Electronic Structure Calculations and the Ising Hamiltonian.

@article{Xia2018ElectronicSC,
  title={Electronic Structure Calculations and the Ising Hamiltonian.},
  author={Rongxin Xia and Teng Bian and Sabre Kais},
  journal={The journal of physical chemistry. B},
  year={2018},
  volume={122 13},
  pages={
          3384-3395
        }
}
Obtaining exact solutions to the Schrödinger equation for atoms, molecules, and extended systems continues to be a "Holy Grail" problem which the fields of theoretical chemistry and physics have been striving to solve since inception. Recent breakthroughs have been made in the development of hardware-efficient quantum optimizers and coherent Ising machines capable of simulating hundreds of interacting spins with an Ising-type Hamiltonian. One of the most vital questions pertaining to these new… Expand

Figures, Tables, and Topics from this paper

Quantum Computation For Electronic Structure Calculations
This dissertation contains four projects: transforming electronic structure Hamiltonian to approximating Ising-type Hamiltonian to enable electronic structure calculations by quantum annealing,Expand
Calculation of molecular vibrational spectra on a quantum annealer.
TLDR
A new methodology is presented to calculate the vibrational spectrum of a molecule on a quantum annealer by mapping of the ground state variational problem onto an Ising or quadratic unconstrained binary optimization (QUBO) problem by expressing the expansion coefficients using spins or qubits. Expand
Computing molecular excited states on a D-Wave quantum annealer
TLDR
The use of a D-Wave quantum annealer for the calculation of excited electronic states of molecular systems is demonstrated and the accuracy is dependent on the accuracy of the intermediate meta-heuristic software called qbsolv. Expand
A quantum algorithm for spin chemistry: a Bayesian exchange coupling parameter calculator with broken-symmetry wave functions†
TLDR
A quantum algorithm, B̲ayesian ex̲change coupling parameter calculator with b̲roken-symmetry wave functions (BxB), which is capable of computing the J value directly, without calculating the energies of individual spin states. Expand
Solving Quantum Chemistry Problems with a D-Wave Quantum Annealer
TLDR
It is found that current quantum annealing technologies result in an exponential scaling for such inherently quantum problems and that new couplers are necessary to make quantumAnnealers attractive for quantum chemistry. Expand
Quantum computing methods for electronic states of the water molecule
TLDR
The second-order direct method provides the most efficient circuit implementations in terms of the gate complexity and the analytical analyses of the error and the gate-complexity for each method are presented. Expand
Reduction of the molecular hamiltonian matrix using quantum community detection.
TLDR
The use of Quantum Community Detection performed using the D-Wave quantum annealer to reduce the molecular Hamiltonian matrix in Slater determinant basis without chemical knowledge is introduced. Expand
Solving complex eigenvalue problems on a quantum annealer with applications to quantum scattering resonances.
TLDR
This work presents the first numerical solution of a complex eigenvalue problem of any kind on a quantum annealer, and it is the first treatment of a quantum scattering resonance on any quantum device. Expand
An adaptive variational algorithm for exact molecular simulations on a quantum computer
TLDR
A new variational hybrid quantum-classical algorithm which allows the system being simulated to determine its own optimal state, and highlights the potential of the adaptive algorithm for exact simulations with present-day and near-term quantum hardware. Expand
Gate-free state preparation for fast variational quantum eigensolver simulations
The variational quantum eigensolver is currently the flagship algorithm for solving electronic structure problems on near-term quantum computers. The algorithm involves implementing a sequence ofExpand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 43 REFERENCES
Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets
TLDR
The experimental optimization of Hamiltonian problems with up to six qubits and more than one hundred Pauli terms is demonstrated, determining the ground-state energy for molecules of increasing size, up to BeH2. Expand
Simulation of electronic structure Hamiltonians using quantum computers
Over the last century, a large number of physical and mathematical developments paired with rapidly advancing technology have allowed the field of quantum chemistry to advance dramatically. However,Expand
Low Depth Quantum Simulation of Electronic Structure
Quantum simulation of the electronic structure problem is one of the most researched applications of quantum computing. The majority of quantum algorithms for this problem encode the wavefunctionExpand
The Bravyi-Kitaev transformation for quantum computation of electronic structure.
TLDR
An alternative method of simulating fermions with qubits, first proposed by Bravyi and Kitaev, is developed that reduces the simulation cost to O(log n) qubit operations for one fermionic operation and demonstrates the superior efficiency of the Bravyi-Kitaev method for all quantum computations of electronic structure. Expand
Realizable Hamiltonians for Universal Adiabatic Quantum Computers
It has been established that local lattice spin Hamiltonians can be used for universal adiabatic quantum computation. However, the two-local model Hamiltonians used in these proofs are general andExpand
Computational complexity of interacting electrons and fundamental limitations of density functional theory
Using arguments from computational complexity theory, fundamental limitations are found for how efficient it is to calculate the ground-state energy of many-electron systems using density functionalExpand
On the NP-completeness of the Hartree-Fock method for translationally invariant systems.
TLDR
This work maps out boundaries of the NP-completeness by investigating restricted instances of HF and constructs two new NP-complete variants of the problem, including a set of Hamiltonians whose translationally invariant Hartree-Fock solutions are trivial, but whose broken symmetry solutions areNP-complete. Expand
Adiabatic Quantum Simulation of Quantum Chemistry
TLDR
A procedure to map electronic structure Hamiltonians to 2-body qubit Hamiltonians with a small set of physically realizable couplings with precision requirements on the coupling strengths and a number of ancilla qubits that scale polynomially in the problem size is described. Expand
Scalable Quantum Simulation of Molecular Energies
We report the first electronic structure calculation performed on a quantum computer without exponentially costly precompilation. We use a programmable array of superconducting qubits to compute theExpand
Quantum annealing with manufactured spins
TLDR
This programmable artificial spin network bridges the gap between the theoretical study of ideal isolated spin networks and the experimental investigation of bulk magnetic samples, and may provide a practical physical means to implement a quantum algorithm, possibly allowing more-effective approaches to solving certain classes of hard combinatorial optimization problems. Expand
...
1
2
3
4
5
...