Along with the development of quantum theory, people have asked whether we can utilize quantum principles for practical purposes. The discovery of new technological advances in a wide range of fields, including communication, cryptography, computation, and sensing tasks, has opened a new research area, quantum information science. In particular, quantum computing lies at the core of such advances as it opens a new possibility to solve complex problems that even the fastest classical computers cannot simulate. The major issues regarding quantum computing are to find the most efficient design of a quantum circuit to protect quantum information from a noisy environment and to fully understand where the computational power of quantum computers comes from.
In this talk, we review the underlying principles of quantum computation and its unique feature to correct errors using entanglement. While the stabilizer formalism provides a powerful toolkit to detect and correct errors in various types of quantum systems, uncorrectable errors can be accumulated throughout a quantum circuit. We show that the fundamental limitation of quantum errorcorrection can be formulated by the dissipated amount of quantum information throughout a quantum circuit. Furthermore, we construct a universal recovery map to recover quantum information close to the optimal rate. This approach of approximate quantum errorcorrection opens a new possibility to lower the threshold value required for faulttolerant quantum computation, beyond the stabilizer formalism. We also introduce a new viewpoint to understand the origin of quantum computational advantages by characterizing classical simulabilty of a quantum circuit based on the negativity in quasiprobability distribution.
