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Quantum Computing: Computational Excellence for Society 5.0
Published in Kavita Taneja, Harmunish Taneja, Kuldeep Kumar, Arvind Selwal, Eng Lieh Ouh, Data Science and Innovations for Intelligent Systems, 2021
Paul R. Griffin, Michael Boguslavsky, Junye Huang, Robert J. Kauffman, Brian R. Tan
There is a class of quantum-classical hybrid algorithms called variational quantum eigensolver algorithms (VQE, a kind of the more general variational quantum algorithms, VGAs). These are suitable for implementation on NISQ devices (Peruzzo et al., 2014). Such algorithms contain both quantum circuits and classical procedures that are invoked iteratively. The quantum circuits in each iteration have a small number (< 100) of qubits and a small number (also < 100) of quantum gates, and these can be run with current NISQ devices. The results of the quantum circuits are then fed to classical procedures for calculation and optimization to determine the parameters of a quantum circuit in the next iteration of the algorithm. This hybrid approach enables harnessing the power of quantum computers in the NISQ era before QEC becomes widely available.
Function Optimization Using IBM Q
Published in Siddhartha Bhattacharyya, Mario Köppen, Elizabeth Behrman, Ivan Cruz-Aceves, Hybrid Quantum Metaheuristics, 2022
Siddhartha Bhattacharyya, Mario Köppen, Elizabeth Behrman, Ivan Cruz-Aceves
Variational Quantum Eigensolver (VQE) [28] is a hybrid between classical and quantum computing. A classical computer controls the preparation of a quantum state using few experimental parameters; then a quantum computer prepares that state and calculates its properties. Optimization problems can be resolved by quantum computer using VQE. In [29], VQE in IBM Q has been applied to solve the MaxCut NP-complete binary optimization problem with 5 qubits.
Theory of chemical bonds in metalloenzymes XXIV electronic and spin structures of FeMoco and Fe-S clusters by classical and quantum computing
Published in Molecular Physics, 2020
Koichi Miyagawa, Mitsuo Shoji, Hiroshi Isobe, Shusuke Yamanaka, Takashi Kawakami, Mitsutaka Okumura, Kizashi Yamaguchi
The UNO FV CI of SCES [37] was our dream as shown in Figure 3. Recently, the diagonalisation of the large CI matrix [45,47] on quantum computer is an interesting and important topic in quantum chemistry. To this end, Martinis et al. performed the great improvement of the qubits consisted of superconductors [91]. Therefore, they opened the door for quantum computing of complex systems [57]. In fact, the hybrid classical and quantum computing methods based on the NISQ (Noisy Intermediate-Scale Quantum) computer [92] have been attracted great interest in quantum chemistry [45,47,93–100]. Therefore, we have also revisited the large-scale UNO CI for strongly correlated electron systems (SCES) [37,72]. The coupling coefficients in the CAS CI are generally derived using second quantisation expression for quantum computation [45,47]. The Hamiltonian is given by this expression is given by where and are the creation and annihilation operators, respectively, for an electron in UNO spin orbital, and one- and two-electron integrals are also expressed by using the notation of UNO spin orbitals, respectively [37,72]. Dimension of the Hamiltonian matrix for UNO CI in Equation (30) increases in the exponential manner with the number of active electrons and active orbitals [92] for SCES such as Fe-S clusters, indicating that it becomes over any allowed memory size in the classical computers based on the classical bits [45,47]. On the other hand, the memory size becomes 2N if the N-qubits are used in the quantum computer, for example 253=1016 [45]. To this end, the creation and annihilation operators in Equation (30) are expressed by the quantum operators based on the Bravyi-Kitaev and/or Jordan-Wigner [101] transformation formula. Recently, several procedures [93–100] to perform the exact diagonalisation of the transformed quantum Hamiltonian on the NISQ computer have been proposed to obtain the ground and lower-lying states by CI procedures such as a large-scale UNO CAS CI [37]. One of these procedures is the hybrid classical and quantum scheme, where the quantum computation is limited for the diagonalisation process, and other parts such as calculations of molecular integrals and total energies are performed using the classical computers as illustrated in Figure 21. Full geometry optimisation for each spin state is also performed using classical computer. The variational quantum eigensolver (VQE) method [93–100] has been proposed to obtain the ground state of UNO CAS CI in the hybrid calculations. Very good trial orbitals for VQE are desirable for good convergence toward the exact ground state of quantum systems [45,47]. For the purpose, we have suggested scope and applicability of UNO [37,72] for efficient VQE processes as illustrated in Figure 21 (see details in SIII.4).
Quantum computing methods for electronic states of the water molecule
Published in Molecular Physics, 2019
Teng Bian, Daniel Murphy, Rongxin Xia, Ammar Daskin, Sabre Kais
Recently the variational quantum eigensolver method has been put forward by Aspuru-guzik and coworkers to calculate the ground state energies [19–22,33], which is a hybrid method of classical and quantum computation. According to this method, an adjustable quantum circuit is constructed at first to generate a state of the system. This state is then used to calculate the corresponding energy under the system's Hamiltonian. Then by a classical optimisation algorithm, like Nelder–Mead method, parameters in circuit can be adjusted and the generated state will be updated. Finally, the minimal energy will be obtained. The detailed circuit for the quantum part of our algorithm is shown in Figure 4. To make the expression more clear, we represent parameters in vector form, as follows: , , , , . We are using d layers of gate in Figure 4 to entangle all qubits together. Here we introduce a hardware-efficient , and we call this method Pairwise VQE. The example gate of for 4 qubits is shown in Figure 5. The entangling gate for 6-qubit system HO is similar: every 2 qubits are modified by single-qubit gates and entangled by CNOT gate. By selecting initial value of all and , system state can be prepared by d layers gates and arbitrary single gates . Then average value of each term in Hamiltonian H, , can be evaluated by measuring qubits many times after going through gates like I or or . For example, if , then So we can let the quantum state after go through gates and and then measure the result state multiple times to get . The energy corresponding to the state can be obtained by . Then and can be updated by classical optimisation method and can reach the minimal step by step.