Publication
Integration of time in a quantum process algebra
| Summary: | Process algebras are mathematical structures used in Computer Science to study, model, and verify concurrent systems. Essentially, a process algebra consists of a language (used to specify a system that one wishes to study), a semantic domain to interpret the language (which allows the interpretation and the study of the system) and a set of axioms related to the language operators (which facilitates the derivation of properties of the system be ing studied). These basic ingredients make process algebras powerful tools, with many applications in the development of concurrent systems and many successful stories in in dustry, Bunte et al. (2019); Groote and Mousavi (2014). The three classical examples of a process algebra are: CCS introduced by Robin Milner, ACP introduced by Jan Bergstra and Jan Willem Klop, and CSP introduced by Tony Hoare. Of the three, the first stands out because of its main goal to isolate and study the elementary principles of communication and concurrency. The development of Quantum Mechanics supports the design of computational systems ruled by quantum laws, which, in the context of certain problems, perform significantly better than any classical computational system. This is exemplified with Shor and Grover algorithms, respectively used in the factorization of integers and in unstructured searching. Moreover, Quantum computing has applications in the communications area, having as main examples the quantum teleportation protocol and the BB84 communication protocol. However, due to their high sensitivity to noise, quantum computers have a very limited memory space, and therefore they usually integrate a QRAM architecture: essentially, a net work of classical computers that process and manage a general task list, invoking quantum computers only when high-cost computational tasks arise. This highlights the importance of extending the theory of process algebras to the quantum domain. In fact, some quantum process algebras were already proposed in last years: examples include qCCS, developed by Mingsheng Ying et al based on CCS, and the CQP algebra, introduced by Simon Gay and Rajagopal Nagarajan. Related to qCCS, a typing system was developed, where the typable processes are exactly the valid qCCS processes. Current quantum process algebras assume the existence of an ideal quantum system, i.e. a quantum system immune to noise. In contrast, the aim of this dissertation is to study and develop a quantum process algebra in which this assumption is discarded. More specifically, we do not assume that a quantum state can be stored indefinitely, it may become corrupted over time, or in other words, have a limited time of coherence. For that goal, 1) we developed a new quantum process algebra that merges the strengths of qCCS and CQP, in particular, recursion, memory allocation, and a typing system, so that we can study complex quantum systems that integrate the QRAM architecture; 2) we extended the new process algebra with a notion of time so that we could study its effects on quantum states; and 3) we developed a number of case studies, via the mentioned extension, in which the coherence time of quantum systems has a central role. This includes, for example, a simplified version of the IBM Cloud, which provides access to a quantum computer via web. |
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| Main Authors: | Fernandes, Vítor Emanuel Gonçalves |
| Subject: | Concurrency Process algebra Quantum Time CCS qCCS TCCS TqCCS Concurrência Álgebra de processos Quântica Tempo Ciências Naturais::Ciências da Computação e da Informação |
| Year: | 2019 |
| Country: | Portugal |
| Document type: | master thesis |
| Access type: | open access |
| Associated institution: | Universidade do Minho |
| Language: | English |
| Origin: | RepositóriUM - Universidade do Minho |
| Summary: | Process algebras are mathematical structures used in Computer Science to study, model, and verify concurrent systems. Essentially, a process algebra consists of a language (used to specify a system that one wishes to study), a semantic domain to interpret the language (which allows the interpretation and the study of the system) and a set of axioms related to the language operators (which facilitates the derivation of properties of the system be ing studied). These basic ingredients make process algebras powerful tools, with many applications in the development of concurrent systems and many successful stories in in dustry, Bunte et al. (2019); Groote and Mousavi (2014). The three classical examples of a process algebra are: CCS introduced by Robin Milner, ACP introduced by Jan Bergstra and Jan Willem Klop, and CSP introduced by Tony Hoare. Of the three, the first stands out because of its main goal to isolate and study the elementary principles of communication and concurrency. The development of Quantum Mechanics supports the design of computational systems ruled by quantum laws, which, in the context of certain problems, perform significantly better than any classical computational system. This is exemplified with Shor and Grover algorithms, respectively used in the factorization of integers and in unstructured searching. Moreover, Quantum computing has applications in the communications area, having as main examples the quantum teleportation protocol and the BB84 communication protocol. However, due to their high sensitivity to noise, quantum computers have a very limited memory space, and therefore they usually integrate a QRAM architecture: essentially, a net work of classical computers that process and manage a general task list, invoking quantum computers only when high-cost computational tasks arise. This highlights the importance of extending the theory of process algebras to the quantum domain. In fact, some quantum process algebras were already proposed in last years: examples include qCCS, developed by Mingsheng Ying et al based on CCS, and the CQP algebra, introduced by Simon Gay and Rajagopal Nagarajan. Related to qCCS, a typing system was developed, where the typable processes are exactly the valid qCCS processes. Current quantum process algebras assume the existence of an ideal quantum system, i.e. a quantum system immune to noise. In contrast, the aim of this dissertation is to study and develop a quantum process algebra in which this assumption is discarded. More specifically, we do not assume that a quantum state can be stored indefinitely, it may become corrupted over time, or in other words, have a limited time of coherence. For that goal, 1) we developed a new quantum process algebra that merges the strengths of qCCS and CQP, in particular, recursion, memory allocation, and a typing system, so that we can study complex quantum systems that integrate the QRAM architecture; 2) we extended the new process algebra with a notion of time so that we could study its effects on quantum states; and 3) we developed a number of case studies, via the mentioned extension, in which the coherence time of quantum systems has a central role. This includes, for example, a simplified version of the IBM Cloud, which provides access to a quantum computer via web. |
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