A current quantum of a reality check for optimization

A quantum computer operates on the principles of quantum mechanics with the computational states being qubits (or qudits), which, unlike classical bits, can exist in multiple states simultaneously (superposition), can be interlinked across distances (entanglement), and interact in a special constructive or destructive way (interference). This allows quantum computers to perform some computational tasks, with a dramatic increase in computational power. The number of qubits indicates a quantum computer's problem size that can be solved, and with it its potential capability. Quantum computing promises to revolutionize business use cases, particularly in fields requiring complex calculations like in optimization or AI, by the potential of solving problems infeasible for classical computers.

First, what does faster or powerful mean? Problems are solved with algorithms. A faster or more powerful algorithm solves a problem with fewer resources than another. Such a resource usually is how many queries or steps an algorithm needs to solve the problem. Each query or step within the algorithm takes time; thus, one says, " This algorithm is powerful; it finds the solution to a problem faster." A quantum computer is thus more powerful and finds a solution much faster if it can solve one problem by executing a quantum algorithm requiring fewer queries or steps to find a solution than its alternative running on a classical computer. This is possible due to the ability of Quantum computers to exploit quantum phenomena within their algorithm steps (or queries) that classical computers can't access because these are trapped within their classical worlds. Three such vital quantum phenomena are superposition, interference, and entanglement. These allow a quantum computer to do more in fewer steps and thereby solve a problem faster. The extent of the performance difference depends on the specific problem instance and can range from none to an exponential advantage. Therefore, it is crucial to have both a classical and a quantum computing solution.

Mostly no and some yes, depending on the context. "Quantum advantage" refers to the point where quantum computers can solve certain problems faster or more efficiently than any current classical computer. Some quantum computers have shown promising results in specific types of problems, suggesting they are approaching or have reached quantum advantage in those areas (e.g. boson sampling, Google’s supremacy experiment in 2019). However, this achievement is specific to a particular type of problem that doesn't have practical applications yet, and as of this moment (January 2024), it is still a subject of ongoing research and debate if quantum advantage or supremacy has been reached in a practical application (e.g. IBM’s utility experiment). However, since the superiority of quantum computers for practical applications has been proven on the theoretical side (e.g., Shor's Algorithm, Quantum Fourier Transformation, Grover's Algorithm) and developments in practical implementation are advancing rapidly, it is crucial for certain areas to be Quantum-Ready. To do this and always provide the best available solution, we choose a hybrid quantum-classical approach, as in our HybridSolver.

The applications of quantum computers are diverse. Quantum computers are well-suited for solving complex problems currently challenging or impractical for classical computers. However, they are not a "magic box" that solves all of these computational problems. For the different application problems, some are more suited to be solved via quantum computing than others. These application problems include cryptography, such as breaking encryption algorithms like RSA; solving large-scale optimization problems found in logistics, finance, and manufacturing (e.g., our optimization cases); simulating molecular structures and reactions for drug discovery and materials science; and certain types of algorithms in artificial intelligence and machine learning. Since particularly in the short term not all quantum approaches will surpass classical ones, and some algorithms will continue to be more sensibly computed with classical computers, it is crucial to consider and integrate both. Only if you can address both the quantum and the classical algorithms, can one provide a solution that delivers a genuinely optimal solution and advantage to an application problem.

At Quantagonia, we take a hybrid quantum-classical approach, specifically in optimization solutions. This distinctly differs from so-called quantum-inspired solutions, i.e., quantum solutions executed on classical computers. Although these are interesting for the development of algorithms, they offer no practical quantum advantage as they do not utilize any quantum resources (simply put: 'Where no quantum hardware is used, there is no quantum advantage'). In our hybrid quantum-classical approach, we develop and implement both pure quantum and pure classical algorithms, which we then integrate and interlink. This allows them to enhance and benefit from each other. Thus, we can provide real value on both the classical and quantum fronts, dynamically adjusting to the algorithm and hardware type, and ensuring the true optimal solution to the application problem at hand.