
DOI: 10.22661/AAPPSBL.2019.30.1.09
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 generations for quantum computing. In terms of research, the IBM Q Hub at NTU works on quantum materials, quantum finances, a quantum random number generator and the applications of quantum algorithms. Regarding promotion, the IBM Q Hub at NTU has consistently contacted not only hightech companies local industries but also traditional and financial industries. The IBM Q Hub at NTU had held many popular talks and IBM Qiskit camps have been held inside Taiwan to attract people's attention and interest. We have had hundreds of researchers, and graduate and undergraduate students now using IBM Q systems. The IBM Q Hub at NTU provides teaching materials for high school and university and quantum games for students (see Fig. 2).
Fig. 2 : The roles of the IBM Q hub at NTU in Taiwan.
APPLICATIONS
A very early idea of quantum computing as suggested by Feynman [44] was to use quantum computing to solve quantum problems. However, the applications of quantum computing, empowered by the parallelism bolstered by superposition and entanglement, are not limited to quantum problems only.
Under the constraints of the current technologies of quantum computers, the immediate applications will be mostly focused on either quantuminspired or specialpurpose applications, rather than general algorithms suitable for a faulttolerant universal quantum computer.
Annealer and photonics
The calculations of the eigenvalue of ground state energy for larger molecules in materials science or pharmaceutical are still far beyond the reach of a NISQ quantum computer. Nevertheless, there are still ways to probe physical properties by specialpurpose devices which are ready for operation in the present day. A quantum annealer [45] and digital annealer [46] (together to be referred to as annealers hereinafter) are not gatebased universal quantum computers; rather, they are designed to solve special optimization problems. Using the natural evolution of energy minimization of a physical system, the problems in real life are mapped onto the energy landscape, manipulated by bias and coupler [45], of the system. The entangled and superposed states then adiabatically evolve to the lowest energy state of the energy landscape constructed from real problems and the solution to the problem is derived from a quantum annealing processes. Since the number of qubits in these kinds of annealers have already reached a few thousand, it is possible to solve combinatory optimization problems in a very efficient way. For instance, chemicals used in drugs typically have tremendous huge molecular numbers, it is completely impossible to identify specific atomic groups which are targeted for particular drugs using the current quantum computer within reasonable clock time. However, using annealers to find a certain shape of molecular which can perform the desired function of that atomic group is feasible. These kinds of innovative utilizations allow annealers to be able to solve many optimization problems even before the universal quantum computing era.
Study of a physical system may be required to use bosonic statistics, such as the molecular vibrational spectrum. Using linear optical operated by photonic qubits is a natural choice. Programmable quantum optic arrays with 20 input photons have been constructed [47]. The machine is also a specialpurpose device which can be applied to boson sampling with 10^{14} state space. It is expected that the number of photons can be fast scaled up due to silicon photonics technology, provided that a decrease in the quantum effect with an increase in the number of qubits can be effectively acheived [47].
Quantum Chemistry
Quantum applications for a quantum computer are the original motif for this fastemerging discipline. Physical sciences are an arena for quantum phenomena, among which, physical chemistry is the most relevant field. Chemistry attracts more attention than physics in the early stage of application for a quantum computer as chemistry has a more focused theme bonding, and it involves only the calculation for the wave functions of molecular openshell electrons, or just the ground state energy of electrons. This provides plenty of room for possibilities for chemistry related disciplines such as pharmaceutical and materials science.
In chemistry, a more common task than calculating the wave function is to calculate the ground state energy directly. It can be performed, for instance, by a digital Hamiltonian simulation [48] with a classical computer, in which the dynamics of the system are approximately mapped to a sequence of quantum gates. Using the aforementioned VQE algorithm, the ground state energy of small molecules, such as H_{2 }[49, 50, 51], HeH_{+ }[32, 52], LiH [50, 53], BeH_{2} [50], D [54], etc., can be derived with single digit number of qubits. It is noted that physics properties such as a quantum magnet can also be derived by a similar approach [50]. These pioneering works are demonstrations for how a quantum computer works even at the NISQ era, as well as preparatory works for quantum computing on a future efficient faulttolerant universal computer.
