum computing language as this enables us to produce equal superposition between the ground and excited states which form the qubits. 11 Another common situation with short pulses is a ladder excitation situation where the individual excited states undergo dephasing through a coupled energy structure with states ͉0͘,͉1͘,͉2͘, etc. in the zero-order basis, as shown in Fig.…”

“…Herein, with the help of the models discussed in the earlier sections, we probe the real part, the imaginary part, the phase angle, and the abso-lute values of the off-diagonal elements of the density matrix model propagations and compare it with the expected population dynamics that our model has been efficiently successful in corresponding to the experimental results. 7,11,19,20 We first discuss the simplest two-level model as depicted in Fig. 1 to understand the behavior of the off-diagonal elements of the density matrix.…”

“…[7][8][9][10][11] In this framework, logical implementation of quantum gates uses the language of ground states, spectral gaps, and Hamiltonians wherein a quantum gate represents a device which performs a unitary transformation on selected qubits within a fixed period of time. Thus, a computational procedure in the adiabatic quantum computation model is a continuous time evolution of a time-dependent Hamiltonian with limited energetic resources.…”

“…Our previous paper 11 showed that an important aspect of the adiabatic quantum computation model lies in addressing an atomic or molecular ensemble and hence in robust implementation. These were based on our earlier experimental demonstration on selective population transfer in a two-level and a three-level system.…”