A New Design of System Architecture for Quantum Computer

Transcription

1 A New Design of System Architecture for Quantum Computer Hongbiao Li 1 * 1. School of Information Engineering, Northeast Electric Power University, Jilin, China Abstract: Quantum computer is a research frontier in future computer science. Using the physical unique features of quantum, quantum computer can behave more efficiently and more secure than classic computer. However, the quantum computer technologies of system architecture have a long way to go before reaching maturity. The key problems that affect quantum computer s development are computing speed, reliability and physical realization, which can be resolved completely by no means except a more premium design of system architecture for quantum computer. In this article, a new design of system architecture, QCSA (Quantum Coherence Sustaining Architecture), for quantum computer is presented by a systematic thinking method allowing for reliability and scalability. The whole procedure of quantum resource scheduling in the system architecture is introduced, in which logical instructions are automatically decomposed into a sequence of elementary operations (SEO). The quantum programming language is designed universal and scalable, which ultimately will be compiled into machine language executable in quantum computer by its language processing system. Finally, compared with other two architectures QLA and CQLA, the target system architecture QCSA exhibits a whole superiority in speed, reliability and physical realization. Keywords: Quantum Computer; Architecture; Quantum Software; Quantum Complier 1. Introduction In 1982, based on Benioff's work, Feynman proposed the effective way to solve the problems confronting the traditional computer simulation of large-scale quantum systems, which can simulate other quantum systems with quantum system itself [1], and even can simulate other complex physics systems by quantum system, because quantum mechanics is considered to be the most fundamental mechanical system that governs all physical phenomena in the universe. This was the first time to put forward the idea of using quantum devices to process information. In 1985, Deutsch put Feynman s thought into practice and proved that it is possible and effective to simulate the complex system by quantum computer, which is impossible for classical computer [2]. In contrast to the classical Turing machine and Boolean logic system based on classical computation, quantum computation has the incomparable advantages. It can be summarized as the following two aspects: 1) The representation and storage of information. In classical computation, the information and data are expressed and stored in the form of binary value, and the bit is the basic unit of measurement of classical information, which can be regarded as a random variable of 0 or 1. Whether in terms of numerical representation or storage, the representation of Boolean logic is a real linear space, and 1 bits in the space can be regarded as one dimension vector of integer with mode 2. When it is to increase the representation and storage capacity of information by extending the number of binary digits, the effect can only be linear growth. In contrast, due to the superposition of quantum states, any quantum state (, ) can be expressed and stored as linear superposition of quantum ground states and. In this way, quantum information and quantum data can be expressed and stored in the form of the quantum states, which is obviously not a real linear space, but Hilbert space. Therefore, in quantum computation, quantum information is measured by qubit which is a storage unit of quantum state. It brings in the advantages that quantum information representation space and storage space will be enhanced by exponential scale with qubit increase. 2) Information processing. In theory, the ability of information processing involves two aspects: one is the capability of data presentation; the other is solution of the space problem. As already mentioned, the calculation based on the classic Turing machine is universal that any classical algorithm can be seen as a function with different input parameters, which will output a solution for the problem. As the data representation space is linear, when the price and the input data of solving the problems scale exponentially, calculation requires exponential size the cost of input data using a deterministic function (time or space). While in Hilbert space, due to the superposition of quantum states, the quantum representation and solution space of the algorithm processing problem both are with scales of exponential input, so certain function can deal with the size of the exponential input in linear time, which is now being used by many quantum algorithms. 2. Calculation Procedure and Characteristics of Quantum Computer According to the current people's understanding, quantum computing is a computing principle based on quantum mechanics. From view of computer science, any computation is required to discuss two elements: one is "what", namely the object to be calculated; the other is "how to calculate", namely the calculation rules. For quantum computation, computing object is to obey the basic principle of quantum mechanics that quantum information is represented by quantum states and calculation rule is unitary transformation and measurement of closed physical environment. Quantum computing steps can be summarized in the following three steps: 1) Initialization: The classical information is transformed into the corresponding quantum states through some form of encoding, namely the initial preparation process. 