Quantum machine learning
Machine learning (ML) is the most active area in the advancement of AI. A number of ML algorithms have been successfully developed. The current focus in applications of quantum computing in ML are the increased speed of existing classical algorithms and the exploration of new algorithms feasible only in quantum computing.
Regarding the first area of focus, a number of algorithms using quantum computing show increased speed as compared to classical computing. Bayesian inference indicates quadratic increases in speed on the problems of supervised learning of binary classifiers, classical Boltzmann machines and quantum reinforcement learning. Moreover, for leastsquares fitting, a quantum Boltzmann machine, quantum principal component analysis (PCA) and a quantum support vector machine (SVM) indicate exponential increases in speed [54].
The second area of focus takes advantage of the fact that quantum computing can generate a quantum state. Consequently, applications using quantum state as original input may be far more useful than the corresponding classical ones, such as a quantum simulator. A quantum simulator does not need to convert huge amounts of classical data through qRAM [55] to quantum state data, which is task with high computation costs, and hence quantum simulation may become the earliest application of quantum computing.
ML involving optimization is also a quantum ML application that had early implementation since that is what the annealer or photonics devices were capable of doing. The deep neural network, which is probably one of the most powerful tools in contemporary ML, also does not require a large faulttolerant universal quantum computer and is also an early adopter of annealer [54].
On top of the challenges which quantum ML faces for continued advancement, in addition to the common problems, building an efficient faulttolerant universal quantum computer, to all the other applications, input and output problems are also on the way. ML is known for its data hunger. Coding a huge amount of data into quantum state typically requires qRAM, which only completes the proof of concept. The coding itself has high computing power consumption. The complete solution from the output of quantum computing is an exponentially long bit of string. Detailed learning of the full result also has a very high computation cost.
While quantum ML has certain applications which may occur in the near future, AI is in high gear with industry implementation; the development of quantum ML may benefit from spillover momentum due to AI's advancement.
Quantum finance
Investment banks are among the firsttier investors in quantum computing research and development (R&D), and the reason is obvious: any improvement, even incremental, of computing speed or accuracy equates to huge financial gains.
The applications of quantum computing in finance focus on three areas: stock market predictions, portfolio optimization, and fraud detection. The tools used in tackling these problems are typically optimization models, ML (such as the deep neural network) and MonteCarlo simulations [55]. Quantum computing is applied to improve these methods.
An optimization model is used, for instance, in portfolio optimization and the search for arbitrage opportunities. As stipulated in the quantum ML section, the combinatory optimization problem in quantum computing can be performed on an annealer, and hence the application has already commenced for quite a while. PCA is also used for portfolio optimization, and quantum PCA enjoys an exponential increase in speed.
Data classification is a tool for fraud detection. Quantum PCA can also be applied for data classification. SVMs are also used for data classification, separating data into two categories by a hyperplane in the data high dimensional space. Quantum SVMs also enjoy an exponential increase in speed.
The Monte Carlo method uses sampling to estimate a system's properties stochastically. In finance, it is mostly for uncertainty assessment. This makes Monte Carlo methods applicable to portfolio evaluation, risk assessment, and derivatives pricing. In quantum computing, quantum amplitude amplification and quantum phase estimation algorithms are used in Monte Carlo simulations and gain a quadratic increase in speed.
A significant portion of financial applications can be performed on an annealer and hence financial applications may be a precursor for quantum computing applications.
Fig. 3: Quantum computer applications. Top: Classical applications: Machine learning, finances, materials and drug design, RSA problems etc. Middle: Faulttolerant quantum computer needs appropriate quantum materials with long coherence time. Effective quantum algorithms operate on faulttolerant quantum computer can solve all kinds of quantum and classical problems and quantum advantage will be in all spectrum of applications. Bottom: Quantum applications: Including sensors, new methods to define time, new security systems, new methods to transfer information and to solve the statistical problem in quantum regimes.
