Quantum Information and Algorithm

To utilize the full power of quantum computer, properly designed quantum algorithm is necessary. For example, Shor's algorithm can run on a classical computer as well, but it turns out to be very inefficient. Also classically efficient algorithms can be run on a quantum computer, but the performance won't be enhanced at all. Therefore it is critical to develop algorithms which are tailored for quantum circuits. Our research group is interested in various problems related to quantum algorithms.

Quantum machine learning

Of various approaches to utilize quantum computers, one of the most promising is using them in machine learning tasks. One of such studies involves usage of parametrized quantum circuits as a part of neural networks to leverage the expressive power or even to express quantum states that are hard to represent with classical computers. With the help of quantum algorithms such as variational quantum eigensolvers, we seek to find machine learning tasks that are suitable for quantum computers and show that quantum computers can solve these problems faster or more accurately than their counterparts.

Cryptanalysis for PQC using quantum computer

Post-Quantum Cryptography (PQC) research is being conducted to replace cryptographic schemes like RSA or ECDSA, which are known to be vulnerable to quantum computers. The security of these schemes is determined by computationally difficult problems. For example, since the factorization problem that underpins RSA is easily solvable with quantum computers, PQC aims to create new cryptographic systems based on problems that are considered difficult to solve even with quantum computers. Notable examples include CRYSTALS-Kyber and CRYSTALS-Dilithium, which utilize Learning with Errors (LWE), a problem based on lattices. One of our research topics is to discover and analyze quantum algorithms capable of solving these computationally difficult problems.

Classical simulation of quantum computer

The classical simulation of a quantum computer is a field of research that focuses on efficiently simulating quantum computer operations using classical computers, utilizing methods such as Matrix Product State (MPS) representation and Stabilizer Simulation. In our research lab, we are working on improving existing algorithms and proposing new ones to compute the expectation value of the operators for quantum states.