
DOI: 10.22661/AAPPSBL.2020.30.1.09
The Second Quantum Revolution with Quantum Computers
CHINGRAY CHANG^{ 1,2}, YEUCHUNG LIN^{2}, KUEILIN CHIU^{3}, TSUNGWEI HUANG^{4} ^{1}DEPARTMENT OF PHYSICS, NATIONAL TAIWAN UNIVERSITY AND IBM Q HUB AT NTU ^{2}DEPARTMENT OF PHYSICS, NATIONAL TAIWAN UNIVERSITY ^{3}DEPARTMENT OF PHYSICS, NATIONAL SUN YATSEN UNIVERSITY, TAIWAN ^{4}DEPARTMENT OF INFORMATION AND COMPUTER ENGINEERING CHUNG YUAN CHRISTIAN UNIVERSITY, TAIWAN
ABSTRACT
The quantum nature of superposition, entanglement, and measurement are applicable to the quantum information industry, and one major disruptive and revolutionary technology is quantum computing. In this article we briefly summarize and discuss the current status of quantum computing and its potential applications. We also present the focused research topics of quantum computing within Taiwan. This review will outline the importance and the possible impact of the emergence of quantum computing.
INTRODUCTION
Quantum mechanics is one of the most successful theories in physics and it has profoundly changed human life in the 21st century. When the scale of a system is narrowed down to atomic levels, the physical rules governing the system is based on quantum mechanics, which is mysterious and sometimes counterintuitive when compared to the classical world. The two most important concepts in quantum mechanics are quantization and the superposition of different quantum states. Quantization refers to the discreteness of a physical quantity, while superposition refers to a situation in which a quantum state can appear in multiple classically measurable states simultaneously.
Ever since Max Plank first introduced the concept of quantum in 1900, quantum mechanics has revolutionized science and industry and has produced many technologies that we might take for granted nowadays. A few examples of these technologies include lasers for optical communication, the internet, transistors for computers and cellphones, and nuclear weapons and power plants. If we refer to this period of early development as the "First Quantum Revolution", in which we have built classical devices based on quantum principles, then the newly emerging "Second Quantum Revolution" is even more ambitious in that it exploits the fundamental properties of quantum mechanics and lets quantum nature deal with the "quantum problems". Quantum information, which can be roughly categorized into two major branches, quantum communication and quantum computing, reaches a radically different level in the Second Quantum Revolution. In 1997, D. Bouwmeester and JW Pan first demonstrated quantum teleportation using polarized photons as individual quanta [1]. Quantum entanglement, in which measurement of the state of one particle collapses the state of the other particles, plays an essential role in the concept of quantum teleportation. Quantum entanglement and the nocloning principle guarantee information transmitted in quantum teleportation is safe, meaning that when information has been eavesdropped on, it will be known and only the receiver who owns the key can decode the information.
Quantum entanglement is also a key element to the second branch of quantum information  quantum computing. Although Moore's law (i.e., the density of devices on silicon chips doubles approximately every 18 months) has been successfully manifested in classical computing devices over several decades, this exponential trend cannot go on indefinitely, due to both physical limitations and expense considerations. Furthermore, erasing a bit of information has an energy cost of at least k_{B}T ln2 (Landauer's principle) [2]. In classical computing, the input information needs to be erased after each calculation, and these irreversible calculations consume energy. With increasing numbers of integrated logic circuits in traditional computers, overheating will then be an inevitable issue. Quantum computing, on the other hand, is based on reversible calculation processes, e.g., the input information can be retrieved from the output. So overheating, hence the energy loss, will in principle be substantially reduced. However, the true advantage of a quantum computer comes from its exponentially faster and stronger computing power in calculating certain nondeterministic polynomial (NP) problems. If the dimension of a question is n, and the steps (or the time) required to solve this question is T(n), then Grover's Search Algorithm can gain a speedup of √n as compared to n in a classical algorithm, while Shor's integer factoring algorithm can gain an n^{2}log(n) speedup as compared to exp(n^{1/3}) in a classical algorithm. The latter places a very severe challenge to our current RSA cryptosystem, and motivates many countries and major companies (such as Google, IBM and Intel) to invest in quantum technology. When the qubit number is over 50 (note that here we refer to the errorcorrected logical qubits), a quantum computer has been predicted to outperform any classical computer in solving certain problems, which is a state known as quantum supremacy, as coined by John Preskill [3]. This supremacy has been claimed by Google recently regarding the generation of random number patterns [4].
Fig. 1: The history of quantum sciences and the quantum revolutions.
With such tremendous computing power in sight, it is anticipated that quantum computing will have various applications in artificial intelligence (AI), in the simulation of molecular interactions and chemical reactions, and in the synthesis of new materials. Large data analysis is crucial for machine learning, optimization of traffic routes and trajectory predictions. The exponentially increased degrees of freedom of a quantum state (2^{n}, n is the number of qubits) allows quantum computers to store and analyze large amounts of data, which can speed up the data processing time. Quantum computing may also be used to analyze sequence of genes in clinical medicine. Traditionally, chemists examine whether a type of drug can improve symptoms or cure diseases by assessing interactions between molecules, proteins and chemicals. This traditional type of analysis is based on running through the numbers in every possible combination, which is both labor intensive and time consuming. Therefore, the fast dataprocessing abilities of a quantum computer can play a substantial role here; it can examine various kinds of molecules, proteins and chemicals at the same time.
