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Journal of Physics Conference Series

Implementing quantum algorithms in hyperfine levels of ultracold polar molecules

Stéphane Vranckx, Philippe Pellegrini, Michèle Desouter-Lecomte

Published Nov 5, 2012• 1 citation
Publisher

Abstract

Using optimal control, we implement simple quantum algorithms using hyperfine states of ultracold polar molecules. The qubits are encoded in hyperfine states of isolated 41K85Rb or 41K87Rb molecules or in hyperfine states of two neighboring molecules.
DOI
10.1088/1742-6596/388/11/112010

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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.
Abstract We discuss how the internal structure of ultracold molecules, trapped in the motional ground state of optical tweezers, can be used to implement qudits. We explore the rotational, fine and hyperfine structure of 40Ca19F and 87Rb133Cs, which are examples of molecules with 2Σ and 1Σ electronic ground states, respectively. In each case we identify a subset of levels within a single rotational manifold suitable to implement a four-level qudit. Quantum gates can be implemented using two-photon microwave transitions via levels in a neighboring rotational manifold. We discuss limitations to the usefulness of molecular qudits, arising from off-resonant excitation and decoherence. As an example, we present a protocol for using a molecular qudit of dimension d = 4 to perform the Deutsch algorithm.
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.
Fine Control of Ultracold Polar MoleculesThe ability to store molecules in reconfigurable optical traps could allow researchers to harness the rich physics of molecules in quantum applications.By Charles Day U ltracold atoms are a promising platform for quantum science.Molecules could be even better thanks to properties that atoms lack, such as polarity and the availability of rotational states.Now two independent groups have succeeded in filling one-dimensional arrays of optical traps with ultracold polar molecules assembled from ultracold atoms [1, 2].The groups also demonstrated that they could set, change, and read out the individual quantum states of the molecules.The feat may enable techniques developed for trapped atoms to be implemented with molecules, making the richer molecular physics available to new quantum applications.
Abstract Quantum states with long-lived coherence are essential for quantum computation, simulation and metrology. The nuclear spin states of ultracold molecules prepared in the singlet rovibrational ground state are an excellent candidate for encoding and storing quantum information. However, it is important to understand all sources of decoherence for these qubits, and then eliminate them, in order to reach the longest possible coherence times. Here, we fully characterise the dominant mechanisms for decoherence of a storage qubit in an optically trapped ultracold gas of RbCs molecules using high-resolution Ramsey spectroscopy. Guided by a detailed understanding of the hyperfine structure of the molecule, we tune the magnetic field to where a pair of hyperfine states have the same magnetic moment. These states form a qubit, which is insensitive to variations in magnetic field. Our experiments reveal an unexpected differential tensor light shift between the states, caused by weak mixing of rotational states. We demonstrate how this light shift can be eliminated by setting the angle between the linearly polarised trap light and the applied magnetic field to a magic angle of arccos(1/√3)≈55°. This leads to a coherence time exceeding 6.9 s (90% confidence level). Our results unlock the potential of ultracold molecules as a platform for quantum computation.