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Quantum Annealing: Principles and Performance Analysis

This article discusses quantum annealing, its advantages, applications, and performance in real-world and industry-relevant applications.

Quantum Annealing, what is quantum annealing

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What is Quantum Annealing?

Quantum annealing is a quantum computing method used to identify the optimal/near-optimal solution of problems with a large number of solutions by exploiting the properties of quantum physics, such as quantum entanglement, superposition, and tunneling.

This method employs quantum physics to find the lowest energy state of a problem. Quantum annealing is a heuristic variational quantum algorithm, as the adiabaticity conditions are not fulfilled in this method. Thus, this approach can be employed to identify the ground state of Ising models, a common nondeterministic polynomial time (NP)-hard task.

Principle of Quantum Annealing

Each state is represented as an energy level in quantum annealers. These states are simulated in a short duration by exploiting the entanglement and superposition properties of qubits to obtain the lowest energy state. The lowest energy state provides the optimal/near-optimal solution.

Each qubit can affect the state of the other qubit, and each solution creates a new state with the quantum entanglement property. The quantum annealer determines the lowest energy level between these states. 

Quantum tunneling is another important property that facilitates the instantaneous transition between states by eliminating the need for electrons to climb the barrier during the transition between energy levels.

Studies have demonstrated that canonical NP-complete and NP-hard combinatorial optimization problems can be transformed into forms that are suitable for quantum annealers.

These problems can be modeled either as a quadratic unconstrained binary optimization (QUBO) problem using the {0, 1} basis and binary variables or in Ising form using a {−1, 1} basis and spin variables. However, problems in one form can be represented easily in the other form using a simple change of basis as both forms are equivalent.

Several steps must be implemented to solve real-world/industry-relevant problems using quantum annealing. For instance, the quantum algorithm workflow on a D-Wave quantum annealer includes QUBO formulation definition and graph representation, minor embedding, programming, initialization, annealing process, solution readout, and resampling.

QUBO is used as the standard input format for quantum annealers and is directly converted into a logical graph after definition. In the graph, every node represents a variable, and every edge represents the interaction term between a pair of variables.

The Ising model is solved during the annealing process. The system transitions from the initial Hamiltonian to the final Hamiltonian based on the predefined annealing functions to minimize energy.

The annealing process can also be integrated with a reverse annealing phase, which initializes the quantum annealer with a classical solution and identifies the state space around the local optimum.

After the annealing phase, the qubits remain in an eigenstate or superposition of eigenstate, where each eigenstate denotes a possible minimum of the final Hamiltonian. Subsequently, the individual qubit spin values are read out and externally stored, which represent a possible solution to the original problem.

Advantages of Quantum Annealing

Quantum annealing displays better performance compared to classical computational methods while solving specific optimization problems that are important for several industries, such as finance and healthcare.

The method is also inherently resilient against noise compared to the analog quantum and quantum gate model approaches. Additionally, quantum annealing will become available commercially before other quantum technologies.

Real-World Applications of Quantum Annealing

Quantum annealing can be used to solve real-world problems in different domains, specifically in the fields of machine learning, scheduling and logistics, mobility, optimization, healthcare, security, financial modeling, and quantum simulation for chemistry, physics, and biology.

In machine learning and computer science, the method can be used to detect statistical anomalies, recognize patterns and images, train neural networks, classify unstructured data, and diagnose circuit faults.

Similarly, quantum annealing can be used to create protein models and generate cancer drug therapies in healthcare. In financial modeling, quantum annealing can detect market instabilities and optimize portfolios, trading trajectories, and asset pricing and hedging.

Other potential applications of quantum annealing include the detection of computer viruses and network intrusion and the optimization of telecommunication networks, traffic flow, web advertising, and e-commerce item listing.

For instance, quantum annealing has been used to minimize the congestion in road segments on overlapping routes to minimize the travel time for a set of cars between individual destinations and sources.

The evaluated dataset was composed of 418 cars with three alternative travel routes generated for each car for traffic redistribution, which led to 1254 logical variables to represent the problem.

qbsolv, a hybrid quantum solver, was used to partition the problem into sub-problems, which were then executed on a D-Wave 2X system. The result demonstrated that qbsolv could effectively redistribute the traffic in a way that decreases the number of congested roads.

Performance Analysis

Inversion problems are one of the major computational challenges in science and industry. These numerical procedures determine the cause of an event from the measurements of its effects.

In a study recently published in the journal Frontiers in Physics, researchers applied a recursive quantum algorithm to a D-Wave quantum annealer to solve small-scale seismic inversion problems. They compared the results obtained from the quantum computer with the results obtained from a classical computer.

Both classical and quantum computers achieved similar levels of accuracy, which indicated the feasibility of using currently available quantum annealers to solve small-scale seismic inversion problems.

To summarize, quantum annealing can effectively address the small problem sizes in different application fields on actual hardware. Thus, more research is required to develop novel features, such as driver Hamiltonians and operators and additional qubit control, to fully exploit the potential of quantum annealing.

More from AZoQuantum: Quantum Tensor Networks: Foundations, Algorithms, and Applications

References and Further Reading

Souza, A. M., Martins, E. O., Roditi, I., Sá, N., Sarthour, R. S., Oliveira, I. S. (2022). An Application of Quantum Annealing Computing to Seismic Inversion. Frontiers in Physics, 9. https://doi.org/10.3389/fphy.2021.748285

Neukart, F., Compostella, G., Seidel, C., von Dollen, D., Yarkoni, S., & Parney, B. (2017). Traffic Flow Optimization Using a Quantum Annealer. Frontiers in ICT, 4. https://doi.org/10.3389/fict.2017.00029

Dilmegani, C. (2022). Quantum Annealing in 2023: Practical Quantum Computing [Online] Available at https://research.aimultiple.com/quantum-annealing/#why-does-it-matter-now (Accessed on 14 April 2023)

Yarkoni, S., Raponi, E., Bäck, T., Schmitt. (2022). Quantum Annealing for Industry Applications: Introduction and Review. Reports on Progress in Physics, 85. https://www.researchgate.net/publication/362918140_Quantum_Annealing_for_Industry_Applications_Introduction_and_Review

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Samudrapom Dam

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Samudrapom Dam

Samudrapom Dam is a freelance scientific and business writer based in Kolkata, India. He has been writing articles related to business and scientific topics for more than one and a half years. He has extensive experience in writing about advanced technologies, information technology, machinery, metals and metal products, clean technologies, finance and banking, automotive, household products, and the aerospace industry. He is passionate about the latest developments in advanced technologies, the ways these developments can be implemented in a real-world situation, and how these developments can positively impact common people.

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