Current status of hardware
A quantum computer consists of atoms and light and the computation relies on the interaction between them. The atom, which is the storage unit called "qubit" in quantum computing language, can be either a real atom or an artificial atom, as long as it possesses two discrete energy levels to couple with light. Depending on whether an optical laser is required to control the qubits, quantum computing platforms can be further classified into two categories: the optical systems and the solidstate systems. The former requires lasers while the latter uses microwaves to manipulate the qubits. In optical systems, trapped ions and diamond vacancies are the two major candidates that have been intensely studied in recent years. In 1995, Cirac and Zoller first proposed the use of atomic ions trapped in space by electromagnetic fields for quantum computation [5]. Once ions are confined within a trap in a vacuum chamber, they are cooled by a laser to near their ground state and controlled by an electromagnetic field for qubit operation. The trapped ions have very long coherence times, with a twoquibit gate fidelity more than 99.9% and a single qubit gate fidelity even reaching 99.9999% [6]. Specifically, the optical qubits of a trapped ion can have coherence times of one to tens of seconds [6, 7], while the hyperfine qubits can have coherence times longer than 600 s [8]. The gate operation time of trapped ions is usually 1100 Î¼s [6], which gives a very good ratio of coherence time to gate time as compared to superconducting qubits (1000). The system of diamond vacancy refers to a nitrogenvacancy (NV) center in a diamond. The defect, consisting of a nearestneighbor pair of a nitrogen atom substituting for a carbon atom and a lattice vacancy, forms a magnetic moment that can be manipulated and measured by light. Remarkably, quantum coherence in such systems can be preserved even at room temperature [9], but the entanglement of qubits is hard to achieve due to the weak interaction between defects and photons [10] (although improvement has been made lately, see table I). In general, qubits in optical systems have longer coherence time and higher gate fidelity, but the gate operation time is also longer. In addition, it is more challenging to upscale them due to the space requirements of the optical setup, as compared to solid state systems.
Table I: The qubit technologies and their basic properties.


For solid state systems, superconducting qubits and spin qubits in quantum dots (QDs) are two very important and promising platforms. Superconducting qubits consist of an Al/Al_{2}O_{3}based Josephson junction as an inductor and a shunted capacitor, which equivalently forms a quantum LC resonator with discrete energy levels. The qubit is capacitively coupled with a superconducting coplanar waveguide whose role is to be a microwave cavity to store the microwave photons and interact with qubit. The control of the qubit is achieved by applying microwave and DC bias; the former couples to the qubit levels while the latter generates magnetic flux threading the loop of SQUID to change qubit energy. The coherence time of such a system can exceed 100 Î¼s [11], with a gate operation as fast as 40 ns [12]. In 2019, an 18 entangled qubit state was demonstrated [13] and the largest announced qubit number (by Google) is 72 [14]. The superconducting system has been financially supported by many major companies, such as Google, IBM and Intel, and is the first platform that demonstrates quantum supermacy [4]. The other candidate in solidstate systems are quantum dots. A quantum dot is an artificial structure where electrons can be confined within a scale of a few tens of nanometers. The charge and spin degrees of freedom of the confined electrons in such a system can both be used as a qubit. The charge qubits usually suffer from the charge noises in the surrounding, which leads to a shorter qubit coherence time (tens of ns) [15]. There are several forms of spin qubits, such as, spinup and spindown states in a single QD, twoelectron singlet and triplet states in a double QD, and spinexchange interaction in a triple QD. In isotopically purified ^{28}Si QDs, where nuclear spin is greatly reduced compared to GaAsbased QDs, the coherence time can approach 30 ms [16] with a gate operation time around 100 ns [17]. The single qubit gate fidelity in this system can reach 99% while the twoqubit CROT gate fidelity exceeds 90% [18, 19]. For spin qubits formed by phosphorus atoms in silicon, the coherence time can even reach 30 s with a gate fidelity greater than 99.99% [20]. The small size of QDs (less than 100 nm) is advantageous for upscaling, but it also has to deal with the crosstalk and fanout issues when designing the control wires, as faced by superconducting systems. Finally, a prospective platform whose existence has not yet been confirmed in solid state systems is the topological qubits. In topological quantum computing, bits of information are encoded through braiding nonAbelian anyons, whose exchange statistics is noncommutative (i.e., particle exchange with different routes will lead to different end states). What makes topological qubits special is the expected very long coherence time, because the qubit operations are protected by topological symmetry. Majorana fermions, which are predicted to exist in 1D or 2D pwave superconductors [21], are a candidate for realizing this operation. However, while important experimental signs of progress have been made to reveal the signature of the Majorana fermion, its nonAbelian exchange statistics have not been confirmed so far.