FUTURE PROSPECTS
The activities in the quantum computing field are gradually evolving from fundamental science research to engineering development, albeit heavily relying upon fundamental science knowledge that is not familiar to conventional industrial society. The main theme of development focuses upon improving the coherence time and fidelity of qubits.
The choice of qubit variety and the manufacturing of qubit chips (quchips) are central to qubit quality. Yet, system integration is necessary to incorporate this core part into a quantum computer, providing its control/readout, a cryogenic environment and other supporting facilities to make a real working system, rather than just an experimental instrument. Semiconductor devices are omnipresent in modern engineering systems. Putting aside those quantum computers using siliconbased qubits, which were originally intended for integration with conventional semiconductor circuitry, systems using other kinds of qubits still require semiconductor devices to facilitate the organization and operation of the systems. Therefore, to construct a working system, it is necessary to integrate semiconductor devices with a quchip. Furthermore, peripheral semiconductor devices also play an essential role in improving the coherence time and fidelity of qubits.
After establishing the engineering pathway of quantum computing, it is already moving toward the industrialization of faulttolerant universal quantum computers. Building an industry requires collective and coherent efforts to accelerate and synchronize the pace of development. A wellorchestrated and industrywide strategy supported by professional society institutions will create and continue momentum.
Semiconductor system integration
Other than the topological qubit, which is still in the process of proofofexistence, most of the existing qubit varieties have been demonstrated to be working for at least twoqubit operations and researchers are in the process of improving coherence time and fidelity in order to scale up the number of operative logical qubits. System engineering works are heavily involved, and semiconductors play a key role in the formation of a viable, reliable and scalable system.
Cryogenic CMOS technology
A quchip (qubit chip) is a device to temporarily store the desired quantum states. A quchip requires a control circuit and devices to initialize, operate and measure the quantum states in qubits on the quchip. As the qubits being processed stay localized at their physical positions, the processing devices, such as microwaves, lasers, etc., and the logic circuitry need to be placed adjacent to the qubits if the system is to be scaled up. In certain apparatus, those devices are built directly neighboring the qubits on the quchip [56]. In other cases, those devices are built on the control/readout board with electronic circuitry. Using semiconductor buzzwords, the current quantum computing architecture is nearmemory computing, if not inmemory computing. Quite a few varieties of qubits demand cryogenic temperatures in order to keep the noise down, the control/readout board in close proximity to the quchip is hence inevitably to be within ultralow temperature. Contemporary CMOS (complementary metaloxidesemiconductor) technology could be compatible with the extremely low temperature, but the testing program and reliability standard would need to be specialized for this particular application. The materials used in the CMOS and the manufacturing process for quantum computers also would need to be customized, as most of the time spent on a job of computing(200Î¼s) by a stateoftheart quantum computer is on the semiconductor circuit(170Î¼s), rather than the quantum gate operation(30Î¼s) [4].
Quantum module
In continued scaling, the main challenge arises from the problems of decoherence and the error rate. Both grow exponentially with increases in the number of qubits. Therefore, it is proposed that qubit modules should be built with acceptable coherence time and fidelity, as those modules could then be used as the building blocks for a largescale quantum computer.
Quantum modules are interconnected by photonic coupling. This is reminiscent of "chiplets" in semiconductors. Chiplets are heterogeneous chips of different functions or manufacturing processes placed on an interposer, and these chips are interconnected by wires. This is an economical and efficient type of system integration. Even though the chips on the interposer are homogeneous, such as the plural memory chips in high performance computing packaging, this approach can still provide an advantage over manufacturing an integrated single chip. This approach reduces the defect density, as the chip area of the chiplets is smaller. The idea of a qubit module is a close analogy of chiplets and may enjoy a similar advantage. While chiplet technology is in an early phase in the semiconductor industry, adopting quchip integration in the development of this trend will also expedite the developmental pace for integration in largescale quantum computer systems.
