Construction of Green's functions on a quantum computer: Quasiparticle spectra of molecules

@article{Kosugi2019ConstructionOG,
  title={Construction of Green's functions on a quantum computer: Quasiparticle spectra of molecules},
  author={Taichi Kosugi and Yu-ichiro Matsushita},
  journal={Physical Review A},
  year={2019}
}
We propose a scheme for the construction of the one-particle Green's function (GF) of an interacting electronic system via statistical sampling on a quantum computer. Although the nonunitarity of creation and annihilation operators for the electronic spin orbitals prevents us from preparing specific states selectively, probabilistic state preparation is demonstrated to be possible for the qubits. We provide quantum circuits equipped with at most two ancillary qubits for obtaining all the… 

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References

SHOWING 1-10 OF 100 REFERENCES

The Bravyi-Kitaev transformation for quantum computation of electronic structure.

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.

Qubit Coupled Cluster Method: A Systematic Approach to Quantum Chemistry on a Quantum Computer.

A qubit coupled cluster (QCC) method that starts directly in the qubit space and uses energy response estimates for ranking the importance of individual entanglers for the variational energy minimization and provides an exact factorization of a unitary rotation of more than two qubits to a product of two-qubit unitary rotations.

Witnessing eigenstates for quantum simulation of Hamiltonian spectra

The concept of an eigenstate witness is introduced and used to find energies of quantum systems with quantum computers and provides a new quantum approach that combines variational methods and phase estimation to approximate eigenvalues for both ground and excited states.

Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets

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.

Comparison of Green's functions for transition metal atoms using self-energy functional theory and coupled-cluster singles and doubles (CCSD).

It is demonstrated via the two approaches that calculations based on the density functional theory (DFT) can fail in predicting the orbital energy spectra for spherically symmetric systems.

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,

Strategies for quantum computing molecular energies using the unitary coupled cluster ansatz

The application of VQE to the simulation of molecular energies using the unitary coupled cluster (UCC) ansatz is studied and an analytical method to compute the energy gradient is proposed that reduces the sampling cost for gradient estimation by several orders of magnitude compared to numerical gradients.

Quasiparticle energy spectra of isolated atoms from coupled-cluster singles and doubles (CCSD): Comparison with exact CI calculations.

It is found that the GFCCSD method reproduces not only the correct quasiparticle peaks but also satellite ones by comparing the exact spectra with the 6-31G basis set, and that open-shell atoms such as C atom exhibit Mott gaps at the Fermi level, which the exact density-functional theory fails to describe.

Variational quantum algorithms for discovering Hamiltonian spectra

Calculating the energy spectrum of a quantum system is an important task, for example to analyse reaction rates in drug discovery and catalysis. There has been significant progress in developing

Hybrid quantum-classical approach to correlated materials

This work shows that by using a hybrid quantum-classical algorithm that incorporates the power of a small quantum computer into a framework of classical embedding algorithms, the electronic structure of complex correlated materials can be efficiently tackled using a quantum computer.
...