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

  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},
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… 

Figures from this paper

Calculation of the Green's function on near-term quantum computers

The Green's function plays a crucial role when studying the nature of quantum many-body systems, especially strongly-correlated systems. Although the development of quantum computers in the near

Calculating the Green’s function of two-site fermionic Hubbard model in a photonic system

The Green’s function has been an indispensable tool to study many-body systems that remain one of the biggest challenges in modern quantum physics for decades. The complicated calculation of the

Quantum Algorithms for Ground-State Preparation and Green's Function Calculation

We propose quantum algorithms for projective ground-state preparation and calculations of the many-body Green’s functions directly in frequency domain. The algorithms are based on the linear

Hybrid quantum-classical approach for coupled-cluster Green's function theory

A quantum-classical implementation of the coupled-cluster Green's function (CCGF) method, which replaces explicit ground state preparation with the task of applying unitary operators to a simple product state for the Anderson impurity model.

Exhaustive search for optimal molecular geometries using imaginary-time evolution on a quantum computer

We propose a nonvariational scheme for geometry optimization of molecules for the first-quantized eigensolver, a recently proposed framework for quantum chemistry using the probabilistic

Probabilistic imaginary-time evolution by using forward and backward real-time evolution with a single ancilla: first-quantized eigensolver of quantum chemistry for ground states

A new PITE approach that uses only one ancillary qubit is proposed that constructs the circuit from forward and backward real-time evolution (RTE) gates as black boxes for the original Hamiltonian and can be used to obtain the Gibbs state at a temperature and partition function.

Variational quantum eigensolver for dynamic correlation functions

Recent practical approaches for the use of current generation noisy quantum devices in the simulation of quantum many-body problems have been dominated by the use of a variational quantum eigensolver

Symmetry-adapted variational quantum eigensolver

We propose a scheme to restore spatial symmetry of Hamiltonian in the variational-quantum-eigensolver (VQE) algorithm for which the quantum circuit structures used usually break the Hamiltonian

Linear-response functions of molecules on a quantum computer: Charge and spin responses and optical absorption

This work proposes a generic construction scheme for the quantum circuit implementing a nonunitary operator appearing in electronic-structure calculations. The authors demonstrate that the scheme

Quantum Power Method by a Superposition of Time-Evolved States

We propose a quantum-classical hybrid algorithm of the power method, here dubbed as quantum power method, to evaluate $\hat{\mathcal{H}}^{n}|\psi\rangle$ with quantum computers, where $n$ is a



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.