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.
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.
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.
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.
We propose a scheme for achieving basic quantum gates using ultracold polar molecules in pendular states. The qubits are encoded in the YbF molecules trapped in an electric field with a certain gradient and coupled by the dipole-dipole interaction. The time-dependent control sequences consisting of multiple pulses are considered to interact with the pendular qubits. To achieve high-fidelity quantum gates, we map the control problem for the coupled molecular system into a Markov decision process and deal with it using the techniques of deep reinforcement learning (DRL). By training the agents over multiple episodes, the optimal control pulse sequences for the two-qubit gates of NOT, controlled NOT, and Hadamard are discovered with high fidelities. Moreover, the population dynamics of YbF molecules driven by the discovered gate sequences are analyzed in detail. Furthermore, by combining the optimal gate sequences, we successfully simulate the quantum circuit for entanglement. Our findings could offer new insights into efficiently controlling molecular systems for practical molecule-based quantum computing using DRL.
In proposals for quantum computers using arrays of trapped ultracold polar molecules as qubits, a strong external field with appreciable gradient is imposed in order to prevent quenching of the dipole moments by rotation and to distinguish among the qubit sites. That field induces the molecular dipoles to undergo pendular oscillations, which markedly affect the qubit states and the dipole-dipole interaction. We evaluate entanglement of the pendular qubit states for two linear dipoles, characterized by pairwise concurrence, as a function of the molecular dipole moment and rotational constant, strengths of the external field and the dipole-dipole coupling, and ambient temperature. We also evaluate a key frequency shift, △ω, produced by the dipole-dipole interaction. Under conditions envisioned for the proposed quantum computers, both the concurrence and △ω become very small for the ground eigenstate. In principle, such weak entanglement can be sufficient for operation of logic gates, provided the resolution is high enough to detect the △ω shift unambiguously. In practice, however, for many candidate polar molecules it appears a challenging task to attain adequate resolution. Simple approximate formulas fitted to our numerical results are provided from which the concurrence and △ω shift can be obtained in terms of unitless reduced variables.
In proposals for quantum computers using arrays of trapped ultracold polar molecules as qubits, a strong external field with appreciable gradient is imposed in order to prevent quenching of the dipole moments by rotation and to distinguish among the qubit sites. That field induces the molecular dipoles to undergo pendular oscillations, which markedly affect the qubit states and the dipole-dipole interaction. We evaluate entanglement of the pendular qubit states for two linear dipoles, characterized by pairwise concurrence, as a function of the molecular dipole moment and rotational constant, strengths of the external field and the dipole-dipole coupling, and ambient temperature. We also evaluate a key frequency shift, △ω, produced by the dipole-dipole interaction. Under conditions envisioned for the proposed quantum computers, both the concurrence and △ω become very small for the ground eigenstate. In principle, such weak entanglement can be sufficient for operation of logic gates, provided the resolution is high enough to detect the △ω shift unambiguously. In practice, however, for many candidate polar molecules it appears a challenging task to attain adequate resolution. Simple approximate formulas fitted to our numerical results are provided from which the concurrence and △ω shift can be obtained in terms of unitless reduced variables.
Abstract Quantum algorithms offer more enhanced computational efficiency in comparison to their classical counterparts when 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 U f 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 the quantum computation of polar molecular systems.