Universal quantum computer, NISQ and quantum annealer
Different companies for their different applications are now developing three types of quantum computers. A universal quantum computer aims to use gate operators to solve all kinds of problems within a reasonable time but it needs millions of logical qubits and it is unlikely to be mature within a decade. International companies implementing the universal quantum computer include IBM, Google, Microsoft, NEC, Fujitsu, and companies in China. However, since the currently available qubits are not enough to achieve a faulttolerant quantum computer, the intermediatescale quantum computer (NISQ) was now adopted for special applications within a noise environment with a limited number of qubits. Even though the full availability of universal quantum computing has not been made available there already are special applications on the market. The digital annealer developed by Fujistu [29] and the quantum annealer used by Dwave [30] can provide a great advantage in optimization problems. The digital annealer is a digital process inspired by quantum phenomena, while quantum annealing needs real quantum entanglement of two qubits at least.
Quantum algorithms
There are more than 50 quantum algorithms available online [31]. In this section, we will introduce a few quantum algorithms and their applications. The quantum amplitude amplification algorithm (QAA) is a genuine quantum algorithm, and both Fujitsu and DWave use QAA to solve the optimization problems within the Ising model through the quantum annealing processes.
The variational quantum eigensolver (VQE) [32] is a hybrid of classical and quantum algorithms. VQE can give the ground state of a large matrix. Hence, VQE can be applied to solve optimization problems in finance, e.g. portfolio optimization problems and trading strategies.
Also, VQE is a good algorithm to determine a stable structure for predicting molecular chemicals and new drugs. Theoretically, to solve molecular simulations with VQE, the number of gate operations will be O(M^{3}N) [33], where M is the number of spinorbitals and N is the number of electrons. The quantum approximate optimization algorithm (QAOA) [34] is a polynomial time algorithm for finding a local solution in optimization problems such as the MaxCut problem [34]. Actually, VQE and QAOA are similar, thus QAOA can be used for chemical simulations, finance optimization, and others. VQE and QAOA are both considered very important milestones in the quest for quantum supremacy in the NISQ era. However, it is expected that the technology of quantum hardware and the new error correction method will catch up with the universal quantum computer era within decades. By then, more powerful and efficient quantum algorithms should be developed and realized. One of the most important algorithms is the quantum Fourier transform (QTF) [35]. QFT using only O(n^{2}) gates is exponentially better than classical discrete Fourier transform which takes O(n2^{n}) gates. Hence, Shor's algorithm for factoring a problem, quantum phase estimation, hidden subgroup problem [35] and other quantum phase related problems can all take advantage of the exponential speedup due to QTF. Because Shor's algorithm can solve the factoring problem very quickly, bank trading security based on RSA codes might get cracked. On the other hand, the Aram Harrow, Avinatan Hassidim and Seth Lloyd (HHL) [36] algorithm, which is also based on the QFT algorithm, can be used for finding the inverse transformation of a large dimensional matrix within polynomial time. HHL algorithm can be applied to deep learning, and scientific and engineering research. Another major branch is Grover's algorithm [37] in an unstructured N database searching problem; the classical search algorithm needs O(N) evaluations but Grover's algorithm just needs O(√N). Therefore, Grover's algorithm can be used in all kinds of search problems in real life.
Current research in Taiwan
In recent years, there have been many important research works based in Taiwan related to the hardware of quantum computing. Prof. YingCheng Chen's group reported on quantum memories and storage efficiency of 92.0% with quantum optical methods in 2018 [38]. Prof. ChinSung Chuu's group works on quantum photonics [39] and built the optical fiber link between National Tsing Hua University and National ChiaoTung University to demonstrate Taiwan's first outdoor quantum key distribution (QKD) [40]. Prof. Io Chun Hoi researches on the amplification of optical couples with a superconducting qubit [41]. Prof. YuehNan Chen's group researches on the measurement of quantum steering, its geometric quantification and observes [2] quantum behaviors. Prof. Ite A. Yu's group works on quantum optics and quantum information and determines the efficient crossphase modulation (XPM) achieved at lowlight intensities without requiring cavities or tightly focusing laser beams [43]. Also, there are some research works in progress at National Taiwan University (NTU), in the study of Sibased qubits, spintronic and quantum devices, as well as quantum computing in ML and AI fields. Moreover, Chung Yuan Christian University has proposed to initiate a quantum computation college to focus on quantum algorithms and their applications in industry.
Table II: Major quantum algorithms and their applications.
IBM Q Hub at NTU
Another important development in Taiwan is the IBM Q Hub at NTU. NTU and IBM signed a contract that allows NTU and the research groups in Taiwan to use the most advanced superconductor qubitbased IBM Q system (i.e., 53 qubits in 2019). Prof. ChingRay Chang is in charge of the IBM Q Hub at NTU, and the Q Hub does not only work on research but also promotes the applications of quantum computing to major companies and financial institutions in Taiwan. Quantum Physics education in high school and for undergraduates is also emphasized in order to prepare the young gener 