# Iterative quantum-assisted eigensolver

@article{Bharti2021IterativeQE, title={Iterative quantum-assisted eigensolver}, author={Kishor Bharti and Tobias Haug}, journal={Physical Review A}, year={2021} }

The task of estimating ground state and ground state energy of Hamiltonians is an important problem in physics with numerous applications ranging from solid-state physics to combinatorial optimization. We provide a hybrid quantum-classical algorithm for approximating the ground state and ground state energy of a Hamiltonian. The description of the Hamiltonian is assumed to be a linear combination of unitaries. Our algorithm is iterative and systematically constructs the Ansatz using any given…

## 6 Citations

Quantum Krylov subspace algorithms for ground and excited state energy estimation

- Physics
- 2021

Quantum Krylov subspace diagonalization (QKSD) algorithms provide a low-cost alternative to the conventional quantum phase estimation algorithm for estimating the ground and excited-state energies of…

Variational Quantum Algorithms

- Computer Science, PhysicsNature Reviews Physics
- 2021

An overview of the field of Variational Quantum Algorithms is presented and strategies to overcome their challenges as well as the exciting prospects for using them as a means to obtain quantum advantage are discussed.

Absence of Barren Plateaus in Quantum Convolutional Neural Networks

- Physics, Computer SciencePhysical Review X
- 2021

This work rigorously analyze the gradient scaling for the parameters in the QCNN architecture and finds that the variance of the gradient vanishes no faster than polynomially, implying that QCNNs do not exhibit barren plateaus.

Connecting ansatz expressibility to gradient magnitudes and barren plateaus

- Computer Science, PhysicsArXiv
- 2021

This paper presents a probabilistic simulation of the response of the immune system to x-ray diffraction and shows clear patterns in response to the proton-proton collision.

Fast-forwarding with NISQ processors without feedback loop

- PhysicsQuantum Science and Technology
- 2021

Simulating quantum dynamics is expected to be performed more easily on a quantum computer than on a classical computer. However, the currently available quantum devices lack the capability to…

Higher order derivatives of quantum neural networks with barren plateaus

- Physics
- 2021

Quantum neural networks (QNNs) offer a powerful paradigm for programming near-term quantum computers and have the potential to speed up applications ranging from data science to chemistry to…

## References

SHOWING 1-10 OF 20 REFERENCES

Quantum inverse iteration algorithm for programmable quantum simulators

- Mathematics, Physics
- 2019

We propose a quantum inverse iteration algorithm, which can be used to estimate ground state properties of a programmable quantum device. The method relies on the inverse power iteration technique,…

Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution

- Mathematics, PhysicsNature Physics
- 2019

The accurate computation of Hamiltonian ground, excited and thermal states on quantum computers stands to impact many problems in the physical and computer sciences, from quantum simulation to…

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

- Physics, MedicineNature
- 2017

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.

Measurement optimization in the variational quantum eigensolver using a minimum clique cover.

- Mathematics, ChemistryThe Journal of chemical physics
- 2020

It is found that the qubit-wise commutativity between the Hamiltonian terms can be expressed as a graph and the problem of the optimal grouping is equivalent to finding a minimum clique cover (MCC) for theHamiltonian graph.

The theory of variational hybrid quantum-classical algorithms

- Computer Science, Physics
- 2015

This work develops a variational adiabatic ansatz and explores unitary coupled cluster where it is shown how the use of modern derivative free optimization techniques can offer dramatic computational savings of up to three orders of magnitude over previously used optimization techniques.

A variational eigenvalue solver on a photonic quantum processor

- Physics, MedicineNature communications
- 2014

The proposed approach drastically reduces the coherence time requirements and combines this method with a new approach to state preparation based on ansätze and classical optimization, enhancing the potential of quantum resources available today and in the near future.

A Multireference Quantum Krylov Algorithm for Strongly Correlated Electrons.

- Physics, MedicineJournal of chemical theory and computation
- 2020

Preliminary benchmarks on linear H6, H8, and BeH2 indicate that MRSQK can predict the energy of these systems accurately using very compact Krylov bases.

Barren plateaus in quantum neural network training landscapes

- Computer Science, PhysicsNature Communications
- 2018

It is shown that for a wide class of reasonable parameterized quantum circuits, the probability that the gradient along any reasonable direction is non-zero to some fixed precision is exponentially small as a function of the number of qubits.

Quantum Chemistry in the Age of Quantum Computing.

- Physics, ChemistryChemical reviews
- 2019

This Review provides an overview of the algorithms and results that are relevant for quantum chemistry and aims to help quantum chemists who seek to learn more about quantum computing and quantum computing researchers who would like to explore applications in quantum chemistry.

Quantum supremacy using a programmable superconducting processor

- Medicine, Computer ScienceNature
- 2019

Quantum supremacy is demonstrated using a programmable superconducting processor known as Sycamore, taking approximately 200 seconds to sample one instance of a quantum circuit a million times, which would take a state-of-the-art supercomputer around ten thousand years to compute.