2) Evolution: The process of unitary evolution of quantum information in the form of a quantum state under basic principle framework of quantum mechanics. In this process, the initial information in accordance with the quantum algorithm gradually steps into the results. 3) Measurement: Transforming the above results of evolution into the classical results by measurement. Based on the physical characteristics of the quantum computation, the advantages of quantum computation are mainly embodied in the following 2 aspects: 1) Quantum parallelism: When the quantum state ( ) with superposition carries out unitary transformation corresponding function f, it can produce results of. According to the postulate of quantum mechanics, the results are the probability linear superposition of the components transformed by function f from the original components of all constituting states. Therefore, all the constituting states about variable x can be generated by once quantum unitary transformation, which is called quantum parallelism. In the classical computer, the above calculation requires n times or n processors to work in parallel; while in the quantum computer, only once transformation to complete the calculations of all the superposition values. It is worth noting that although quantum computation with one operation can produce n implicit results, only one result can be read from them. In addition, due to the quantum no-cloning theorem, an unknown quantum state cannot be copied accurately, which means that the results of quantum computation cannot be saved by copying. Journal of Residuals Science & Technology, Vol. 13, No. 8,

2 2) Entanglement state: Quantum entanglement is a unique phenomenon in quantum mechanics and its physical representation and process are not clear at present, which may be related to the deep physical principles, for example, non fixed domain and so on [3]. The mathematical expression of quantum entanglement can be depicted as that if a state of multiple qubits cannot be represented by tensor product of sub-states in a quantum system, the multiple qubits are in entanglement state. Entanglement state was first proposed by Einstein et al. in 1935, for example Bell state is a typical entanglement state, in which two qubits states cannot be expressed as tensor product. When multiple qubits being in entanglement state, the measurement of the states for some qubits will certainly affect the measurement of other qubits states, even though these qubits located in different spatial positions. For example, when measuring Bell state, measuring for a qubit s state will make to another qubit s state opposite inevitably. Quantum entanglement is an important resource in quantum information, which plays an important role in quantum teleportation, quantum communication, quantum super-dense encoding, quantum key distribution, quantum computation acceleration, quantum error correction, error proofing, etc. Quantum entanglement makes quantum computer more superior than traditional computer. Two entangled quantum states far apart with each other have the instantaneous correlation, i.e. when changing one s state, the other s state changes immediately, which crosses space and time. The related quantum teleportation communication tests have been succeeded. In the case of quantum entanglement, n qubits can possess at most 2 n different states at the same time, these different states can be calculated concurrently in the their qubit carriers, which generates exponential acceleration for quantum computation relative to the classical computation. In addition, quantum Fourier transformation (QFT), quantum teleportation, etc. all may be other potential sources for quantum computing beyond classical computing. Many of the computing problems with high computational complexity (NP problem) are still not effectively calculated in classical computer; while quantum parallelism can make some of quantum algorithms with exponential acceleration. 3. Design of quantum computer architecture 3.1 Quantum computer architecture The definition of a classical computer architecture is proposed in 1964 by Amdahl when introducing the IBM 360 computer system, which can be described as Conceptual structure and functional properties programmers can see in computer [4]. Common quantum computer architecture can also be defined by similar way, i.e. common quantum computer architecture can be regarded as hardware of a set of attributes and functions visible to programmers. The key design of a common quantum computer is its architecture. The architecture of quantum computers not only affects the composition and structure of hardware, but also affects the design of quantum computer software. In order to construct a common quantum computer system with practical application, some basic framework and theoretical and technical barriers must be developed and broken through. Fig. 1 shows the importance of the architecture in the whole quantum computing system and its relationship with other components. Figure 1. The architecture of quantum computer in the context of quantum computation. Quantum computer is a kind of computing system, and its ultimate goal is to run quantum program, which required that the system is not only composed of hardware logic, but also should be composed of control logic and software logic. However, there is less research on the latter. In the hardware logic, quantum computer system should also include fault-tolerant (mainly refers to logical fault tolerance) system, instruction system, quantum compiler, interpreter and the future quantum application. In fact, one of the most important goals of computer architecture research is to determine the components of computer hardware and the connection between the hardware and the software [5]. Therefore, we believe that the establishment of a reasonable, reliable and scalable common quantum computer architecture needs not only physicists, but also computer experts who will consider problems from the view of the computer system, for example, the connections both between the components and functions and the interfaces between hardware and software. In addition, after the establishment of the basic components, we should consider the balance between the system resources in the architecture from the perspective of computer science, which includes following factors: 1) Quantum computing reliability and load balancing of quantum communication. 