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Approaches to Simultaneously Solving Variational Quantum Eigensolver Problems

Adam Hutchings, Eric Yarnot, Xinpeng Li, Qiang Guan, Ning Xie, Shuai Xu, Vipin Chaudhary

Abstract

The variational quantum eigensolver (VQE), a type of variational quantum algorithm, is a hybrid quantum-classical algorithm to find the lowest-energy eigenstate of a particular Hamiltonian. We investigate ways to optimize the VQE solving process on multiple instances of the same problem, by observing the process on one instance of the problem to inform initialization for other processes. We aim to take advantage of the VQE solution process to obtain useful information while disregarding information which we can predict to not be very useful. In particular, we find that the solution process produces lots of data with very little new information. Therefore, we can safely disregard much of this repetitive information with little effect on the outcome of the solution process.

Approaches to Simultaneously Solving Variational Quantum Eigensolver Problems

Abstract

The variational quantum eigensolver (VQE), a type of variational quantum algorithm, is a hybrid quantum-classical algorithm to find the lowest-energy eigenstate of a particular Hamiltonian. We investigate ways to optimize the VQE solving process on multiple instances of the same problem, by observing the process on one instance of the problem to inform initialization for other processes. We aim to take advantage of the VQE solution process to obtain useful information while disregarding information which we can predict to not be very useful. In particular, we find that the solution process produces lots of data with very little new information. Therefore, we can safely disregard much of this repetitive information with little effect on the outcome of the solution process.

Paper Structure

This paper contains 8 sections, 2 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Approaches to Simultaneous Solving
  3. The MaxCut Problem
  4. Observing Points on Target Graphs
  5. Three Approaches
  6. Experimental Setup
  7. Experimental Results
  8. Conclusion

Figures (5)

  • Figure 1: The sum total of how much parameters change between iterations, with some given metric, to illustrate how the VQE process tends to work on a real problem. Clearly, the parameters barely change at all in the later stages of the solution process, so the points are extremely close together in the state space.
  • Figure 2: Results for our three strategies: considering all points in the seed graph, considering only half of the points, and considering none of the points. This is the run on 5-node graphs, with a TwoLocal circuit with five layers.
  • Figure 3: Results for a TwoLocal circuit with 2 layers, on 6-node graphs.
  • Figure 4: Results for a TwoLocal circuit with 3 layers, on 6-node graphs.
  • Figure 5: Results for a TwoLocal circuit with 3 layers, on 7-node graphs.