Quantum computers carry out computations leveraging special characteristics of quantum mechanics, making it so they will be able to solve large-scale problems that are unsolvable with traditional computers. In quantum computers, information can be embedded in quantum states. Quantum computations are carried out by manipulating these states and measuring the resulting states to extract some information. By using these states, we can simultaneously express a space exponential to the number of qubits. For example, if we have 300 qubits, there are 2^300 possible states. This number is greater than the number of atoms in the entire universe. Using this special characteristic allows us to perform large-scale computations that existing computers could not. However, to retrieve all of the information embedded in a quantum state, we would need to make an exponentially large number of measurements, which would negate the advantages of quantum computations. To counter this, we need to develop smart algorithms that produce quantum states that allow us to retrieve the information we want with a small number of measurements.
It has been proven in theory that these algorithms are possible. For example, Shor’s algorithm can efficiently solve the integer factorization problem. With traditional computers, it is thought that finding prime factors of sufficiently large numbers is extremely difficult, and RSA encryption was created based on the difficulty of this problem. In this sense, implementing quantum computers would break RSA encryption, and public key cryptography will be in danger. Currently, fundamental quantum algorithms utilizing the superiority of quantum computers, such as physics simulations and linear algebra calculations, have been proposed. Based on these fundamentalalgorithms, solutions to issues directly connected to quantum mechanics, such as material design and drug development, and applications in areas such as machine learning and financial engineering have also been proposed. However, the number of tasks shown to be possible and more efficient with quantum computers than with traditional computers is still small, and the range of applications is limited. This is because there is only a limited variation of fundamental quantum algorithms, and they have different properties than traditional computer algorithms, so algorithms cannot be easily repurposed for other uses.
In our research of quantum algorithms, Mercari aims to build fundamental quantum algorithms with wide ranges of applications, such as mathematical programming problems and numerical solutions to nonlinear equations, and expand the possibilities of quantum computing.
In order for quantum computers to solve social issues, we must develop quantum computing architecture, not just quantum algorithms. In current quantum computers, errors occur during computations. As the circuit size and number of computational steps increase, the likelihood the computations will fail drastically increases as well. As such, algorithms that can reap the benefits of quantum computers using only small circuits and a small number of computational steps have been proposed. On the other hand, ideal quantum computers must be able to perform error correction. These computers will not have any limitations on the circuit size or number of steps, so they will be able to execute more advanced quantum algorithms, and demonstrate the full potential of quantum computers. In our research of quantum computing architecture, we are carrying out collaborative research with the National Institute of Advanced Industrial Science and Technology (AIST) to implement a “surface code”, which allows quantum computations to be performed while protecting data from errors using quantum error correcting codes.
In summary, Mercari aims to solve issues important to humanity by conducting research into fundamental quantum algorithms and the quantum computing architecture necessary to execute them.