Optimizing adiabatic quantum program compilation using a graph-theoretic framework

  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},
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… 

Graph Minor Embedding for Adiabatic Quantum Computing

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

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

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

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

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

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

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

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

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

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.



An integrated programming and development environment for adiabatic quantum optimization

An integrated programming and development environment for AQO called Jade Adiabatic Development Environment (JADE) is presented that provides control over all the steps taken during program synthesis and its potential use for benchmarking AQO programs by the quantum computer science community is discussed.

Adiabatic quantum programming: minor embedding with hard faults

Algorithms for embedding arbitrary instances of the adiabatic quantum optimization algorithm into a square lattice of specialized unit cells are presented and are shown to be more resilient to faulty fabrics than naive embedding approaches.

Minor-embedding in adiabatic quantum computation: I. The parameter setting problem

  • V. Choi
  • Computer Science, Physics
    Quantum Inf. Process.
  • 2008
The embedded Ising Hamiltonian for solving the maximum independent set (MIS) problem via adiabatic quantum computation (AQC) using an Ising spin-1/2 system is demonstrated.

What is the Computational Value of Finite Range Tunneling

It is demonstrated how finite range tunneling can provide considerable computational advantage over classical processors for a crafted problem designed to have tall and narrow energy barriers separating local minima, the D-Wave 2X quantum annealer achieves significant runtime advantages relative to Simulated Annealing.

Minor-embedding in adiabatic quantum computation: II. Minor-universal graph design

  • V. Choi
  • Mathematics, Computer Science
    Quantum Inf. Process.
  • 2011
The intertwined adiabatic quantum architecture design problem, which is to construct a hardware graph U that satisfies all known physical constraints and, at the same time, permits an efficient minor-embedding algorithm, is described.

Quantum Annealing amid Local Ruggedness and Global Frustration

A recent Google study [Phys. Rev. X, 6:031015 (2016)] compared a D-Wave 2X quantum processing unit (QPU) to two classical Monte Carlo algorithms: simulated annealing (SA) and quantum Monte Carlo

Image recognition with an adiabatic quantum computer I. Mapping to quadratic unconstrained binary optimization

This work describes how to formulate image recognition, which is a canonical NP-hard AI problem, as a Quadratic Unconstrained Binary Optimization (QUBO) problem, which corresponds to the input format required for D-Wave superconducting adiabatic quantum computing (AQC) processors.

High-Performance Computing with Quantum Processing Units

This work identifies two integration pathways that are differentiated by infrastructure constraints on the QPU and the use cases expected for the HPC system, and finds that the performance of both approaches is likely to depend on the quantum interconnect that serves to entangle multiple QPUs.

Fast clique minor generation in Chimera qubit connectivity graphs

A combinatorial class of native clique minors in Chimera graphs with vertex images of uniform, near minimal size are defined and a polynomial-time algorithm is provided that finds a maximumnative clique minor in a given induced subgraph of a Chimera graph.

Ollivier-Ricci curvature and fast approximation to tree-width in embeddability of QUBO problems

  • Chi WangE. JonckheereT. Brun
  • Computer Science, Mathematics
    2014 6th International Symposium on Communications, Control and Signal Processing (ISCCSP)
  • 2014
A novel, fast approximation to tree-width based on the differential geometric concept of Ollivier-Ricci curvature is proposed which could significantly reduce the overall complexity of determining whether a QUBO problem is solvable on the D-Wave architecture.