# The theory of variational hybrid quantum-classical algorithms

@inproceedings{JarrodRMcClean2016TheTO, title={The theory of variational hybrid quantum-classical algorithms}, author={JarrodRMcClean and JonathanRomero and RyanBabbush and andAl{\'a}nAspuru-Guzik}, year={2016} }

Many quantum algorithms have daunting resource requirements when compared to what is available today. To address this discrepancy, a quantum-classical hybrid optimization scheme known as ‘ the quantum variational eigensolver ’ was developed ( Peruzzo et al 2014 Nat. Commun. 5 4213 ) with the philosophy that even minimal quantum resources could be made useful when used in conjunction with classical routines. In this work we extend the general theory of this algorithm and suggest algorithmic…

## 707 Citations

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## References

SHOWING 1-10 OF 12 REFERENCES

### 2014Molecular Electronic-Structure Theory (NewYork:Wiley

- New J. Phys
- 2016

### 2014Molecular Electronic-Structure Theory (NewYork:Wiley) 21

- New J. Phys
- 2016

### andWinograd T 1999The PageRankCitation Ranking: BringingOrder to theWeb (http://ilpubs.stanford

- 1999

### andWright S 2006Numerical Optimization (Berlin: Springer

- 2006

### HastingsMB andTroyerM

- Phys . Rev . A
- 2014

### 2009Many—BodyMethods in Chemistry and Physics (Cambridge: CambridgeUniversity Press (CUP)

- 2009

### 2014Advances in Chemical Physics, Quantum Information andComputation for Chemistry vol

- 2014

### GreenbaumD,Mostame S andAspuru-Guzik A 2014New

- J. Phys
- 2014

### andPittner J (ed) 2010Recent Progress in Coupled ClusterMethods (Berlin: Springer

- 2010

### User's Guide for TOMLAB

- 2015