Optimizing Quantum Annealers for Improved Accuracy

The development of quantum technology has led to the emergence of quantum machines, such as the D-Wave quantum annealer (D-Wave QA), which implements quantum annealing in the parameterized Hamiltonian of a transverse-field Ising model. While the DWave QA has rapidly increased its qubit capacity, approaching computational speed comparable to classical digital machines, the qubits are designed on a Pegasus graph that is different from the structure of combinatorial optimization problems. This requires embedding with chains connected by ferromagnetic coupling, which can reduce the accuracy of quantum annealing measurements.

The determination of optimal chain coupling is crucial for improving the accuracy of QA measurements. This paper presents an algorithm for determining the optimal coupling strength that maximizes the possible correct rate of QA measurements. The extracted optimal coupling has been shown to be much better than the default coupling in QA measurements of various parameters of frustrated and fully connected combinatorial optimization problems.

The open code is available at httpsgithubcomHunpyoLeeOptimizeChainStrength, providing a comprehensive framework for determining optimal chain coupling using the algorithm presented in this paper.

Can Quantum Annealers Be Optimized?

In recent years, the development of quantum technology has led to the emergence of quantum machines. One such machine is the D-Wave quantum annealer (DWave QA), which is an example of a quantum machine that implements quantum annealing in the parameterized Hamiltonian of a transverse-field Ising model containing binary superconducting qubits. The primary advantage of this architecture is that qubits can be added much easier than gate-type quantum computers, while maintaining the accuracy of results due to short quantum coherence time.

The DWave QA has been rapidly increasing its qubit capacity, approaching computational speed comparable to classical digital machines. However, the qubits in a D-Wave QA are designed on a Pegasus graph that is different from the structure of a combinatorial optimization problem. This situation requires embedding with chains connected by ferromagnetic (FM) coupling Jc between the qubits. Weak and strong Jc values induce chain breaking and enforcement of chain energy, which reduce the accuracy of quantum annealing (QA) measurements respectively.

The Importance of Optimal Chain Coupling

In addition to the challenges posed by the Pegasus graph structure, the DWave Ocean package provides a default coupling Jdefault c that is not necessarily optimal for maximizing the possible correct rate of QA measurements. In fact, even though the default coupling is provided, it has been confirmed that it is not an optimal coupling Joptimal c that maximizes the possible correct rate of QA measurements.

The determination of optimal chain coupling is crucial for improving the accuracy of QA measurements. This paper presents an algorithm for determining Joptimal c with the maximum probability p for observing the possible lowest energy. The extracted Joptimal c has been shown to be much better than Jdefault c in QA measurements of various parameters of frustrated and fully connected combinatorial optimization problems.

Embedding in DWave Quantum Annealer

The embedding process involves connecting chains between qubits using FM coupling Jc. This process is necessary because the qubits in a D-Wave QA are designed on a Pegasus graph that is different from the structure of a combinatorial optimization problem. The weak and strong Jc values induce chain breaking and enforcement of chain energy, which reduce the accuracy of QA measurements respectively.

The embedding process requires careful consideration of the FM coupling strength between qubits. Weak and strong Jc values can induce chain breaking and enforcement of chain energy, which can reduce the accuracy of QA measurements respectively. The optimal FM coupling strength is crucial for maximizing the possible correct rate of QA measurements.

Determining Optimal Chain Coupling

The determination of optimal chain coupling is a critical step in improving the accuracy of QA measurements. This paper presents an algorithm for determining Joptimal c with the maximum probability p for observing the possible lowest energy. The extracted Joptimal c has been shown to be much better than Jdefault c in QA measurements of various parameters of frustrated and fully connected combinatorial optimization problems.

The algorithm involves embedding chains between qubits using FM coupling Jc, and then determining the optimal FM coupling strength that maximizes the possible correct rate of QA measurements. The extracted Joptimal c has been shown to be much better than Jdefault c in QA measurements of various parameters of frustrated and fully connected combinatorial optimization problems.

Open Code Availability

The open code is available at httpsgithubcomHunpyoLeeOptimizeChainStrength. This code provides a comprehensive framework for determining optimal chain coupling using the algorithm presented in this paper. The code can be used to improve the accuracy of QA measurements and to explore the properties of frustrated and fully connected combinatorial optimization problems.

Conclusion

In conclusion, the determination of optimal chain coupling is a critical step in improving the accuracy of QA measurements. This paper presents an algorithm for determining Joptimal c with the maximum probability p for observing the possible lowest energy. The extracted Joptimal c has been shown to be much better than Jdefault c in QA measurements of various parameters of frustrated and fully connected combinatorial optimization problems.

The open code is available at httpsgithubcomHunpyoLeeOptimizeChainStrength, providing a comprehensive framework for determining optimal chain coupling using the algorithm presented in this paper. The code can be used to improve the accuracy of QA measurements and to explore the properties of frustrated and fully connected combinatorial optimization problems.

Future Directions

Future directions include exploring the properties of frustrated and fully connected combinatorial optimization problems, and developing new algorithms for determining optimal chain coupling. Additionally, the development of new quantum annealing architectures that can be optimized using the algorithm presented in this paper is an exciting area of research.

The study of unconventional dynamics observed in real materials is a very interesting research topic as it is not easy to study using numerical simulation methods. Ca 3Co2O6 compound is an example with unconventional dynamics that has remained a puzzle.