# Applying the Quantum Alternating Operator Ansatz to the Graph Matching Problem

@article{Chatterjee2020ApplyingTQ, title={Applying the Quantum Alternating Operator Ansatz to the Graph Matching Problem}, author={Sagnik Chatterjee and Debajyoti Bera}, journal={ArXiv}, year={2020}, volume={abs/2011.11918} }

The Quantum Alternating Operator Ansatz (QAOA+) framework has recently gained attention due to its ability to solve discrete optimization problems on noisy intermediate-scale quantum (NISQ) devices in a manner that is amenable to derivation of worst-case guarantees. We design a technique in this framework to tackle a few problems over maximal matchings in graphs. Even though maximum matching is polynomial-time solvable, most counting and sampling versions are #P-hard.
We design a few…

## References

SHOWING 1-10 OF 11 REFERENCES

Quantum Supremacy through the Quantum Approximate Optimization Algorithm

- Computer Science
- 2016

It is argued that beyond its possible computational value the QAOA can exhibit a form of Quantum Supremacy in that, based on reasonable complexity theoretic assumptions, the output distribution of even the lowest depth version cannot be efficiently simulated on any classical device.

From the Quantum Approximate Optimization Algorithm to a Quantum Alternating Operator Ansatz

- PhysicsAlgorithms
- 2019

The essence of this extension, the quantum alternating operator ansatz, is the consideration of general parameterized families of unitaries rather than only those corresponding to the time evolution under a fixed local Hamiltonian for a time specified by the parameter.

A Quantum Approximate Optimization Algorithm

- Computer Science, Mathematics
- 2014

A quantum algorithm that produces approximate solutions for combinatorial optimization problems that depends on a positive integer p and the quality of the approximation improves as p is increased, and is studied as applied to MaxCut on regular graphs.

A Quantum Approximate Optimization Algorithm Applied to a Bounded Occurrence Constraint Problem

- Mathematics, Computer Science
- 2014

This paper applies the recent Quantum Approximate Optimization Algorithm to the combinatorial problem of bounded occurrence Max E3LIN2 and shows that the level one QAOA will efficiently produce a string that satisfies $\left(\frac{1}{2} + 1}{101 D^{1/2}\, l n\, D}\right)$ times the number of equations.

On the Representation of Boolean and Real Functions as Hamiltonians for Quantum Computing

- Computer ScienceACM Transactions on Quantum Computing
- 2021

A goal of this work is to provide a design toolkit for quantum optimization which may be utilized by experts and practitioners alike in the construction and analysis of new quantum algorithms, and at the same time to provided a unified framework for the various constructions appearing in the literature.

Quantum Algorithms for Matching and Network Flows

- Computer Science, MathematicsSTACS
- 2006

We present quantum algorithms for some graph problems: finding a maximal bipartite matching in time $O(n\sqrt{m}logn)$, finding a maximal non-bipartite matching in time $O(n^2(\sqrt{m/n}+log n)log…

Quantum Algorithms for Scientific Computing and Approximate Optimization

- Computer Science, Physics
- 2018

The performance of the quantum approximate optimization algorithm (QAOA) is studied, and a generalization of QAOA is shown, particularly suitable for constrained optimization problems and low-resource implementations on near-term quantum devices.

Three qubits can be entangled in two inequivalent ways

- Physics
- 2000

Invertible local transformations of a multipartite system are used to define equivalence classes in the set of entangled states. This classification concerns the entanglement properties of a single…

Quantum computational supremacy

- Computer Science, PhysicsNature
- 2017

This work presents the leading proposals to achieve quantum supremacy, and discusses how to reliably compare the power of a classical computer to thePower of a quantum computer.

The Complexity of Enumeration and Reliability Problems

- Mathematics, Computer ScienceSIAM J. Comput.
- 1979

For a large number of natural counting problems for which there was no previous indication of intractability, that they belong to the class of computationally eqivalent counting problems that are at least as difficult as the NP-complete problems.