Quantum Algorithms in Open Quantum Systems
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Beschreibung
This book offers a comprehensive introduction to quantum computation in the presence of noise: how noise arises in real quantum hardware, how it limits computation, and the strategies developed to correct and mitigate it. Designed to be accessible, it requires only a basic knowledge of quantum mechanics.
The book begins by laying the foundations of quantum computation — qubits, gates, universality, and computational complexity — and works through the canonical quantum algorithms, from Deutsch–Jozsa and Grover to the quantum Fourier transform, phase estimation, Shor's factoring algorithm, and quantum key distribution. It then turns to variational quantum algorithms as a practical, near-term application of noisy devices. Next, it characterises the main sources of noise affecting quantum systems and develops the central ideas of quantum error correction, building from the repetition codes to the stabiliser formalism, the surface code, and the principles of fault-tolerant and measurement-based quantum computation.
While fully fault-tolerant quantum computation remains a future goal, the book also explores techniques to suppress and mitigate noise on present-day hardware, such as dynamical decoupling and quantum error mitigation, framed within the theory of open quantum systems. Throughout the text, worked examples and exercises are provided.
This book offers a comprehensive introduction to quantum computation in the presence of noise: how noise arises in real quantum hardware, how it limits computation, and the strategies developed to correct and mitigate it. Designed to be accessible, it requires only a basic knowledge of quantum mechanics.
The book begins by laying the foundations of quantum computation — qubits, gates, universality, and computational complexity — and works through the canonical quantum algorithms, from Deutsch–Jozsa and Grover to the quantum Fourier transform, phase estimation, Shor's factoring algorithm, and quantum key distribution. It then turns to variational quantum algorithms as a practical, near-term application of noisy devices. Next, it characterises the main sources of noise affecting quantum systems and develops the central ideas of quantum error correction, building from the repetition codes to the stabiliser formalism, the surface code, and the principles of fault-tolerant and measurement-based quantum computation.
While fully fault-tolerant quantum computation remains a future goal, the book also explores techniques to suppress and mitigate noise on present-day hardware, such as dynamical decoupling and quantum error mitigation, framed within the theory of open quantum systems. Throughout the text, worked examples and exercises are provided.
Fills a gap in educational materials by covering modern quantum error correction and error mitigation algorithms Written in a clear and intuitive style, ideal for advanced undergraduate and graduate courses Includes fully detailed calculations to ensure readers can thoroughly understand every step of the process
Autor*in
Matteo Carlesso
Themen in »Quantum Algorithms in Open Quantum Systems«
Foundations of Quantum Computation Quantum Fourier Transform and Phase Estimation Harrow-Hassidim-Lloyd (HHL) Algorithm Quantum Annealing and Optimization Techniques Quantum Error Correction Codes (Shor, Surface, and Repetition) Stabilizer Codes and Fault-Tolerant Quantum Computation Adiabatic Theorem in Quantum Computing Variational Quantum Eigensolver (VQE) and QAOA Applications Noisy Intermediate-Scale Quantum (NISQ) Computing Dynamical Decoupling and Error Mitigation Techniques