In this paper, molecular quantum computation is numerically studied with the quantum search algorithm (Grover's algorithm) by means of optimal control simulation. Qubits are implemented in the vibronic states of I 2 , while gate operations are realized by optimally designed laser pulses. The methodological aspects of the simulation are discussed in detail. We show that the algorithm for solving a gate pulse-design problem has the same mathematical form as a state-to-state control problem in the density matrix formalism, which provides monotonically convergent algorithms as an alternative to the Krotov method. The sequential irradiation of separately designed gate pulses leads to the population distribution predicted by Grover's algorithm. The computational accuracy is reduced by the imperfect quality of the pulse design and by the electronic decoherence processes that are modeled by the non-Markovian master equation. However, as long as we focus on the population distribution of the vibronic qubits, we can search a target state with high probability without introducing error-correction processes during the computation. A generalized gate pulse-design scheme to explicitly include decoherence effects is outlined, in which we propose a new objective functional together with its solution algorithm that guarantees monotonic convergence.
In this paper, molecular quantum computation is numerically studied with the quantum search algorithm (Grover's algorithm) by means of optimal control simulation. Qubits are implemented in the vibronic states of I 2 , while gate operations are realized by optimally designed laser pulses. The methodological aspects of the simulation are discussed in detail. We show that the algorithm for solving a gate pulse-design problem has the same mathematical form as a state-to-state control problem in the density matrix formalism, which provides monotonically convergent algorithms as an alternative to the Krotov method. The sequential irradiation of separately designed gate pulses leads to the population distribution predicted by Grover's algorithm. The computational accuracy is reduced by the imperfect quality of the pulse design and by the electronic decoherence processes that are modeled by the non-Markovian master equation. However, as long as we focus on the population distribution of the vibronic qubits, we can search a target state with high probability without introducing error-correction processes during the computation. A generalized gate pulse-design scheme to explicitly include decoherence effects is outlined, in which we propose a new objective functional together with its solution algorithm that guarantees monotonic convergence.
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.
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.
This paper develops and analyzes Grover’s quantum search algorithm in 2- and 3-qubit systems in terms of the number of gates, representation of state vectors, and state vector measurement probabilities. We designed, verified and simulated the quantum circuit using QCAD. We present a theoretical implementation of the search algorithm in different qubit systems. We may observe that our circuit design for 2-qubit systems is accurate and does not allow any error when a small error occurs in the design of a 3-qubit quantum system. it was considered to what extend given information about object of the research is used purposefully in the modeling process, as a result of mathematical analysis of Grover’s method of the quantum algorithm, i.e. it is important to provide the adequacy of the model. The results of the optimization performed with the quantum algorithm based on Grover’s method are presented.
Quantum optimal control is a powerful tool for designing a pulse that executes a specified gate, i.e., a unitary transformation in quantum computation. If we consider qubits characterized by different spectroscopic properties, we may design a pulse that executes a specified gate on a specified qubit (S qubit) with the inclusion of neighboring qubits (B qubits) but does not explicitly include the other qubits. In this situation, first we introduce sets of reduced time-evolution operators associated with the S and B qubits. Then, we apply quantum optimal control to these sets to design optimal pulses that could selectively execute the specified gate on the S qubit while actively removing the effects of the pulse on the B qubits, which would lead to a scalable pulse-design procedure. The present pulse design is applied to the quantum computation proposed by DeMille with the aim of executing the Hadamard and controlled-not gates on the S qubits while actively suppressing the pulse-induced population transitions of the B qubit states. The numerical results illustrate high fidelity even after introducing the extra qubits that are not included in the pulse design.
This work studies pulse based variational quantum algorithms (VQAs), which are designed to determine the ground state of a quantum mechanical system by combining classical and quantum hardware. In contrast to more standard gate based methods, pulse based methods aim to directly optimize the laser pulses interacting with the qubits, instead of using some parametrized gate based circuit. Using the mathematical formalism of optimal control, these laser pulses are optimized. This method has been used in quantum computing to optimize pulses for quantum gate implementations, but has only recently been proposed for full optimization in VQAs. Pulse based methods have several advantages over gate based methods such as faster state preparation, simpler implementation and more freedom in moving through the state space. Based on these ideas, we present the development of a novel adjoint based variational method. This method can be tailored towards and applied in neutral atom quantum computers. This method of pulse based variational quantum optimal control is able to approximate molecular ground states of simple molecules up to chemical accuracy and is able to compete with the gate based variational quantum eigensolver in terms of total number of quantum evaluations. The total evolution time T and the form of the control Hamiltonian Hc are important factors in the convergence behavior to the ground state energy, both having influence on the quantum speed limit and the controllability of the system.
The difference between classical and quantum algorithms (QA) is following: problem solved by QA is coded in the structure of the quantum operators. Input to QA in this case is always the same. Output of QA says which problem coded. In some sense, give a function to QA to analyze and QA returns its property as an answer without quantitative computing. QA studies qualitative properties of the functions. The core of any QA is a set of unitary quantum operators or quantum gates. In practical representation, quantum gate is a unitary matrix with particular structure. The size of this matrix grows exponentially with an increase in the number of inputs, which significantly limits the QA simulation on a classical computer with von Neumann architecture. Quantum search algorithm (QSA) - models apply for the solution of computer science problems as searching in unstructured data base, quantum cryptography, engineering tasks, control system design, robotics, smart controllers, etc. Grovers algorithm is explained in details along with implementations on a local computer simulator. The presented article describes a practical approach to modeling one of the most famous QA on classical computers, the Grover algorithm.