# Quantum Krylov subspace algorithms for ground and excited state energy estimation

@inproceedings{Cortes2021QuantumKS, title={Quantum Krylov subspace algorithms for ground and excited state energy estimation}, author={Cristian L. Cortes and Stephen K. Gray}, year={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 a quantum many-body system. While QKSD algorithms typically rely on using the Hadamard test for estimating Krylov subspace matrix elements of the form, 〈φi|e |φj〉, the associated quantum circuits require an ancilla qubit with controlled multi-qubit gates that can be quite costly for near-term… Expand

#### 2 Citations

A Theory of Quantum Subspace Diagonalization

- Computer Science, Physics
- ArXiv
- 2021

A theoretical analysis of this surprising phenomenon is provided, proving that under certain natural conditions, a quantum subspace diagonalization algorithm can accurately compute the smallest eigenvalue of a large Hermitian matrix. Expand

Accessing ground state and excited states energies in many-body system after symmetry restoration using quantum computers

- Physics
- 2021

We explore the possibility to perform symmetry restoration with the variation after projection technique on a quantum computer followed by additional post-processing. The final goal is to develop… Expand

#### References

SHOWING 1-10 OF 60 REFERENCES

Quantum Filter Diagonalization: Quantum Eigendecomposition without Full Quantum Phase Estimation

- Mathematics, Physics
- 2019

We develop a quantum filter diagonalization method (QFD) that lies somewhere between the variational quantum eigensolver (VQE) and the phase estimation algorithm (PEA) in terms of required quantum… Expand

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

- Mathematics, Physics
- Nature 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… Expand

Quantum phase estimation of multiple eigenvalues for small-scale (noisy) experiments

- Physics, Mathematics
- New Journal of Physics
- 2019

Quantum phase estimation is the workhorse behind any quantum algorithm and a promising method for determining ground state energies of strongly correlated quantum systems. Low-cost quantum phase… Expand

Witnessing eigenstates for quantum simulation of Hamiltonian spectra

- Physics, Medicine
- Science Advances
- 2018

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. Expand

Efficient symmetry-preserving state preparation circuits for the variational quantum eigensolver algorithm

- Physics
- 2019

The variational quantum eigensolver is one of the most promising approaches for performing chemistry simulations using noisy intermediate-scale quantum (NISQ) processors. The efficiency of this… Expand

Iterative quantum-assisted eigensolver

- Physics
- Physical Review A
- 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… Expand

Hybrid Quantum-Classical Hierarchy for Mitigation of Decoherence and Determination of Excited States

- Physics
- 2017

Author(s): McClean, JR; Kimchi-Schwartz, ME; Carter, J; De Jong, WA | Abstract: © 2017 American Physical Society. Using quantum devices supported by classical computational resources is a promising… Expand

Quantum Algorithm for Spectral Measurement with a Lower Gate Count.

- Medicine, Physics
- Physical review letters
- 2018

Two techniques are presented that can greatly reduce the number of gates required to realize an energy measurement, with application to ground state preparation in quantum simulations, and a unitary operator is proposed which can be implemented exactly, circumventing any Taylor or Trotter approximation errors. Expand

Barren plateaus in quantum neural network training landscapes

- Computer Science, Physics
- Nature 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. Expand

Variational Quantum Algorithms

- Computer Science, Physics
- Nature 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. Expand