Integration and packaging
The assembly of quchips, control/readout boards and other components requires packaging technology. Quchip and control/readout boards are assembled using flipchip bonding, but with much more sophisticated requirements as compared to conventional semiconductor chips. For instance, the cooling of a quchip requires areal contact and some of the operating or measuring devices also require a low temperature environment. The stress caused by a large temperature gradient inside of the package needs to be managed.
With continued scaling, the quchip and the control/readout circuit become much more complicated. For instance, in the modularized qubits approach, plural quchips each have an adjacent control/readout board. The quchips may extend in a horizontal direction or can stack in a vertical direction, atop of underlying control/readout boards. This is what the semiconductor industry currently strives toward, heterogeneous integration. A similar heterogeneous integration technology (but with different content) could be immediately applied to the quantum computing field.
Fig. 4: It is necessary to develop a faulttolerant logical qubit system with reasonable coherent time. An easy and intuitive quantum compiler system needs to be developed for daily use so that quantum computers can be used for commercial applications. The core of a quantum computer is the quantum chip, called the QCPU because it plays a role similar to that of the CPUs in classical computers. Quantum technology (blue area) to manipulate the quantum states is necessary when building quantum computers. The cavity QED and quantum channels (red area) provide a means of communication between classical and quantum computers. The quantum algorithms (green area) operate on the quantum computer to calculate or simulate problems that classical computers would find difficult to do.
Scientific and industrial development strategy
While some fundamental research subjects are still ongoing, industrial and commercial efforts, from the passage from NISQ to a faulttolerant universal quantum computer, have already slipped in and unfolded in parallel. The advantage of this parallelism is obvious. Fueled with financial investment, system engineering works and applicationoriented driving force from the industry, the pace of development toward truly practical quantum computing applications is expected to be significantly expedited. Yet there is price to pay, as every penny of the investment from commercial institutions demands substantial fiscal return, in the long term or even in midterm; therefore, an orchestrated strategy for the R&D for the next stage of quantum computing is highly desirable.
Industry wide consensus and standards
The power of Moore's Law is a prominent, positive example of controlled development from the semiconductor industry. Moore's law was an empirical trend in the inception of industry's development of semiconductors, it later became a selffulfilling law and lasted for over 60 years. The reason behind its phenomenal success of continued chip size shrinkage is that the developmental pace of each sector of the valueadded chain, including the materials, equipment, design, manufacturing, packaging and testing, applications, etc., throughout the whole semiconductor industry was synchronized by the envisioned progress of Moore's Law. The concept of annealers and NISQ are a good start for quantum computing, as it precisely positions the current status of the development of quantum computing and tempers expectations regarding what quantum computing can actually do.
A more detailed guideline about quantum computing's technological developments, analogous to the International Technology Roadmap of Semiconductors (ITRS) by the Semiconductor Industry Association (SIA) or the Heterogeneous Integration Roadmap (HIR) by the Institute of Electrical and Electronics Engineers (IEEE) and Semicon, would benefit scientific and industrial societies even more. Rough indications of the technological milestones pertaining to coherence time, fidelity, error rate, number of qubits, etc., would certainly help to converge resources to feasible targets and to use collective and coherent efforts to overcome the common bottlenecks of further development.
Standards, benchmarks [57] and interfaces for hardware and software could also help to synchronize the results of development and to avoid redundant works.
Fig. 5: Roadmap for quantum computing. Y2Q stands for the "year to the quantum computer".
Staged technology goals and associated applications
The commercialization of a faulttolerant universal quantum computer is expected to take at least a decade. Participation of industrial forces in this early stage of development has a certain drawback, as aforementioned, that notable and evident continuous progress needs to be present in the pathway before reaching the longterm goal, in particular in the aspects of technology progress and applications affiliated with it. The AI winters in the mid1970s and the late1980s experienced by the AI industry provided an opportunity to learn how to proceed and how to avoid certain pitfalls.
Staging the longterm technological development into various phases appears to be a good strategy. For each phase of technological development, there should be associated applications with it, e.g., the combinatory optimization type programs, which can be applied in various commercial fields. The newly developed capabilities in each stage, though limited, then can have corresponding progressive applications, and then the investment on quantum computing can be justified and the momentum can be maintained.
