Quantum information science / Riccardo Manenti, Mario Motta.

Format:

Book

Author/Creator:

Manenti, Riccardo, author.

Motta, Mario, author.

Series:

Oxford scholarship online.

Oxford scholarship online

Language:

English

Subjects (All):

Quantum computing.

Quantum theory.

Physical Description:

1 online resource (769 pages)

Place of Publication:

Oxford : Oxford University Press, 2023.

Summary:

This title explains quantum information, the science at the basis of the new quantum revolution of this century. Aimed at students who are about to begin a master's program or their graduate studies, it teaches the reader to build and program a quantum computer and leverage its potential.

Contents:

Cover

Titlepage

Copyright

Preface

Contents

PART I FOUNDATIONS

1 Mathematical tools

1.1 Basic notions

1.2 Decision problems

2 Computational models

2.1 Deterministic automata

2.2 Turing machines and complexity classes

2.3 Circuit model

2.4 Church{Turing thesis

2.5 Non-deterministic machines

2.6 Quantum Turing machines

2.7 Quantum algorithms

2.8 QMA problems

3 Linear algebra

3.1 Vector spaces

3.2 Linear operators

4 Quantum mechanics

4.1 Postulates of quantum mechanics

4.2 Expectation value of an observable

4.3 Evolution of quantum systems and projective measurements

4.4 The Hamiltonian of a qubit

4.5 Quantum harmonic oscillator

4.6 Coherent states

4.7 The Jaynes{Cummings Hamiltonian

5 Quantum circuits

5.1 Qubits

5.2 Quantum circuits and Di Vincenzo criteria

5.3 Single-qubit rotations and measurements

5.4 Two-qubit gates

5.5 Universality

5.6 State preparation

5.7 The Clifford group and the Gottesman-Knill theorem

PART II MODERN QUANTUM MECHANICS

6 Density operators

6.1 De nition and examples

6.2 Unitary evolution of a quantum state

6.3 The measurement of a quantum state

6.4 The quantum state of a qubit

6.5 Thermal states

6.6 Composite systems

6.7 Quantum state tomography

7 Quantum maps

7.1 De nition of a quantum map

7.2 Depolarizing channel

7.3 Amplitude damping

7.4 Dephasing

7.5 Transposition

7.6 Kraus representation of a quantum map

7.7 The a ne map

7.8 Quantum maps from unitary evolutions

7.9 Choi{Jamiolkowski isomorphism

7.10 Quantum process tomography

8 Decoherence

8.1 Born-Markov master equation

8.2 The Red eld equation

8.3 Microscopic derivation of amplitude damping

8.4 Relationship between

and the power spectral density.

8.5 Microscopic derivation of pure dephasing

8.6 Decoherence under free evolution: the Bloch equations

Relation between T˚ and the PSD under free evolution

8.8 Hahn-echo experiment

8.9 CPMG sequence

8.10 Decoherence under driven evolution

PART III APPLICATIONS

9 Entanglement

9.1 Definition and examples

9.2 The Schmidt decomposition

9.3 Quantifying entanglement for pure states

9.4 Quantum dense coding

9.5 Quantum teleportation of a qubit state

9.6 Entanglement swapping

9.7 Realism and locality

9.8 Entanglement for mixed states

9.9 Quantifying entanglement of mixed states

10 Early quantum algorithms

10.1 Function evaluation with a quantum computer

10.2 Black-box problems

10.3 Deutsch's algorithm

10.4 Bernstein-Vazirani algorithm

10.5 Grover's algorithm

10.6 Simon's algorithm

10.7 The discrete Fourier transform

10.8 Period finding

10.9 Shor's algorithm

11 Quantum simulation of Hamiltonian dynamics

11.1 Trotterization

11.2 Trotterization at higher orders

11.3 Trotterization of sparse Hamiltonians

11.4 LCU: linear combination of unitaries

11.5 Taylor series

11.6 Qubitization

11.7 Hamiltonian simulation is BQP complete

12 Quantum simulation of Hamiltonian eigenstates

12.1 Quantum phase estimation

12.2 Adiabatic state preparation

12.3 Quantum approximate optimization algorithm

12.4 Variational quantum eigensolver

12.5 Introduction to quantum chemistry

12.6 The variational method

12.7 The Hartree{Fock method

12.8 Second quantization

12.9 Simulating the hydrogen molecule on a quantum computer

PART IV QUANTUM ENGINEERING

13 Microwave resonators for superconducting devices

13.1 Planar resonators

13.2 Parallel resonant circuit

13.3 Transmission lines

13.4 Microwave resonators coupled to a feedline.

13.5 Temperature and power dependence

13.6 Quantization of an LC resonator

13.7 Driving a microwave resonator

13.8 Photon losses

13.9 Preparing a cat state

14 Superconducting qubits

14.1 Introduction

14.2 The Josephson effect

14.3 The Cooper pair box

14.4 The transmon

14.5 The tunable transmon

14.6 Driving a transmon

14.7 Circuit quantum electrodynamics

14.8 Two-qubit gates

Appendix A The rotating wave approximation

A.1 The Rabi model

Appendix B Advanced quantum mechanics

B.1 Pure bipartite states and matrices

B.2 Thermal density operators

Appendix C The quantum Fourier transform

C.1 De nition and circuit implementation

Appendix D The molecular Hamiltonian in second quantization

D.1 The one-body operator

Appendix E Oblivious amplitude ampli cation lemma

E.1 The lemma

Appendix F Quantum signal processing

F.1 Numerical determination of parameters

References

Index.

Notes:

Also issued in print: 2023.

Includes bibliographical references and index.

Description based on online resource and publisher information; title from PDF title page (viewed on August 25, 2023).

Other Format:

Print version: Manenti, Riccardo Quantum Information Science

ISBN:

9780191829598

0191829595

9780191091407

0191091405

OCLC:

1390922597