Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
Sequential abstract-state machines capture sequential algorithms
ACM Transactions on Computational Logic (TOCL)
Quantum computing
Quantum computation and quantum information
Quantum computation and quantum information
Logician in the Land of OS: Abstract State Machines in Microsoft
LICS '01 Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science
Abstract state machines capture parallel algorithms
ACM Transactions on Computational Logic (TOCL)
A Guarded Fragment for Abstract State Machines
Journal of Logic, Language and Information
Quantum programming languages: survey and bibliography
Mathematical Structures in Computer Science
Can abstract state machines be useful in language theory?
Theoretical Computer Science
Can abstract state machines be useful in language theory?
DLT'06 Proceedings of the 10th international conference on Developments in Language Theory
SOFSEM'12 Proceedings of the 38th international conference on Current Trends in Theory and Practice of Computer Science
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The ASM thesis says that every algorithm, of any kind, can be modeled step by step and on its natural abstraction level by an abstract state machine. The thesis has been derived from basic principles for sequential algorithms, and for parallel synchronous algorithms. The main result of this paper is that the ASM thesis also holds for quantum algorithms. We first show that, and how, a general model of quantum algorithms (based on the combination of a classical computer with quantum circuits) can be modeled by abstract state machines. Following the approach of Blass and Gurevich to parallel algorithms, we then formulate general postulates for quantum algorithms and show that every algorithm satisfying these postulates is simulated by an appropriate ASM. These "quantum ASMs" are special cases of the parallel ASMs of Blass and Gurevich, but the only unbounded parallelism is inside the quantum operations (unitary transformations and measurements).