Boost from other industries
There are four areas of technology that are considered critical to modern technological competitiveness: 5G, advanced manufacturing, AI and quantum information. Quantum computing falls into the category of quantum information. These four technologies are closely intertwined. For instance, the implementation of advanced manufacturing necessitates the deployment of a 5G infrastructure first because only the 5G highlighted standard massive machinetype communication (mMTC) can support the communication of a huge amount of machinetypes. The deployment of 5G also gives rise to an extraordinary amount of information flow; highspeed communications then drives the demand of silicon photonics devices that deliver information in a much faster, energy conservative manner. In turn, this demand may benefit the development of quantum communication and possibly quantum computing, as photons are one of the viable candidates for qubits. ML is probably the most highly developed subdiscipline in AI, and combinatory optimization is one of the central themes of ML. As mentioned in the previous paragraph, combinatory optimization is one of the earliest applications of quantum computing, which may start to unfold in the notsodistant future.
As 5G is obviously in the process of quickly ramping up, advanced manufacturing will soon follow. AI, despite the productivity paradox [57] that has been recently been raised, is actually steadily moving forward.
Quantum computing, being one of the latest technologies to be commercially implemented, can get a boost from these technologies that were deployed earlier. Tighter association with other technologies and their applications, such as applications in ML, may divert resources in AI to quantum computing, and this is likewise in 5G and advanced manufacturing.
Cloud Service
As part of the developmental strategy, promotion for quantum computing on the cloud is provided by quite a few commercial companies, including Google, IBM, Microsoft (Azure), Amazon (AWS), DWave, Fujitsu, and Huawei, for education, algorithm development, academic collaborations and commercial applications. The services provided range from basic learning materials, design toolkits and training, to operations on stateoftheart quantum computing devices. Certain design tool kits provide open source code, which helps to converge the developmental direction and saves societal resources.
QIS investments
The R&D of quantum information science (QIS) is progressing rapidly throughout the world. In addition to the United States, China and the European Union (EU), which have the most aggressive QIS plans, the United Kingdom, Canada, Australia, the Netherlands, Japan, and South Korea are also actively investing. Even though there is currently no clear nationallevel QIS development strategy, Russia, Germany, Austria, and Taiwan are also investing in basic QIS R&D and applications.
USA
The total amount invested by the US government in QIS so far is about US$ 249 million (M) [58]. In September 2018, the National Science Foundation (NSF) announced that it had provided US$ 31 M in input, and at the same time, the United States Department of Energy (DOE) announced that it had committed US$ 218 M for next 2 to 5 years. The government has continuously supported QIS R&D under the National Quantum Initiative (NQI).
China
Quantum communication and computing has been one of the six main goals since 20062020. China's annual funding for QIS R&D is estimated to be US$ 244 M. More investment in various basic and commercial initiatives in the next fiveyear, medium (20212035) and longterm plans will be conducted [59].
Japan
The government of Japan will invest about 30 billion yen (US$ 276 M) in quantum research starting in April 2020. According to the government's roadmap, Japan's goal is to produce 100qubit machines in about 10 years, and then produce more powerful quantum computers in about 19 years, around 2039 [60].
Taiwan
The Ministry of Science and Technology (MOST) will invest NT$ 70 M (US$ 2.39 M) annually in the quantum computing field for the next three to five years. Taiwan's preexisting semiconductor, information, and communications technology industry give Taiwan an advantage in the future development of quantum computer technologies [61].
European Union
The EU Quantum Flagship Program is a 10year program aimed at commercializing EU's basic QIS R&D. The goal of the plan is to cultivate a competitive European quantum industry, which will give Europe a leading position in the future global industrial landscape. The EU is expected to invest US$ 120 M over a decade [62].
Germany
The German government will invest 650 M euros in the next two years to support the application of quantum technology to the wider market. According to the cooperation agreement with IBM, IBM Q System One will be installed in Germany and "will be the first installation of its kind in Europe" [63].
