arXiv subjects

Teng Bian

Publications and source records attributed to Teng Bian.

5 recordsLinked to original sources

arXiv2021

Quantum Computing for Atomic and Molecular Resonances

The complex-scaling method can be used to calculate molecular resonances within the Born-Oppenheimer approximation, assuming the electronic coordinates are dilated independently of the nuclear coordinates. With this method, one will calculate the complex energy of a non-Hermitian Hamiltonian, whose real part is associated with the resonance position and the imaginary part is the inverse of the lifetime. In this study, we propose techniques to simulate resonances on a quantum computer. First, we transformed the scaled molecular Hamiltonian to second-quantization and then used the Jordan-Wigner transformation to transform the scaled Hamiltonian to the qubit space. To obtain the complex eigenvalues, we introduce the Direct Measurement method, which is applied to obtain the resonances of a simple one-dimensional model potential that exhibits pre-dissociating resonances analogous to those found in diatomic molecules. Finally, we applied the method to simulate the resonances of the H$_2^-$ molecule. Numerical results from the IBM Qiskit simulators and IBM quantum computers verify our techniques.

quant-ph↗

arXiv2019

Context aware quantum simulation of a matrix stored in quantum memory

In this paper a storage method and a context-aware circuit simulation idea are presented for the sum of block diagonal matrices. Using the design technique for a generalized circuit for the Hamiltonian dynamics through the truncated series, we generalize the idea to (0-1) matrices and discuss the generalization for the real matrices. The presented circuit requires $O(n)$ number of quantum gates and yields the correct output with the success probability depending on the number of elements: for matrices with $poly(n)$, the success probability is $1/poly(n)$. Since the operations on the circuit are controlled by the data itself, the circuit can be considered as a context aware computing gadget. In addition, it can be used in variational quantum eigensolver and in the simulation of molecular Hamiltonians.

quant-ph↗

arXiv2019

Quantum computing methods for electronic states of the water molecule

We compare recently proposed methods to compute the electronic state energies of the water molecule on a quantum computer. The methods include the phase estimation algorithm based on Trotter decomposition, the phase estimation algorithm based on the direct implementation of the Hamiltonian, direct measurement based on the implementation of the Hamiltonian and a specific variational quantum eigensolver, Pairwise VQE. After deriving the Hamiltonian using STO-3G basis, we first explain how each method works and then compare the simulation results in terms of gate complexity and the number of measurements for the ground state of the water molecule with different O-H bond lengths. Moreover, we present the analytical analyses of the error and the gate-complexity for each method. While the required number of qubits for each method is almost the same, the number of gates and the error vary a lot. In conclusion, among methods based on the phase estimation algorithm, the second order direct method provides the most efficient circuit implementations in terms of the gate complexity. With large scale quantum computation, the second order direct method seems to be better for large molecule systems. Moreover, Pairwise VQE serves the most practical method for near-term applications on the current available quantum computers. Finally the possibility of extending the calculation to excited states and resonances is discussed.

quant-ph↗

arXiv2017

Electronic Structure Calculations and the Ising Hamiltonian

The exact solution of the Schrodinger equation for atoms, molecules and extended systems continues to be a "Holy Grail" problem for the field of atomic and molecular physics since inception. Recently, breakthroughs have been made in the development of hardware- efficient quantum optimizers and coherent Ising machines capable of simulating hundreds of interacting spins through an Ising-type Hamiltonian. One of the most vital questions associated with these new devices is: "Can these machines be used to perform electronic structure calculations?" In this study, we discuss the general standard procedure used by these devices and show that there is an exact mapping between the electronic structure Hamiltonian and the Ising Hamiltonian. The simulation results of the transformed Ising Hamiltonian for H2, He2, HeH+, and LiH molecules match the exact numerical calculations. This demonstrates that one can map the molecular Hamiltonian to an Ising-type Hamiltonian which could easily be implemented on currently available quantum hardware.

quant-ph↗

arXiv2016

Electronic Structure Calculatins and the Ising Machine

The exact solution of Schrodinger equation for atoms, molecules and extended systems continues to be a "Holy Grail" problem that the entire field has been striving to solve since its inception. Recently, breakthroughs have been made in the development of quantum annealing and coherent Ising machines capable of simulating hundreds of connected spins interacting with an Ising type Hamiltonian. One of the most vital questions pertaining to these new devices is: 'can these machine be used to perform electronic structure calculations?' Here we discuss the general procedure used by these devices and show that there is an exact mapping between the electronic structure Hamiltonian of the Hydrogen molecule and the Ising Hamiltonian

quant-ph↗