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American Journal of Physics

Building an adiabatic quantum computer simulation in the classroom

Javier Rodríguez-Laguna, Silvia N. Santalla

Published Apr 19, 2018• 4 citations
Publisher

Abstract

We present a didactic introduction to adiabatic quantum computation (AQC) via the explicit construction of a classical simulator of quantum computers. This constitutes a suitable route to introduce several important concepts for advanced undergraduates in physics: quantum many-body systems, quantum phase transitions, disordered systems, spin-glasses, and computational complexity theory.

DOI
10.1119/1.5021360

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We present a didactic introduction to adiabatic quantum computation (AQC) via the explicit construction of a classical simulator of quantum computers. This constitutes a suitable route to introduce several important concepts for advanced undergraduates in physics: quantum many-body systems, quantum phase transitions, disordered systems, spin-glasses, and computational complexity theory.
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Abstract This book is an introduction to explicitly time-dependent physics. We describe the theory of the dynamic regime that we refer to as “quasi-adiabatic”. It pertains to time-dependent evolution that, while slow, is not genuinely adiabatic. It is rich in effects that can be understood even in quantum systems with complex many-body interactions. Examples from research in quantum computing, phase transitions, Bose-Enstein condensates, and quantum control will be used to illustrate these effects. Prerequisites include undergraduate introductory courses in quantum and classical mechanics, as well as complex analysis. Our book aims to fill the gap in the literature by providing an accessible, for early graduate and advanced undergraduate students, introduction to both geometric phases and nonadiabatic transitions at a level sufficient to consider numerous applications.
In this thesis we summarize the principles of quantum computing. We specifically consider adiabatic quantum computing, whose principles are explained and shown on several examples. To explain the principle of adiabatic quantum computing we review the adiabatic theorem. We also outline possibility of using a particular Hamiltonian by Berry, which enables us to evolve system adiabatically in arbitrarily short time. In the final part of this thesis, we explain the concept of quantum phase transitions. We discuss a relationship between quantum phase transitions and adiabatic quantum computing and show that adiabatic quantum computing scales polynomially with the number of qubits only for quantum phase transitions of second or higher order. Powered by TCPDF (www.tcpdf.org)
Adiabatic Quantum Computation (AQC) is a quantum model proposed by Farhi, et al., in 2000, and has been proven to be equivalent to conventional quantum computation (quantum gate model). Unlike classical computation or conventional quantum (gate) model in which an algorithm is discrete, an adiabatic quantum algorithm is continuous. In this talk, I will give an introduction of AQC, in particular, on the design and analysis of adiabatic quantum algorithms for the NP-hard maximum independent set problem. I will also discuss the adiabatic quantum architecture design and minor-embedding problems.
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Quantum computing introduces a revolutionary approach to solving problems that are computationally beyond the reach of classical systems. Among its most promising applications is the simulation of many-body systems, where strong particle interactions lead to complex quantum behaviors. Traditional computational techniques often fail due to exponential resource requirements, but quantum simulators can efficiently model these interactions through entanglement and superposition. Recent advances in superconducting qubits, trapped ions, and photonic quantum devices have enabled small- scale experimental demonstrations of spin models, Hubbard systems, and correlated electron dynamics. These developments offer new insights into condensed matter physics and quantum phase transitions. As quantum technologies continue to evolve, they hold the potential to transform the study of materials, superconductivity, and other many-body phenomena with remarkable precision and scalability.