# Driver Hamiltonians for constrained optimization in quantum annealing

@article{Hen2016DriverHF, title={Driver Hamiltonians for constrained optimization in quantum annealing}, author={Itay Hen and Marcelo S. Sarandy}, journal={Physical Review A}, year={2016}, volume={93} }

One of the current major challenges surrounding the use of quantum annealers for solving practical optimization problems is their inability to encode even moderately sized problems---the main reason for this being the rigid layout of their quantum bits as well as their sparse connectivity. In particular, the implementation of constraints has become a major bottleneck in the embedding of practical problems, because the latter is typically achieved by adding harmful penalty terms to the problem…

#### 25 Citations

Constructing Driver Hamiltonians for Several Linear Constraints

- Computer ScienceArXiv
- 2020

A simple and intuitive algebraic framework for reasoning about the commutation of Hamiltonians with linear constraints is developed - one that allows us to classify the complexity of finding a driver Hamiltonian for an arbitrary set of constraints as NP-hard.

Breaking limitation of quantum annealer in solving optimization problems under constraints

- Computer Science, PhysicsScientific Reports
- 2020

The present study proposes an alternative approach to solve a large-scale optimization problem on the chimera graph via a well-known method in statistical mechanics called the Hubbard-Stratonovich transformation or its variants and can be used to deal with a fully connected Ising model without embedding on the Chimera graph.

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

- Physics, MathematicsAlgorithms
- 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.

Applying the Hubbard-Stratonovich Transformation to Solve Scheduling Problems Under Inequality Constraints With Quantum Annealing

- Frontiers in Physics
- 2021

Quantum annealing is a global optimization algorithm that uses the quantum tunneling effect to speed-up the search for an optimal solution. Its current hardware implementation relies on D-Wave’s…

Domain wall encoding of integer variables for quantum annealing and QAOA

- Mathematics
- 2019

In this paper I propose a new method of encoding integer variables into Ising model qubits for quantum optimization. The new method is based on the physics of domain walls in one dimensional Ising…

Domain wall encoding of discrete variables for quantum annealing and QAOA

- PhysicsQuantum Science and Technology
- 2019

In this paper I propose a new method of encoding discrete variables into Ising model qubits for quantum optimization. The new method is based on the physics of domain walls in one dimensional Ising…

Trotterized adiabatic quantum simulation and its application to a simple all-optical system

- Physics
- 2020

As first proposed for the adiabatic quantum information processing by Wu et al (2002 Phys. Rev. Lett. 89 057904), the Trotterization technique is a very useful tool for universal quantum computing,…

Quantum Approximate Optimization Algorithm Based Maximum Likelihood Detection

- Computer Science, MathematicsArXiv
- 2021

This paper considers the maximum likelihood (ML) detection problem of binary symbols transmitted over a multipleinput and multiple-output (MIMO) channel, where finding the optimal solution is exponentially hard using classical computers and demonstrates that the QAOA based ML detector is capable of approaching the performance of the classical ML detector.

Quantum Approximate Optimization with Hard and Soft Constraints

- Computer Science
- 2017

This work provides a framework for designing QAOA circuits for a variety of combinatorial optimization problems with both hard constraints that must be met and soft constraints whose violation the authors wish to minimize.

An Automatic Approach for Combinational Problems on a Hybrid Quantum Architecture

- Computer ScienceSPIN
- 2021

This paper proposes an optimization problem’s automatic hybird quantum framework (OpAQ) for solving user-specified problems on a hybrid computing architecture including both quantum and classical computing resources and shows that quantum solver can achieve almost the same optimal solutions with the classical.

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