Primary Use Cases
Quantum Annealing (QA) is a metaheuristic optimization algorithm that exploits the principles of quantum mechanics to solve complex optimization problems[1]. It is inspired by the process of annealing in metallurgy, where a metal is heated and then slowly cooled to remove defects and reach a low-energy crystalline state. Similarly, QA explores the solution space of an optimization problem by slowly evolving a quantum system from an initial state to a final state that encodes the optimal solution.
Problem Target
QA algorithms are particularly well-suited for solving combinatorial optimization problems, such as the Traveling Salesman Problem, the Max-Cut Problem, and the Quadratic Unconstrained Binary Optimization (QUBO) problem[2]. These problems are characterised by a large number of discrete variables and a complex energy landscape with many local minima, making them difficult to solve using classical optimization methods.
Quantum Approach The key idea behind QA is to map the optimization problem onto a physical system of interacting qubits, where the energy of the system corresponds to the cost function of the problem[3]. The system is initialised in a state of quantum superposition, where each qubit represents a possible solution to the problem. The system is then slowly evolved according to a time-dependent Hamiltonian, which gradually changes the strength of the interactions between the qubits and drives the system towards the ground state, which corresponds to the optimal solution[4].
Practical Applications
QA holds the promise of outperforming classical optimization algorithms in several key aspects. One notable advantage is its potential for faster convergence. By harnessing quantum tunnelling and quantum entanglement, QA can navigate the solution space more efficiently, potentially finding the optimal solution faster than classical methods, especially for problems with complex energy landscapes where classical algorithms might become trapped in local minima[5].
Another compelling advantage lies in its scalability potential. QA can potentially tackle larger and more intricate problems that overwhelm classical algorithms. This is due to the exponential nature of quantum state spaces, where a relatively small number of qubits can represent and manipulate exponentially large superpositions.
Furthermore, QA benefits from an inherent robustness to certain types of noise and errors, such as thermal fluctuations and control errors. This resilience stems from the adiabatic nature of the algorithm, making it well suited for near-term quantum hardware, which is often prone to such disturbances[6].
Implementation Challenges
Despite its promising potential, the practical implementation of QA faces several hurdles. One significant challenge lies in the limited connectivity between qubits in current quantum annealing hardware. This limitation can make mapping certain problems onto the hardware difficult, leading to additional overhead in problem encoding and a potential reduction in performance[7].
Another issue is the sensitivity of QA’s performance to various parameters, such as the annealing schedule, the initial and final Hamiltonians, and other settings. Determining the optimal parameter configuration for a specific problem can be a complex task, often requiring extensive empirical tuning and experimentation.
Furthermore, comparing QA with classical optimization algorithms is crucial for assessing its true potential. In some cases, classical methods like simulated annealing or tensor networks can perform as well as or even outperform it, particularly when dealing with small problem sizes or less complex energy landscapes. Therefore, rigorous benchmarking and comparison with classical approaches are essential for understanding the specific scenarios where QA can offer a quantum advantage[8].
Bottom Line
Quantum Annealing is a powerful metaheuristic optimization algorithm that uses the principles of quantum mechanics to solve complex combinatorial optimization problems. By mapping the problem onto a system of interacting qubits and slowly evolving the system towards the ground state, QA has the potential to provide faster convergence, better scalability, and robustness to noise compared to classical optimization methods.
QA has been extensively studied and applied to various optimization problems in fields such as machine learning, finance, logistics, and materials science. Experimental demonstrations have been performed on quantum annealing hardware, such as the D-Wave systems, as well as on gate-based quantum computers and quantum simulators.
Ongoing research in QA aims to develop more efficient and scalable algorithms, improve the mapping and encoding of problems, and benchmark the performance of it against classical methods, paving the way for the practical deployment in real-world applications.
Implementation Steps
Problem encoding
The optimization problem is mapped onto a QUBO or Ising Hamiltonian, which describes the energy of the quantum system as a function of the binary variables. The mapping involves defining the couplings between the qubits and the local fields acting on each qubit, based on the constraints and objectives of the problem.
Initialisation
The quantum system is initialised in a state of uniform superposition, where each qubit is in an equal superposition of the |0⟩ and |1⟩ states. This state represents a equal probability distribution over all possible solutions to the problem.
Annealing
The quantum system is slowly evolved according to a time-dependent Hamiltonian, which consists of two terms: a problem Hamiltonian that encodes the QUBO or Ising model, and a driver Hamiltonian that provides the quantum fluctuations needed to explore the solution space. The strength of the driver Hamiltonian is gradually decreased over time, while the strength of the problem Hamiltonian is increased, guiding the system towards the ground state.
Measurement
After the annealing process is complete, the quantum system is measured in the computational basis, collapsing the superposition into a classical state that represents a candidate solution to the problem. The measurement is repeated multiple times to obtain a statistical distribution of the solutions.
Post-processing
The candidate solutions are post-processed using classical optimization techniques, such as local search or simulated annealing, to further improve their quality and remove any invalid or suboptimal solutions.