2) The balance of operation between quantum transport bus-load and quantum information exchange (quantumswap). 3) The balance of quantum application layer requirements and the realization complexity of common quantum logic gates. 4) The balance of computational reliability and complexity of fault tolerant system. 5) The balance between the overhead of quantum storage time and the hierarchical error correcting structure of memory. We have had tracked the studies of quantum computer architecture for many years. The studied are independent with each other and rarely took all factors, such as quantum algorithm, quantum software and quantum resource scheduling, together for consideration of a more balanced computer. Therefore, we propose a scalable quantum computer architecture under consideration of all above factors, called QCSA (Quantum Coherence Sustaining Architecture), which can maintain the quantum coherence in the computational space. The composition of QCSA inherits several major components and main functions of the classic computer, which includes the quantum storage unit, quantum computing and logic processing unit, quantum operation control and resource scheduling unit, quantum initialization unit, and quantum measurement and classical output unit. QCSA is a quantum computer architecture with storage as its center [6-9], of which storage components are depicted as Fig. 2. Journal of Residuals Science & Technology, Vol. 13, No. 8,

3 Figure 2. Quantum storage components of QCSA. In the QCSA architecture, the quantum storage is a core component, which is not only the storage of quantum information (not storing classical information), but also the quantum computing (quantum logic operation) components. In order to protect coherence of quantum information and quantum logic gates operating and avoid the influence of decoherence of environment, we divide qubits in the quantum memory into several unequal blocks, called quantum memory banks, which are responsible for the storage and computation. For each memory bank, two ways are used to protect quantum information: zero decoherence subspace and hierarchical quantum error correcting coding. This design effectively avoids environmental decoherence effects, at the same time reduces the overhead of storage space overhead coming from using of unified quantum error-correcting codes, which makes the lowest rate of logic and physical qubit up to 1:4 [6,10]. Between the storage banks, the channel for quantum communication is called quantum wire [11], which is realized by the Swap command and the Bell state in the instruction set of quantum computer. The quantum wire is a kind of logic channel based on quantum teleportation, and its communication capacity can reach the limit of quantum channel capacity theoretically. In 1999, Gottesman proposed that single quantum logic gate can be calculated while the quantum communication of Bell state is processing. The phenomenon of quantum computing and quantum communication occurring at the same time is called "quantum gate teleportation" [12]. In 2001, Raussendor et al. proved that the calculation of teleportation was not affected by transportation of teleportation [13]. Additionally, in 2003 Neilsen proved that arbitrary bounded error unitary transformation can be realized in the way of teleportation [14]. In this paper, the quantum teleportation, to which is not paid attention in the past, can greatly improve the efficiency of quantum computation in quantum wires introduced in the QCSA architecture. In order to effectively carry out the teleportation of quantum gates in quantum memory, we introduce the long quantum wires, quantum gate teleportation unit (GTU), quantum repeater (QRPT), quantum state purification unit (SPU), entropy exchange unit (EEU) and other special devices in the QCSA architecture. Furthermore, these devices are protected by zero decoherence subspace and hierarchical quantum error correcting codes [10]. Based on the generality of CNOT gates and single qubit gates, Fig. 3 shows a calculation path of quantum information transportation via quantum gate teleportation and Bell measurement and the parallel communication and calculation via remote CNOT [15]. Figure 3. The parallel communication and calculation of quantum information Figure 4. The comparisons of speed, reliability and physical volume between QLA, CQLA and QCSA. Fig.4 shows the comparisons of speed, reliability and physical realization between the QLA, CQLA and QCSA quantum computer architectures by the pyramid form [16]. The results illustrated that QCSA has a whole superiority over other two architectures of OLA and CQLA. 3.2 Quantum Resource Scheduling Journal of Residuals Science & Technology, Vol. 13, No. 8,

