• Corpus ID: 41414357

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… 

Figures from this paper

Variational Quantum Information Processing

This dissertation presents the application of the variational quantum computing approach to problems in quantum simulation, quantum state preparation, quantum error-correction, and generative modeling, and establishes practical guidelines to implement these methods on near-term quantum computers.

Error Analysis of the Variational Quantum Eigensolver Algorithm

It is shown through explicit simulation that the VQE algorithm effectively collapses already when single errors occur during a quantum processing call, and the significant implications are discussed in the context of being able to run any variational type algorithm without resource expensive error correction protocols.

Variational quantum state diagonalization

Variational hybrid quantum-classical algorithms are promising candidates for near-term implementation on quantum computers. In these algorithms, a quantum computer evaluates the cost of a gate

Resource-efficient encoding algorithm for variational bosonic quantum simulations

This work presents a resource-efficient quantum algorithm for bosonic ground and excited state computations using the Variational Quantum Eigensolver algorithm with the Unitary Coupled Cluster ansatz and proves to increase accuracy with a simultaneous reduction of required quantum resources compared to current approaches.

Surviving The Barren Plateau in Variational Quantum Circuits with Bayesian Learning Initialization

The fast-and-slow algorithm is introduced, which uses Bayesian Learning to identify a promising region in parameter space and is used to initialize a fast local optimizer to find the global optimum point efficiently.

Single-component gradient rules for variational quantum algorithms

This work provides a comprehensive picture of the family of gradient rules that vary parameters of quantum gates individually, and proposes a generalized PSR that expresses all members of the aforementioned family as special cases, and introduces a novel perspective for approaching new gradient rules.

Hybrid quantum variational algorithm for simulating open quantum systems with near-term devices

An HQC algorithm is developed using an efficient variational optimization approach to simulate open system dynamics under the Noisy-Intermediate Scale Quantum computer using the time-dependent variational principle and McLachlan TDVP.

Algorithm for initializing a generalized fermionic Gaussian state on a quantum computer

We present explicit expressions for the central piece of a variational method developed by Shi et al (2018 Ann. Phys. 390 245) which extends variational wave functions that are efficiently computable

Improved variational quantum eigensolver via quasi-dynamical evolution

This work proposes and extensively test a quantum annealing inspired heuristic that supplements VQE, and can be expected to help accurate estimations of the ground state energies beyond 50 qubits when the complete state vector can be stored on a classical computer, thus enabling quantum advantage.

Optimization of Quantum Algorithm Protocols without Barren Plateaus

This work presents an approach to quantum algorithm optimization that is based on trainable Fourier coefficients of Hamiltonian system parameters and proposes the ansatz as a viable parametrization candidate for near-term quantum machine learning.
...

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