Randomized Linear Algebra with Random Quantum Circuits

Random quantum states are different from classical random states. Simply, random quantum states are column vectors of a random unitary matrix. Sampling of random unitary matrices is related to the Haar measure on a group, random Euler rotations, random matrix theory, quantum chaos, laser speckles, etc.  A quantum computer can generate random states using random quantum circuits. In 2019 Google claimed the quantum supremacy of random circuit sampling with 53 superconducting qubits. Google's Sycamore quantum processor sampled million strings of 53 bits in 200 seconds while it was estimated that Summit at Oak Ridge National Laboratory, the most powerful supercomputer at that time, was expected to take 10,000 years.

My research interests on random quantum circuits are as follows. 

• How to generate random quantum states.

• How to characterize random quantum states.

• How to prove quantum computers perform well random circuit sampling.

• Apply random quantum states to randomized linear algebra.

Quantum Machine Learning

Artificial Intelligence/Machine learning is transforming the world. For example, Google AlphaGo defeated a Go world champion, and Google Alpha Fold won the protein folding competition, the CASP 14 competition. Recently, Chat GPT is very successful in natural language processing. The power of quantum computers may accelerate AI/Machine learning. 

I'm interested in following topics  in connection with quantum machine learning.

• Restricted Boltzmann machines

• Diffusion models

• Quantum advantages in quantum machine learning

Quantum Simulation

Quantum teleportation is a quantum mechanical way of transferring quantum information via an entangled quantum channel. As shown in Fig. 4, I studied how noise affects the fidelity of quantum teleportation (PRA 66 022316, (2002)). Right panel in Fig. 4 shows the average fidelity decays as a function of the strength of noise for different types of noise sources. Quantum teleportation with the W state among three parties was proposed. I also investigated how inaccurate gate pulses of superconducting charge qubits affect the fidelity of the quantum gate. Also, I proposed a quantum computational method to calculate the ground-state energy and expectation values using Hellman-Feynman theorem and adiabatic quantum computing. Adiabatic quantum computing is one of quantum computational models and based on the quantum adiabatic theorem. If an initial Hamiltonian is slowly changed into a target Hamiltonian, then an input state is changed into a target state.