Quantum computers were once talked about as futuristic technology, but in recent years, some of them have actually been produced and are in operation. Currently, there are still severe performance restrictions, but some companies have already started commercial operation of quantum computers.

【Quantum Annealing】

Quantum computers are roughly divided into "annealing method" and "gate method". While the gate method is expected to be used for more general purposes, the annealing method is positioned as a dedicated computer specialized for combinatorial optimization problems. Canada's D-Wave Systems Inc. was the first company to start commercial operation with an annealing-type quantum computer, and it can be said that the annealing method has a long way to go in terms of general development so far.

Annealing is "annealing", and in the original sense, it refers to the process of metal refining, etc., where the heated metal changes into something with different properties as it cools. Quantum annealing is a calculation method that searches for the minimum value of a given potential field by gradually cooling electrons that have been heated to a high energy state and converging the quantum state to a lower energy state. If you set the shape of this potential field according to the mathematical problem you want to solve, you can search for the minimum value with a quantum computer. Searching for the minimum value is like searching for the deepest valley on a map, and a normal computer cannot find the minimum value without exhaustively examining the entire potential field. Quantum annealing, on the other hand, enables highly parallel and efficient exploration due to quantum mechanical effects.

【Combinatorial optimization problem】

Since quantum operations are based on quantum mechanics, the problems that can be solved by quantum annealing are limited to those that conform to the properties of quantum mechanics. Specifically, it is a problem given in a form called QUBO (Quadratic Unconstrained Binary Optimization), which is a modification of the Ising model. QUBO is basically described by the following formula.

The table below explains the variables and coefficients in the above formula.

Applications of such combinatorial optimization problems include the traveling salesman problem that seeks the shortest distance of a selective route, and the knapsack that maximizes the value of cargo from items with different values and weights within the load capacity limit. problems, etc. However, in reality, real-world problems that can be described as QUBO are rare, and the number of qubits that can be handled simultaneously by current quantum computers is by no means large. Therefore, it can be said that the key to practical application of quantum annealing is how to reduce the problem to be solved into a feasible QUBO format.

[Application of quantum computer to 3D point cloud data analysis]

Our company, Tengun-label, is conducting original research and development using quantum computers in the field of computer vision, mainly in 3D point cloud data analysis. At present, quantum computers are still severely constrained in terms of performance, but they have great potential for further development in the future.

The figure shown below is a simple example of the registration of 3D point cloud data that we performed using quantum annealing. In the left figure, the data (red and blue) generated from the same chair model are placed at arbitrary positions and angles that are 3-dimensionally shifted, and this is the initial state. Alignment with the red point cloud data is performed by applying an appropriate affine transformation matrix to the coordinates of the blue point cloud data in the left figure. is defined under the condition that the sum of This condition is described as a QUBO problem, and the optimal solution is calculated using quantum annealing.

Chair registration represented by point cloud data. As an initial state (left figure), data of the same type are placed at different positions, and the result of alignment by quantum annealing (right figure) based on the condition of minimizing the distance between corresponding points.

[Conclusion]

This time, I explained the current state of quantum computers, especially the computation using quantum annealing. Finally, we introduced an example of quantum computer application to 3D point cloud data analysis, which is being researched by our company Tengun-label. It can be said that the application of quantum computers in the field of computer vision is still an unexplored area. In the analysis of 3D point cloud data, computational efficiency is often very poor due to recursive calculations such as parameter searches, and dramatic progress is expected with future quantum computer technology.

## Comments