Our research is mainly focused on hardware development of quantum computer and quantum repeater based on ion trap system and application of quantum algorithms and quantum protocols to real quantum system.

# Quantum Computer (양자 컴퓨터)

There are several different architectures for quantum computers, and most of them utilize the superposition property which allows quantum parallelism. The most famous quantum algorithm is Shor's algorithm which is expected to find the prime factors of a big integer number with exponential speed-up compared to the existing classical algorithms. Another well-known application for quantum computer is quantum simulation which is necessary for the development of chemical compounds for biology and chemistry. Generally the computational complexity of quantum simulation using classical computers increases exponentially as the size of the problem increases, but with quantum computer, it increases only linearly. If you want to read brief introduction to quantum computer (written in Korean), please check an article "Introduction and Prospect of Quantum Computer" in the magazine of the IEIE vol. 45, issue 4 (2018). Also, if you want to read more about quantum computer based on ion trap (written in Korean), please check "Trapped Ion Quantum Computer" in the Physics & High Technology 2019 March issue.

Currently many global IT companies such as IBM, Google, intel, Alibaba and many start-up companies including IonQ, Rigetti Computing, D-Wave, AQT are developing its own quantum computing systems and some of the prototype systems are publicly available.

Example of typical quantum circuits composed of multiple qubits, quantum gates, and measurement stage.

To implement a quantum circuit, we need to choose a physical quantum system, and there are a few different hardware platforms such as ion trap qubit (quantum bit), superconducting qubit, and solid state qubit. We are mainly focused on developing quantum computers based on ion trap qubits that have relatively long memory time (i.e. coherence time) and do not need dilution refrigerator systems compared to other hardware platforms.

We already developed several working ion trap chips using micro-electro-mechanical system (MEMS) technology based on silicon fabrication method and demonstrated basic quantum operation such as Rabi oscillation (equivalent to single-qubit gate) in 2014.

Measurement result of Rabi oscillation

The first working ion trap chip fabricated at SNU in 2013. The red dots show individual Ytterbium ions trapped by the shown ion trap chip and a single ion can be used as single quantum bit (qubit).

We are currently working to implement two-qubit gate which is the most important ingredient of universal quantum gates in addition to single-qubit gate.

# Quantum Cryptography (양자 암호)

Quantum cryptography protocols are designed to distribute secret keys securely by detecting any kind of eavesdropping attempt with the help of superposition property. Once the secret keys are securely distributed, it will be used to encrypt digital messages and the encrypted messages are being transmitted by regular communication channels. Based on this idea, the first quantum key distribution (QKD) protocol was proposed by C. Bennett and G. Brassard in 1984 and therefore it is called BB84 protocol. BB84 protocol was first commercialized in early 2000s, and since then, many quantum cryptography companies released various products based on BB84 protocol and its variants, but they generally have limitations in long-distance application.

The distance limitation can be overcome by another quantum cryptography protocol proposed by A. Ekert in 1991 (E91) based on quantum entanglement. To demonstrate E91 protocol over long distance, China recently launched a quantum satellite which contains entanglement photon pair source which was first developed by Prof. Taehyun Kim in 2005 while he was a graduate student at MIT.

Instead of using expensive quantum satellite, we have been developing entanglement generator which can be used to extend the distance of the entanglement by using quantum teleportation protocol. To generate and store the entanglement until necessary, we use trapped ion qubits. We recently demonstrated Hong-Ou-Mandel interference which is the last challenge before entanglement generation between two ionic qubits.

# Quantum Algorithms and Quantum Information Theory (양자 알고리즘 및 양자 정보 이론)

To utilize the full power of quantum computer, properly designed quantum algorithm is necessary. For example, Shor's algorithm can be run on a classical computer as well, but it will 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.

To execute quantum algorithms on a real quantum computer, it is necessary to convert abstract quantum algorithms to quantum circuit composed of abstract quantum gates, and again abstract quantum gates should be mapped to physical system. To minimize the error intrinsic to quantum system, we need additional layer of abstraction (quantum error correction code) to encode logical qubit into physical qubit. These overall structure has strong resemblance to multiple layers of system software in classical computer, and therefore we need a lot of effort to optimize these layers and these stages still need similar concepts used in quantum algorithms. Therefore, we are interested in developing and applying practical quantum algorithms necessary to implement quantum computer system.