4 As shown in Fig. 1, the quantum computer architecture contains an important part, namely the quantum resource scheduling system. From the point of view of computer architecture, the scheduling of quantum resources mainly includes the scheduling of the physical layer and the scheduling of quantum logic gates, both of which involve the instruction set architecture (ISA). ISA is the intermediate architecture between the hardware and software platforms, which is related to the upper processing system of quantum programming language, and the lower system of instruction set. ISA is a kind of structural resource which is independent of the physical realization technology and can be called directly by the quantum language processing system. The quantum instructions in application layer are corresponding to logic qubit logic instructions which directly reflect the quantum algorithm itself without any explicit fault tolerance or error correction commands. When mapping to bottom of the architecture (physical layer), these logical instructions will be automatically decomposed into a sequence of elementary operations (SEO) with fault tolerance or error correction. SEO is a kind of low level quantum language similar to assembly language, which varies according to the current physics platform of quantum computing, which ensures that the QCSA architecture can be run on any of the actual quantum computing devices without any modification, except giving the corresponding SEO of that device. On the instruction scheduling of physical layer, at present, most of the physical platforms of quantum computing have conducted based on the quantum circuit model, so SEO in the physical layer corresponds to the basic quantum logic gate. These logical gates perform different functions, some of which also have requirements for the execution order or have different responses on the physical system after execution. In physical layer, how to schedule the execution order of logical gates, how to reduce the communication and fault physical resource consumption and how to maximize parallel execution of logic gates are problems worth studying. The theory and technology of instruction-level parallelism (ILP) are very mature in the classical computer architecture, but there are still some problems in quantum computing. Studies are aiming to propose a quantum instruction scheduling system of physical layer running on a classical computer, in which accurate predictions of communication, fault tolerance, and computational load can be achieved through analyzing quantum programs; thus, the physical layer instructions can be reasonably scheduled within the fault tolerance threshold in the premise of ensuring the correctness of the program, so as to maximize the degree of ILP as well as balance the system resources for communication and fault tolerance. 3.3 Quantum Software System Software system is very important for any kind of computer system. Software system is the creative minds behind computers or programs. Some develop the application software for clients and companies analyzing the needs of the users. Some develop the system software used to run the devices and to control the networks. Whatever be the nature of work, software system is one of highest-paid fields in this modern day and age. It s an up-and-coming field, as it s believed that it s likely to grow much faster than the average compared to other professions. If you have strong problem solving skills, an eye for details and good understanding at mathematical functions, then you may consider this lucrative field of study that could give you various benefits including higher level of job satisfaction recompensing your creative efforts. Just as the key function to classical computer, quantum software system is indispensable for quantum computer, which need consider the flexibility, extendibility, correctness, practicability, conciseness, device independence, high-level abstraction, transparency, and classical simulation. The quantum software system is located in the upper part of the whole quantum computer system. Although there is no clear definition of quantum software system, we believe that quantum software systems should be similar to classical computer software system, which can be divided into two categories: quantum system software and application software. The quantum computer system can be divided into several levels: quantum application, quantum algorithm, quantum computing model, quantum compiler, quantum operating system, quantum scheduler, and quantum instruction set from view of software, in which the abstract level increases from the bottom to the top [9, 17-20] as illustrated in Fig. 5. The codes of upper level software will be translated into codes or instructions of lower level software until capable of being executed by the quantum hardware while quantum applications are running on a quantum computer. Firstly, quantum applications will call quantum algorithms according to the contents of codes when necessary. Then the quantum algorithms are to be translated into codes of quantum computing model, which are supported by both classical and quantum programming languages. Furthermore, the translated codes of classical and quantum programming languages are compiled or interpreted by quantum compiler and interpreter into specific machine forms capable of being processed by quantum operating system. Finally, quantum operating system will call the quantum scheduler to execute machine codes by scheduling quantum machine instructions set, which is supported by quantum fault-tolerant system. The quantum hardware is the final execution platform of quantum machine codes, which is responsible for execution of the quantum instructions. Figure 5. The architecture of quantum computer from software view. 3.4 Quantum Programming Language and Its Processing System Journal of Residuals Science & Technology, Vol. 13, No. 8,

