# Optimizing adiabatic quantum program compilation using a graph-theoretic framework

@article{Goodrich2018OptimizingAQ, title={Optimizing adiabatic quantum program compilation using a graph-theoretic framework}, author={Timothy Goodrich and Blair D. Sullivan and T. Humble}, journal={Quantum Information Processing}, year={2018}, volume={17}, pages={1-26} }

Adiabatic quantum computing has evolved in recent years from a theoretical field into an immensely practical area, a change partially sparked by D-Wave System’s quantum annealing hardware. These multimillion-dollar quantum annealers offer the potential to solve optimization problems millions of times faster than classical heuristics, prompting researchers at Google, NASA and Lockheed Martin to study how these computers can be applied to complex real-world problems such as NASA rover missions…

## 33 Citations

### Graph Minor Embedding for Adiabatic Quantum Computing

- Computer Science
- 2021

Extensions to two papers are presented, which implements an existing simulated annealing algorithm with an improved guiding pattern and shifting rule and extends an integer programming formulation to allow embedding on Chimera graphs with faulty qubits to show marked improvement in embeddability.

### Integer Programming Techniques for Minor-Embedding in Quantum Annealers

- Computer ScienceCPAIOR
- 2020

The proposed integer programming techniques for solving the minor-embedding problem are able to detect instance infeasibility and provide bounds on solution quality, capabilities not offered by currently employed heuristic methods.

### Efficiently embedding QUBO problems on adiabatic quantum computers

- Computer ScienceQuantum Inf. Process.
- 2019

This work proposes an efficient embedding algorithm, that lets us embed QUBO problems fast, uses less qubits and gets the objective function value close to the global minimum value, and compares the performance of the algorithm to that of D-Wave’s embedding algorithms.

### Template-based Minor Embedding for Adiabatic Quantum Optimization

- Computer Science, MathematicsINFORMS J. Comput.
- 2022

This work shows that integer linear programming can be successfully used as a preprocessing step for adiabatic quantum optimization by determining how a quadratic unconstrained binary optimization problem can be solved by a quantum annealer in which the qubits are coupled as in a Chimera graph.

### Embedding Equality Constraints of Optimization Problems into a Quantum Annealer

- Computer ScienceAlgorithms
- 2019

This paper proposes an alternative approach for implementing constraints based on a combinatorial design and solving mixed-integer linear programming (MILP) problems in order to find better embeddings of constraints of the type ∑ x i = k for binary variables x i.

### Mapping graph coloring to quantum annealing

- Computer ScienceQuantum Mach. Intell.
- 2020

This work introduces the mapping of a graph coloring problem based on pseudo-Boolean constraints to a working graph of the D-Wave Systems Inc. graph using the SATyrus approach to transform this set of constraints to an energy minimization problem.

### Practical Graph Bipartization with Applications in Near-Term Quantum Computing

- Computer ScienceArXiv
- 2018

A preprocessing suite of fast input reduction routines from the odd cycle transversal and vertex cover literature is assembled, allowing the slower branching algorithms to be compared on identically-preprocessed data.

### Quantum annealing: next-generation computation and how to implement it when information is missing

- Computer Science
- 2018

This work proposes a method to estimate the unknown parameters in the Ising Hamiltonian using compressed sensing and analyzes the theoretical limitations of the proposed method by employing the replica method, which is a sophisticated tool in statistical mechanics.

### Graph Partitioning using Quantum Annealing on the D-Wave System

- Computer ScienceArXiv
- 2017

Results for graph partitioning using quantum and hybrid classical-quantum approaches are shown to be comparable to current "state of the art" methods and sometimes better.

### EQUAL: Improving the Fidelity of Quantum Annealers by Injecting Controlled Perturbations

- Computer Science2022 IEEE International Conference on Quantum Computing and Engineering (QCE)
- 2022

Equal (Ensemble QUantum AnneaLing) generates an ensemble of QMIs by adding controlled perturbations to the program QMI, which steers the program away from encountering the same bias during all trials and thus, improves the quality of solutions.

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