Multi-target Optimal Control Theory Research Articles

Efficient implementation of quantum permutation algorithm using a polar SrO molecule in pendular states

Abstract Quantum algorithms offer enhanced computational efficiency compared to their classical counterparts in solving specific tasks. In this study, we implement the quantum permutation algorithm utilizing a polar molecule within an external electric field. The selection of the molecular qutrit involves the utilization of field-dressed states generated through the pendular modes of SrO. Through the application of multi-target optimal control theory, we strategically design microwave pulses to execute logical operations, including Fourier transform, oracle Uf operation, and inverse Fourier transform within a three-level molecular qutrit structure. The observed high fidelity of our outcomes is intricately linked to the concept of the quantum speed limit, which quantifies the maximum speed of quantum state manipulation. Subsequently, we design the optimized pulse sequence to successfully simulate the quantum permutation algorithm on a single SrO molecule, achieving remarkable fidelity. Consequently, a quantum circuit comprising a single qutrit suffices to determine permutation parity with just a single function evaluation. Therefore, our results indicate that the optimal control theory can be well applied to quantum computation of polar molecular systems.

Simulation of quantum walks on a circle with polar molecules via optimal control.

Quantum walks are the quantum counterpart of classical random walks and have various applications in quantum information science. Polar molecules have rich internal energy structure and long coherence time and thus are considered as a promising candidate for quantum information processing. In this paper, we propose a theoretical scheme for implementing discrete-time quantum walks on a circle with dipole-dipole coupled SrO molecules. The states of the walker and the coin are encoded in the pendular states of polar molecules induced by an external electric field. We design the optimal microwave pulses for implementing quantum walks on a four-node circle and a three-node circle by multi-target optimal control theory. To reduce the accumulation of decoherence and improve the fidelity, we successfully realize a step of quantum walk with only one optimal pulse. Moreover, we also encode the walker into a three-level molecular qutrit and a four-level molecular ququart and design the corresponding optimal pulses for quantum walks, which can reduce the number of molecules used. It is found that all the quantum walks on a circle in our scheme can be achieved via optimal control fields with high fidelities. Our results could shed some light on the implementation of discrete-time quantum walks and high-dimensional quantum information processing with polar molecules.

Optimization two-qubit quantum gate by two optical control methods in molecular pendular states

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.

Implementation of three-qubit quantum computation with pendular states of polar molecules by optimal control

Ultracold polar molecules have been considered as the possible candidates for quantum information processing due to their long coherence time and strong dipole-dipole interaction. In this paper, we consider three coupled polar molecules arranged in a linear chain and trapped in an electric field with gradient. By employing the pendular states of polar molecules as qubits, we successfully realize three-qubit quantum gates and quantum algorithms via the multi-target optimal control theory. Explicitly speaking, through the designs of the optimal laser pulses with multiple iterations, the triqubit Toffoli gate, the triqubit quantum adders, and the triqubit quantum Fourier transform can be achieved in only one operational step with high fidelities and large transition probabilities. Moreover, by combining the optimized Hadamard, oracle, and diffusion gate pulses, we simulate the Grover algorithm in the three-dipole system and show that the algorithm can perform well for search problems. In addition, the behaviors of the fidelity and the average transition probability with respect to iteration numbers are compared and analyzed for each gate pulse. Our findings could pave the way toward scalability for molecular quantum computing based on the pendular states and could be extended to implement multi-particle gate operation in the molecular system.

A multi target approach to control chemical reactions in their inhomogeneous solvent environment

Shaped laser pulses offer a powerful tool to manipulate molecular quantum systems. Their application to chemical reactions in solution is a promising concept to redesign chemical synthesis. Along this road, theoretical developments to include the solvent surrounding are necessary. An appropriate theoretical treatment is helpful to understand the underlying mechanisms. In our approach we simulate the solvent by randomly selected snapshots from molecular dynamics trajectories. We use multi target optimal control theory to optimize pulses for the various arrangements of explicit solvent molecules simultaneously. This constitutes a major challenge for the control algorithm, as the solvent configurations introduce a large inhomogeneity to the potential surfaces. We investigate how the algorithm handles the new challenges and how well the controllability of the system is preserved with increasing complexity. Additionally, we introduce a way to statistically estimate the efficiency of the optimized laser pulses in the complete thermodynamical ensemble.

Simulation of the elementary evolution operator with the motional states of an ion in an anharmonic trap.

Following a recent proposal of L. Wang and D. Babikov [J. Chem. Phys. 137, 064301 (2012)], we theoretically illustrate the possibility of using the motional states of a Cd(+) ion trapped in a slightly anharmonic potential to simulate the single-particle time-dependent Schrödinger equation. The simulated wave packet is discretized on a spatial grid and the grid points are mapped on the ion motional states which define the qubit network. The localization probability at each grid point is obtained from the population in the corresponding motional state. The quantum gate is the elementary evolution operator corresponding to the time-dependent Schrödinger equation of the simulated system. The corresponding matrix can be estimated by any numerical algorithm. The radio-frequency field which is able to drive this unitary transformation among the qubit states of the ion is obtained by multi-target optimal control theory. The ion is assumed to be cooled in the ground motional state, and the preliminary step consists in initializing the qubits with the amplitudes of the initial simulated wave packet. The time evolution of the localization probability at the grids points is then obtained by successive applications of the gate and reading out the motional state population. The gate field is always identical for a given simulated potential, only the field preparing the initial wave packet has to be optimized for different simulations. We check the stability of the simulation against decoherence due to fluctuating electric fields in the trap electrodes by applying dissipative Lindblad dynamics.

