We simulate the implementation of a 3-qubit quantum Fourier transform gate in the hyperfine levels of ultracold polar alkali dimers in their first two lowest rotational levels. The chosen dimer is (41)K(87)Rb supposed to be trapped in an optical lattice. The hyperfine levels are split by a static magnetic field. The pulses operating in the microwave domain are obtained by optimal control theory. We revisit the problem of phase control in information processing. We compare the efficiency of two optimal fields. The first one is obtained from a functional based on the average of the transition probabilities for each computational basis state but constrained by a supplementary transformation to enforce phase alignment. The second is obtained from a functional constructed on the phase sensitive fidelity involving the sum of the transition amplitudes without any supplementary constrain.
We simulate the implementation of a 3-qubit quantum Fourier transform gate in the hyperfine levels of ultracold polar alkali dimers in their first two lowest rotational levels. The chosen dimer is (41)K(87)Rb supposed to be trapped in an optical lattice. The hyperfine levels are split by a static magnetic field. The pulses operating in the microwave domain are obtained by optimal control theory. We revisit the problem of phase control in information processing. We compare the efficiency of two optimal fields. The first one is obtained from a functional based on the average of the transition probabilities for each computational basis state but constrained by a supplementary transformation to enforce phase alignment. The second is obtained from a functional constructed on the phase sensitive fidelity involving the sum of the transition amplitudes without any supplementary constrain.
We numerically implement quantum algorithms in hyperfine levels of ultracold polar molecules. Logical operations are driven by pulses optimized by optimal control theory. All implementations take place in the lowest two rotational levels of the ground vibrational state of the ground (1)Σ(+) electronic state, exploiting the richness of the hyperfine energy structure and state mixing in static external fields. We show that it is possible to realize high fidelity complex logical operations with microsecond pulses. The possibility to run algorithms implemented on two interacting molecules is also demonstrated. (41)K(85)Rb and (41)K(87)Rb molecules are considered for the numerical simulations but the results are general and can be extended to other species.
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.
Quantum Fourier transform (QFT) is a quantum analogue of the classical discrete Fourier transform. It is a fundamental quantum gate in quantum algorithms which has an exponential advantage over the classical computation and has been excessively studied. Normally, an n-qubit quantum Fourier transform could be resolved into the tensor product of n single-qubit operations, and each operation could be implemented by a Hadamard gate and a controlled phase gate. Then the complexity of an n-qubit QFT is of order O(n2). To reduce the complexity of quantum operations, optimal control (OC) method has recently been used successfully to find the minimum time for implementing a quantum operation. Up to now, two types of quantum optimal control methods have been presented, i.e. analytical and numerical methods. The analytical approach is to change the problem of efficient synthesis of unitary transformations into the geometrical one of finding the shortest paths. Numerical optimal control procedures are based on the gradient methods (GRAPE, Gradient Ascent Pulse Engineering) and Krotov methods. Notable application mainly focus on nuclear magnetic resonance fields, including imaging, liquid-state NMR, solid-state NMR, and NMR quantum computation. One obvious advantage of optimal control NMR quantum computation is that the OC unitary evolution transformation pulse sequences are normally shorter than the conventional corresponding ones. Here we use the optimal control method to find the minimum duration for implementing QFT quantum gate. A linear spin chain with nearest-neighbor Ising interaction is used to find the optimization. And the optimized pulse sequence is experimentally demonstrated on an NMR quantum information processor. By using optimal control method with numerical calculation, a three-qubit QFT in an indirect-linear-coupling chain system is optimized. The duration of the OC QFT is obviously shorter than that of conventional approaches. The OC pulse sequence has been experimentally implemented on a liquid-state NMR spectrometer. To verify the optimally controlled pulse sequence for the three-qubit QFT, different initial states are assumed. The accuracy of the OC pulse sequence could be demonstrated by the consistency of theoretical simulation spectra with the experimental results. The good consistency between the simulation and the experimental spectra demonstrates that the OC QFT is of high fidelity.
Abstract Theoretical schemes for the implementation of the Grover search algorithm are proposed based on ultracold polar molecules in an electric field. The molecular qubits and qudit are chosen as the field‐dressed states formed by the rotational modes of CH 3 CN. With the help of multi‐target optimal control theory, the microwave pulses for the elementary logic operations including the one‐qubit Hadamard gates and the conditional phase gates in a dipole‐dipole system are designed and the factorized Grover algorithm demonstrated using two coupled CH 3 CN molecules. To reduce the accumulation of imprecision and decoherence resulting from the combination of multiple elementary gates, the optimal pulses that can achieve the two‐qubit Hadamard gate and diffusion operation in one step are designed successfully. In this way, the probabilities to find the states corresponding to the desired elements in an unsorted database are enhanced to some extent. Moreover, the optimal pulse sequence suitable for a four‐level molecular qudit, which can be used to simulate the quantum search on a single CH 3 CN molecule with high fidelity, is designed. These results can shed some light on the physical realization of quantum computing based on ultracold polyatomic molecules.
We demonstrate coherent microwave control of rotational and hyperfine states of trapped, ultracold, and chemically stable ^{23}Na^{40}K molecules. Starting with all molecules in the absolute rovibrational and hyperfine ground state, we study rotational transitions in combined magnetic and electric fields and explain the rich hyperfine structure. Following the transfer of the entire molecular ensemble into a single hyperfine level of the first rotationally excited state, J=1, we observe lifetimes of more than 3 s, comparable to those in the rovibrational ground state, J=0. Long-lived ensembles and full quantum state control are prerequisites for the use of ultracold molecules in quantum simulation, precision measurements, and quantum information processing.
We investigate the microwave spectra of ultracold alkali metal dimers in magnetic, electric and combined fields taking into account the hyperfine structure due to nuclear spins. We consider the molecules 41 K 87 Rb and 7 Li 133 Cs, which are the targets of current experiments, and demonstrate two extremes of large and small nuclear quadrupole couplings. We calculate the frequencies and intensities of transitions that may be used to transfer ultracold molecules between hyperfine states in a magnetic field, employing different polarizations of microwave radiation. In an electric field, the hyperfine levels display narrow avoided crossings at specific fields that we explain in terms of molecular alignment. The hyperfine splittings that arise in electric fields may hinder individual addressing in schemes that use ultracold molecules in quantum computation, but the structure of the spectra is suppressed in combined fields.