# Hybrid quantum-classical hierarchy for mitigation of decoherence and determination of excited states

## Abstract

Using quantum devices supported by classical computational resources is a promising approach to quantum-enabled computation. One powerful example of such a hybrid quantum-classical approach optimized for classically intractable eigenvalue problems is the variational quantum eigensolver, built to utilize quantum resources for the solution of eigenvalue problems and optimizations with minimal coherence time requirements by leveraging classical computational resources. These algorithms have been placed as leaders among the candidates for the first to achieve supremacy over classical computation. Here, we provide evidence for the conjecture that variational approaches can automatically suppress even nonsystematic decoherence errors by introducing an exactly solvable channel model of variational state preparation. Moreover, we develop a more general hierarchy of measurement and classical computation that allows one to obtain increasingly accurate solutions by leveraging additional measurements and classical resources. In conclusion, we demonstrate numerically on a sample electronic system that this method both allows for the accurate determination of excited electronic states as well as reduces the impact of decoherence, without using any additional quantum coherence time or formal error-correction codes.

- Authors:

- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Division
- Univ. of California, Berkeley, CA (United States). Quantum Nanoelectronics Lab., Dept. of Physics

- Publication Date:

- Research Org.:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)

- OSTI Identifier:
- 1393218

- DOE Contract Number:
- AC02-05CH11231

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review A; Journal Volume: 95; Journal Issue: 4

- Country of Publication:
- United States

- Language:
- English

### Citation Formats

```
McClean, Jarrod R., Kimchi-Schwartz, Mollie E., Carter, Jonathan, and de Jong, Wibe A.
```*Hybrid quantum-classical hierarchy for mitigation of decoherence and determination of excited states*. United States: N. p., 2017.
Web. doi:10.1103/PhysRevA.95.042308.

```
McClean, Jarrod R., Kimchi-Schwartz, Mollie E., Carter, Jonathan, & de Jong, Wibe A.
```*Hybrid quantum-classical hierarchy for mitigation of decoherence and determination of excited states*. United States. doi:10.1103/PhysRevA.95.042308.

```
McClean, Jarrod R., Kimchi-Schwartz, Mollie E., Carter, Jonathan, and de Jong, Wibe A. Thu .
"Hybrid quantum-classical hierarchy for mitigation of decoherence and determination of excited states". United States.
doi:10.1103/PhysRevA.95.042308.
```

```
@article{osti_1393218,
```

title = {Hybrid quantum-classical hierarchy for mitigation of decoherence and determination of excited states},

author = {McClean, Jarrod R. and Kimchi-Schwartz, Mollie E. and Carter, Jonathan and de Jong, Wibe A.},

abstractNote = {Using quantum devices supported by classical computational resources is a promising approach to quantum-enabled computation. One powerful example of such a hybrid quantum-classical approach optimized for classically intractable eigenvalue problems is the variational quantum eigensolver, built to utilize quantum resources for the solution of eigenvalue problems and optimizations with minimal coherence time requirements by leveraging classical computational resources. These algorithms have been placed as leaders among the candidates for the first to achieve supremacy over classical computation. Here, we provide evidence for the conjecture that variational approaches can automatically suppress even nonsystematic decoherence errors by introducing an exactly solvable channel model of variational state preparation. Moreover, we develop a more general hierarchy of measurement and classical computation that allows one to obtain increasingly accurate solutions by leveraging additional measurements and classical resources. In conclusion, we demonstrate numerically on a sample electronic system that this method both allows for the accurate determination of excited electronic states as well as reduces the impact of decoherence, without using any additional quantum coherence time or formal error-correction codes.},

doi = {10.1103/PhysRevA.95.042308},

journal = {Physical Review A},

number = 4,

volume = 95,

place = {United States},

year = {Thu Apr 06 00:00:00 EDT 2017},

month = {Thu Apr 06 00:00:00 EDT 2017}

}