# Electron-Phonon Systems on a Universal Quantum Computer

## Abstract

We present an algorithm that extends existing quantum algorithms forsimulating fermion systems in quantum chemistry and condensed matter physics toinclude phonons. The phonon degrees of freedom are represented with exponentialaccuracy on a truncated Hilbert space with a size that increases linearly withthe cutoff of the maximum phonon number. The additional number of qubitsrequired by the presence of phonons scales linearly with the size of thesystem. The additional circuit depth is constant for systems with finite-rangeelectron-phonon and phonon-phonon interactions and linear for long-rangeelectron-phonon interactions. Our algorithm for a Holstein polaron problem wasimplemented on an Atos Quantum Learning Machine (QLM) quantum simulatoremploying the Quantum Phase Estimation method. The energy and the phonon numberdistribution of the polaron state agree with exact diagonalization results forweak, intermediate and strong electron-phonon coupling regimes.

- Authors:

- Fermilab

- Publication Date:

- Research Org.:
- Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)

- OSTI Identifier:
- 1438542

- Report Number(s):
- FERMILAB-PUB-18-050-CD-T; arXiv:1802.07347

1657311

- DOE Contract Number:
- AC02-07CH11359

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: TBD

- Country of Publication:
- United States

- Language:
- English

### Citation Formats

```
Macridin, Alexandru, Spentzouris, Panagiotis, Amundson, James, and Harnik, Roni.
```*Electron-Phonon Systems on a Universal Quantum Computer*. United States: N. p., 2018.
Web.

```
Macridin, Alexandru, Spentzouris, Panagiotis, Amundson, James, & Harnik, Roni.
```*Electron-Phonon Systems on a Universal Quantum Computer*. United States.

```
Macridin, Alexandru, Spentzouris, Panagiotis, Amundson, James, and Harnik, Roni. Tue .
"Electron-Phonon Systems on a Universal Quantum Computer". United States.
doi:. https://www.osti.gov/servlets/purl/1438542.
```

```
@article{osti_1438542,
```

title = {Electron-Phonon Systems on a Universal Quantum Computer},

author = {Macridin, Alexandru and Spentzouris, Panagiotis and Amundson, James and Harnik, Roni},

abstractNote = {We present an algorithm that extends existing quantum algorithms forsimulating fermion systems in quantum chemistry and condensed matter physics toinclude phonons. The phonon degrees of freedom are represented with exponentialaccuracy on a truncated Hilbert space with a size that increases linearly withthe cutoff of the maximum phonon number. The additional number of qubitsrequired by the presence of phonons scales linearly with the size of thesystem. The additional circuit depth is constant for systems with finite-rangeelectron-phonon and phonon-phonon interactions and linear for long-rangeelectron-phonon interactions. Our algorithm for a Holstein polaron problem wasimplemented on an Atos Quantum Learning Machine (QLM) quantum simulatoremploying the Quantum Phase Estimation method. The energy and the phonon numberdistribution of the polaron state agree with exact diagonalization results forweak, intermediate and strong electron-phonon coupling regimes.},

doi = {},

journal = {TBD},

number = ,

volume = ,

place = {United States},

year = {Tue Feb 20 00:00:00 EST 2018},

month = {Tue Feb 20 00:00:00 EST 2018}

}