United Kingdom
The UK embarked on a fiveyear (20132018) national quantum technology plan and spent US$ 440 M to transform QIS R&D into commercial technologies. In September 2018, the UK announced that it would invest more than US$ 105 M in four quantum technology development centers in the next five years [62].
In summary, quantum computing now is not only an area of fundamental research for physicists but it is also gradually phasing into an engineering and industrialization stage and necessary measures for cultivating a new industry need to be taken seriously. Integration with existing and forthcoming semiconductor technologies will expedite the system's integration pace. Furthermore, working out the technological roadmap, standards, benchmarks, interface, etc., by organizations of professional societies will help us reach a consensus within the field. Staging technology developments and their associated applications will keep the momentum ongoing. It is also a good time to get a boost from the lead technologies that are unfolding. Fortunately, quite a few industries are even now showing great interest in quantum computing and the associated applications. However, as we mentioned previously, a real quantum computer system needs all kinds of expertise and thus the most urgent prerequisite, before the universal quantum computer era begins, will be the education and training of the researchers, engineers and programmers in quantum computing.
Acknowledgements: KueiLin Chiu would like to thank Chaoyang Lu, Gang Cao, Georgios A. Siviloglou, Tao Xin, Weicheng Kong and Dawei Lu for their useful discussions. We are thankful for the support of the NTUIBM Q Hub at National Taiwan University from the Ministry of Science and Technology, Taiwan, under grant No. MOST 1072627E002001MY3 and 1082627E002002.
Corresponding author: ChingRay Chang crchang@phys.ntu.edu.tw
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ChingRay Chang received his BS in physics from National Taiwan University (NTU), Taipei, Taiwan, in 1979, then received his PhD degree in physics from the University of California, San Diego, in 1988.
Prof. Chang has worked in micromagnetic numerical modeling since the 1980s. He was the president of the Asia Union of Magnetic Societies (AUMS) and director of the Center for Theoretical Physics at NTU. He also served as the president of both the Taiwanese Physical Society and the Taiwan Association of Magnetic Technologies. He is a fellow of the American Physical Society (APS) and is also a fellow of the Institute of Electrical and Electronics Engineers (IEEE). He has authored more than 270 published papers and held more than 30 magnetic related patents.
He is currently the director of the IBM Q Hub at NTU and also the chair of the quantum computer promotion office at MOST (Taiwan's Ministry of Science and Technology). 

KueiLin Chiu is currently an assistant professor in the Department of Physics, National Sun Yatsen University, Taiwan. Prior to this, he was an associate research fellow (faculty) in the Key Laboratory of Quantum Information, University of Science and Technology of China (USTC) and a postdoc at the Department of Physics at MIT (20152017). He obtained his PhD from the Cavendish Laboratory in Cambridge University where he worked on quantum transport in 2D materialbased quantum dots. He received his BSc degree in applied physics from National ChiaYi University (20002004) and his MSc degree in physics from National ChiaoTung University (20042006). His current research focuses on topological materials and superconducting quantum circuits. 

Yeuchung Lin is a columnist in DigiTimes and is a visiting research fellow of the Department of Physics, National Taiwan University. After receiving his PhD from the University of Massachusetts, he worked at National Central University, and then moved to the semiconductor industry. He was elected as chairman of the supervisory board of the Taiwan Semiconductor Industry Association in 2002. His research areas are theoretical particle physics and condensed matters. 

TsungWei Huang is currently an assistant professor in the Department of Information and Computer Engineering at Chung Yuan Christian University, Taiwan. He received his PhD and MS degree in physics from National Taiwan University (NTU). For his MS degree he worked on optimal gate operation in open quantum systems and for his PhD he worked on quantum transport in graphene systems with defects. In his postdoc research period, he worked on quantum phenomena in nitrogenvacancy (NV) centers and implemented quantum algorithms on the quantum computer at the NTUIBM quantum computer center. 