References
Kadowaki, T., & Nishimori, H. (1998). Quantum annealing in the transverse Ising model. Physical Review E, 58(5), 5355.
Lucas, A. (2014). Ising formulations of many NP problems. Frontiers in Physics, 2, 5.
Farhi, E., Goldstone, J., Gutmann, S., & Sipser, M. (2000). Quantum computation by adiabatic evolution. arXiv preprint quant-ph/0001106
Denchev, V. S., Boixo, S., Isakov, S. V., Ding, N., Babbush, R., Smelyanskiy, V., … & Neven, H. (2016). What is the computational value of finite-range tunneling? Physical Review X, 6(3), 031015.
Dickson, N. G., Johnson, M. W., Amin, M. H., Harris, R., Altomare, F., Berkley, A. J., … & Rose, G. (2013). Thermally assisted quantum annealing of a 16-qubit problem. Nature Communications, 4(1), 1-6.
Choi, V. (2008). Minor-embedding in adiabatic quantum computation: I. The parameter setting problem. Quantum Information Processing, 7(5), 193-209.
Rønnow, T. F., Wang, Z., Job, J., Boixo, S., Isakov, S. V., Wecker, D., … & Troyer, M. (2014). Defining and detecting quantum speedup. Science, 345(6195), 420-424.
Related Case Studies
D-Wave, DENSO, and Toyota Tsusho Partnership for Traffic Flow Optimization Using Quantum Computing
D-Wave Systems partnered with DENSO Corporation and Toyota Tsusho Corporation to apply quantum computing technology to optimize traffic flow in Thailand. This collaboration demonstrated one of the first real-world applications of quantum annealing to solve complex urban mobility challenges, potentially reducing traffic congestion in cities worldwide.
D-Wave and Toyota tackle traffic flow optimization
D-Wave Systems partnered with Toyota and Denso to explore quantum annealing technology for optimizing traffic flow in smart cities.
Fujitsu-Coca-Cola Japan Quantum Computing Partnership for Supply Chain Optimization
Fujitsu and Coca-Cola Japan collaborated to leverage quantum computing technology for optimizing complex supply chain and logistics operations. This partnership focused on applying Fujitsu's quantum-inspired digital annealer technology to solve combinatorial optimization problems in beverage distribution networks.
D-Wave and Lockheed Martin Quantum Computing Partnership for Aerospace Optimization
D-Wave and Lockheed Martin formed a groundbreaking partnership in 2011, making Lockheed Martin the first commercial customer of D-Wave's quantum annealing systems. This collaboration focused on exploring quantum computing applications for complex aerospace optimization problems, software verification, and machine learning tasks critical to defense and aerospace operations.
Google-NASA Quantum Artificial Intelligence Laboratory Partnership
Google and NASA established the Quantum Artificial Intelligence Laboratory in 2013 to explore quantum computing applications for complex optimization and machine learning problems. This partnership has been instrumental in advancing quantum supremacy research and developing practical quantum algorithms for aerospace and artificial intelligence applications.
Quantinuum and Mitsui & Co. evaluate broad quantum utility
Quantinuum and Mitsui & Co. trading company explore quantum computing potential across a range of its portfolio of activities.
D-Wave and Airbus explore aerospace manufacturing
Applying quantum annealing to aerospace challenges, optimizing manufacturing, flight operations, and supply chain management.
IBM and Daimler (Mercedes-Benz) explore battery design
Daimler and IBM Quantum simulate chemistry for next-generation lithium-sulfur batteries, exploring quantum computing for materials discovery in the automotive industry.
QuEra Computing and Massachusetts Government Quantum Computing Partnership for Optimization and Public Services
QuEra Computing, a Boston-based quantum computing company specializing in neutral atom quantum computers, partnered with Massachusetts state government agencies to explore quantum computing applications in public sector optimization problems. This collaboration aims to leverage QuEra's analog quantum computing capabilities to address complex computational challenges in transportation planning, resource allocation, and public health optimization.
CQC and Crown Bioscience explore drug discovery
Exploring quantum computing for drug discovery and molecular simulation, demonstrating up to 100x speedup in specific molecular property calculations.
QC Ware and Roche explore biomedical image analysis
A collaboration to explore quantum neural networks for biomedical image analysis.
Qilimanjaro and BBVA explore financial portfolio optimisation
Using a quantum annealer for financial portfolio optimization, reducing the computation time for complex problems from days to minutes.
IBM and Daimler AG Strategic Partnership for Automotive Quantum Computing Applications
IBM Quantum and Daimler AG formed a strategic partnership to explore quantum computing applications in automotive manufacturing, materials science, and logistics optimization. The collaboration focuses on leveraging quantum algorithms to solve complex computational challenges in vehicle design, battery technology, and supply chain management.