Implementation of quantum logic gates using polar molecules in pendular states

We present a systematic approach to implementation of basic quantum logic gates operating on polar molecules in pendular states as qubits for a quantum computer. A static electric field prevents quenching of the dipole moments by rotation, thereby creating the pendular states; also, the field gradient enables distinguishing among qubit sites. Multi-target optimal control theory is used as a means of optimizing the initial-to-target transition probability via a laser field. We give detailed calculations for the SrO molecule, a favorite candidate for proposed quantum computers. Our simulation results indicate that NOT, Hadamard and CNOT gates can be realized with high fidelity, as high as 0.985, for such pendular qubit states.

Free-time and fixed end-point multi-target optimal control theory: Application to quantum computing

An extension of free-time and fixed end-point optimal control theory (FRFP-OCT) to monotonically convergent free-time and fixed end-point multi-target optimal control theory (FRFP-MTOCT) is presented. The features of our theory include optimization of the external time-dependent perturbations with high transition probabilities, that of the temporal duration, the monotonic convergence, and the ability to optimize multiple-laser pulses simultaneously. The advantage of the theory and a comparison with conventional fixed-time and fixed end-point multi-target optimal control theory (FIFP-MTOCT) are presented by comparing data calculated using the present theory with those published previously [K. Mishima, K. Yamashita, Chem. Phys. 361, (2009), 106]. The qubit system of our interest consists of two polar NaCl molecules coupled by dipole–dipole interaction. The calculation examples show that our theory is useful for minor adjustment of the external fields.

Quantum computing using molecular vibrational and rotational modes of the open-shell 14N16O molecule

In this paper, we investigate the possibility of using internal molecular vibrational and rotational modes of an open-shell molecule for one of the most important quantum algorithms: the Deutsch-Jozsa algorithm. The molecular system of interest is one of the representative open-shell molecules: 14 N 16 O. The gate pulses are constructed by utilizing multi-target optimal control theory (MTOCT). The gate fidelities of each quantum gate are more than 95.23%. Upon implementing the Deutsch-Jozsa algorithm combining these elementary gates, we obtained fidelity of at least 94.76%. This indicates that vibrational and rotational qubits of the open-shell 14 N 16 O molecule are about as promising for processing quantum algorithms as those of the closed-shell molecule 12 C 16 O that we studied earlier.

Quantum computing using rotational modes of two polar molecules

In this paper, we numerically constructed general-purpose phase-correct global quantum gates by using intermolecular rotational modes of two polar molecules coupled by dipole–dipole interaction to encode two qubits and implement the Deutsch–Jozsa algorithm. The calculations were based on the multi-target optimal control theory (MTOCT). The molecular systems we examined were NaCl–NaBr, NaCl–NaCl, and NaBr–NaBr polar molecular systems. The rotational states in the ground vibrational state of the ground electronic state of these pairs were taken as two qubits. When implementing the Deutsch–Jozsa algorithm by combining these elementary gates, we obtained a maximum probability 97.95% for NaBr–NaBr system with the interval R = 5.0 nm in the repulsive configuration, which is the best performance of the two-state Deutsch–Jozsa algorithm compared with intramolecular vibrational–vibrational, vibrational–rotational, and electronic–vibrational qubits reported so far.

NOT gate in acis-transphotoisomerization model

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

Optimal control simulation of the Deutsch-Jozsa algorithm in a two-dimensional double well coupled to an environment

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.

Manganese pentacarbonyl bromide as candidate for a molecular qubit system operated in the infrared regime

Our concept for a quantum computational system is based on qubits encoded in vibrational normal modes of polyatomic molecules. The quantum gates are implemented by shaped femtosecond laser pulses. We adopt this concept to the new species manganese pentacarbonyl bromide [MnBr(CO)5] and show that it is a promising candidate in the mid-infrared (IR) frequency range to connect theory and experiment. As direct reference for the ab initio calculations we evaluated experimentally the absorption bands of MnBr(CO)5 in the mid-IR as well as the related transition dipole moments. The two-dimensional potential-energy surface spanned by the two strongest IR active modes and the dipole vector surfaces are calculated with density-functional theory. The vibrational eigenstates representing the qubit system are determined. Laser pulses are optimized by multitarget optimal control theory to form a set of global quantum gates: NOT, CNOT, Pi, and Hadamard. For all of them simply structured pulses with low pulse energies around 1 microJ could be obtained. Exemplarily for the CNOT gate we investigated the possible transfer to experimental shaping, based on the mask function for pulse shaping in the frequency regime as well as decomposition into a train of subpulses.