5 In classical computer systems, programming language and its processing system is an important part of the system software. Quantum programming language has the same status in quantum computer system, which is beneficial to the theoretical verification and complexity analysis of quantum algorithms, to the description and verification of quantum communication protocols, and to the realization of quantum algorithms and quantum protocols. Quantum programming languages are used to write quantum programs to implement quantum algorithms, quantum protocols, and general quantum computation. From the point of view of program theory, software engineering and programming, the design of a suitable quantum programming language and its processing system should comply with the following guidelines: 1) Correctness: The programming language can correctly describe the set of elements of quantum and classical computation, quantum/classical data structures and all known quantum algorithms. The syntax and semantics are accurate, the program is unambiguous, and the language processing system should be able to translate the well-defined program into the target code. 2) Practicability: The practicability of common quantum programming language means that the programming language can be implemented in certain device (classical device, hybrid device, and pure quantum device) and can write a variety of quantum algorithms running in the corresponding equipment. 3) Conciseness: The conciseness of quantum programming language refers to grammar, structure, interface, document should be simple and clear, in order to make the program easy to write, read and maintain. 4) Device independence: Device independence refers to that the writing and the implementation of quantum programs have nothing to do with the physical device running the quantum program. The processing system of the quantum programming language should be able to translate the source program into the target language instruction set of the related platform automatically. 5) High-level abstraction: A good quantum programming language should have a high level of abstraction, which can describe the characteristics of classical computation, especially quantum computation in the semantic layer. 6) Transparency: A good quantum programming language should make some of the features and problems of quantum computing transparent to the user. 7) Classical simulation: Although the ultimate goal of a quantum programming language is oriented to a quantum computer, it should first support simulation on a classical computer. Compared with the programming language, the design of quantum language processing system is more comprehensive. The quantum processing program is located at the bottom of the software logic layer above the ISA and quantum fault-tolerant micro architecture (FTMA) with less dependence on architecture interface layer and hardware logic layer illustrated as Fig. 6. Figure 6. The composition of quantum language processing program. The quantum processing program transforms the quantum language with high level semantics into the interface layer instruction language by the way of quantum wire optimization. The design flow of a quantum compiler that considers the overall reliability and scalability of a fault-tolerant quantum computer architecture is shown in Fig Expectation Figure 7. The design of a quantum program complier with the reliability and scalability. From the current research situation, the realization of common quantum computer is not smooth. For a long time in the future, the research of quantum computer is still a challenge. The following efforts on quantum computing field may take a chance to change the present situation in the future. 1) Improve the reliability of quantum system [21-30]. The hierarchical fault-tolerant architecture and the hierarchical quantum error correcting codes can be considered to balance the time and physical cost of fault tolerance. At the same time, the method of zero decoherence subspace may be introduced to improve the immunity of the system to decoherence. 2) Improving the scalability of quantum systems. The effect of quantum long distance may be considered as an extension of different quantum storage. In the latest report, multiple degrees of freedom of a single qubit carrier (such as photon) have been used as teleportation of multi-degree of freedom and super-dense transmission [21, 31-42]. Since there are physical isolations between degrees of freedom, it may also help to improve the scalability of quantum systems. Journal of Residuals Science & Technology, Vol. 13, No. 8,

6 3) Research on quantum algorithm [43-57]. Compared with the classical algorithm, the proposed quantum algorithm is far less than the former in terms of type and scope of solving the problem [58-62]. Especially in the past 15 years, the research of quantum algorithms is lagging behind the research of quantum computing devices. Research on quantum algorithm is a valuable direction in quantum computer for researchers who have the background of Computer Science. Acknowledgements The authors acknowledge the National Natural Science Foundation of China ( , , ) and the National Basic Research Program of China (973 Program, 2012CB821478). References [1] Feynman R P. Simulating physics with computers. International journal of theoretical physics, 1982, 21(6): [2] Deutsch D. Quantum theory, the Church-Turing principle and the universal quantum computer//proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences. 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