IBM and Daimler Partnership: Advancing Automotive Innovation through Quantum Computing
IBM Quantum and Daimler AG partnered to explore quantum computing applications in automotive manufacturing, focusing on battery chemistry optimization, route optimization, and materials science. This collaboration represents one of the earliest and most comprehensive quantum computing partnerships in the automotive industry, demonstrating practical applications of quantum technology in solving complex industrial challenges.
LightSolver and Ansys Partnership: Laser-Based Quantum Computing for Engineering Simulation
LightSolver and Ansys formed a strategic partnership to integrate LightSolver's laser-based quantum computing platform with Ansys's engineering simulation software suite. This collaboration aims to accelerate complex computational fluid dynamics (CFD) and finite element analysis (FEA) calculations for industrial applications.
1QBit and Dow Chemical explore optimisation and risk analysis
Applying quantum computing for financial portfolio optimisation and risk analysis, improving investment decision-making.
D-Wave and DENSO Partnership: Quantum Computing for Automotive Manufacturing Optimization
D-Wave Systems and DENSO Corporation, a leading automotive components manufacturer, partnered to apply quantum annealing technology to complex optimization problems in automotive manufacturing and logistics. This collaboration aimed to leverage D-Wave's quantum computing systems to solve factory automation challenges, traffic flow optimization, and supply chain management problems that are computationally intractable for classical computers.
1QBit explore drug discovery with Accenture and Biogen
Accenture Labs and 1QBit work with Biogen to apply quantum computing to accelerate the research around drug discovery.
Google and Volkswagen advance traffic optimisation and battery research
Optimising urban traffic flow and simulating advanced battery materials using Google's quantum processors and algorithms.
Amazon AWS Braket and BMW explore automotive solutions
A partnership to run a series of quantum computing innovation challenges for automotive applications.
Amazon Web Services and BMW Group: Quantum Computing for Industrial Challenges
BMW Group partnered with Amazon Web Services (AWS) through Amazon Braket to explore quantum computing applications for optimizing manufacturing processes, supply chain logistics, and materials research. This collaboration leverages AWS's cloud-based quantum computing platform to address complex industrial challenges in automotive manufacturing and design.
D-Wave and Pattison Food Group Partnership: Quantum-Powered Supply Chain Optimization
D-Wave Systems partnered with Pattison Food Group, Canada's largest food and pharmacy retailer, to implement quantum annealing solutions for complex supply chain optimization challenges. This collaboration demonstrated practical quantum computing applications in retail logistics and inventory management.
Zapata Computing and Andretti Autosport: Quantum Computing for Formula E Race Strategy Optimization
Zapata Computing partnered with Andretti Autosport to apply quantum computing algorithms to optimize race strategy and vehicle performance in Formula E racing. The collaboration focused on leveraging quantum-inspired optimization techniques to analyze complex race scenarios, energy management strategies, and real-time decision-making processes that traditional computing methods struggled to handle efficiently.
SandboxAQ and Deloitte Strategic Alliance for Enterprise Quantum and AI Solutions
SandboxAQ and Deloitte formed a strategic alliance to accelerate enterprise adoption of quantum technologies and AI solutions across multiple industries. The partnership combines SandboxAQ's advanced quantum simulation and AI platforms with Deloitte's global consulting expertise to deliver transformative solutions for complex business challenges.
D-Wave and NEC partner for applications in Japan
A strategic partnership in Japan to deploy quantum annealing solutions for optimizing manufacturing, logistics, and financial services.
D-Wave and Pattison Food Group explore driver scheduling
D-Wave and Pattison Food Group explore the potential of quantum-powered workforce scheduling optimization.
Microsoft Azure Quantum and Ford: Advancing Automotive Manufacturing through Quantum Computing
Ford Motor Company partnered with Microsoft Azure Quantum to explore quantum computing applications in automotive manufacturing, focusing on traffic optimization and materials discovery. This collaboration aims to leverage quantum computing's potential to solve complex optimization problems that are computationally intensive for classical computers.
D-Wave and Save-On-Foods explore optimization
Using quantum annealing for optimizing complex supply chain logistics, including delivery routes and inventory management.
D-Wave and Volkswagen explore optimisation and scheduling
Applying quantum annealing to automotive optimization challenges, including urban traffic management and paint shop scheduling.
D-Wave and DB Schenker pursue logistics optimisation
Applying quantum annealing to complex logistics challenges, optimizing freight forwarding, warehouse management, and route planning.
1QBit and BMW explore automotive optimisation
1QBit and BMW applied quantum-inspired algorithms to optimise automotive manufacturing, logistics, and supply chain challenges.
Classiq and Sumitomo Corporation explore risk
Exploring quantum computing for financial risk management, achieving up to 95% compression of quantum circuits for Monte Carlo simulations.
Microsoft and Ford explore traffic flow optimisation
Microsoft Azure Quantum and Ford explore opportunities to improve traffic flow optimisation.
1QBit and NatWest explore financial portfolio optimisation
Explore quantum computing for financial portfolio optimisation and risk management, enhancing traditional modeling.