Qunet wiki https://www2.physics.siu.edu/qunet/wiki/index.php/Quantum_Computation_and_Quantum_Error_Prevention MediaWiki 1.31.7 first-letter Media Special Talk User User talk Qunet Qunet talk File File talk MediaWiki MediaWiki talk Template Template talk Help Help talk Category Category talk Gadget Gadget talk Gadget definition Gadget definition talk 0 1 3081 2809 2022-09-04T19:24:58Z Mbyrd 4 /* Appendices */ wikitext text/x-wiki QUNET IS FREE TO READ! If you would like to ''contribute'' to the qunet wiki book, in other words, if you want to edit QUNET, you must have an account. Click [https://qunet.physics.siu.edu/submit/requestform.html here] to request one. NOTICE -- This site is incomplete. There is no doubt that it has small mistakes and typos and the citations are far from complete. Also, this is a living document so a final form may never exist. Please email errors, typos, corrections and/or comments to Mark Byrd. Please see the [[Appendix G - NOTES and CREDITS|Notes and Credits]] for further information and a list of contributors. ===Table of Contents: Part I -- The Basics=== :&nbsp;&nbsp; <big>[[Preface]]</big> #<big>[[Chapter 1 - Introduction]]</big> ##[[Chapter 1 - Introduction#Introduction|Introduction]] ##[[Chapter 1 - Introduction#An Introduction to Quantum Computation|An Introduction to Quantum Computation]] ##[[Chapter 1 - Introduction#Bits and qubits: An Introduction|Bits and qubits: An Introduction]] ##[[Chapter 1 - Introduction#Obstacles to Building a Reliable Quantum Computer|Obstacles to Building a Reliable Quantum Computer]] #<big>[[Chapter 2 - Qubits and Collections of Qubits]]</big> ##[[Chapter 2 - Qubits and Collections of Qubits#Introduction|Introduction]] ##[[Chapter 2 - Qubits and Collections of Qubits#Qubit States|Qubit States]] ##[[Chapter 2 - Qubits and Collections of Qubits#Qubit Gates|Qubit Gates]] ##[[Chapter 2 - Qubits and Collections of Qubits#The Pauli Matrices|The Pauli Matrices]] ##[[Chapter 2 - Qubits and Collections of Qubits#States of Many Qubits|States of Many Qubits]] ##[[Chapter 2 - Qubits and Collections of Qubits#Quantum Gates for Many Qubits|Quantum Gates for Many Qubits]] ##[[Chapter 2 - Qubits and Collections of Qubits#Measurement|Measurement]] #<big>[[Chapter 3 - Physics of Quantum Information]]</big> ##[[Chapter 3 - Physics of Quantum Information#Introduction|Introduction]] ##[[Chapter 3 - Physics of Quantum Information#Schrodinger.27s_Equation|Schrodinger’s Equation]] ##[[Chapter 3 - Physics of Quantum Information#Density Matrix for Pure States|Density Matrix for Pure States]] ##[[Chapter 3 - Physics of Quantum Information#Measurements Revisited|Measurements Revisited]] ##[[Chapter 3 - Physics of Quantum Information#Density Matrix for Mixed States|Density Matrix for a Mixed State]] ##[[Chapter 3 - Physics of Quantum Information#Expectation Values|Expectation Values]] <!--##[[Chapter 3 - Physics of Quantum Information#Types of Two-state Systems|Types of Two-state Systems]]--> #<big>[[Chapter 4 - Entanglement]]</big> ##[[Chapter 4 - Entanglement#Introduction|Introduction]] ##[[Chapter 4 - Entanglement#Entangled Pure States|Entangled Pure States]] ##[[Chapter 4 - Entanglement#Entangled Mixed States|Entangled Mixed States]] ##[[Chapter 4 - Entanglement#Extensions and Open Problems|Extensions and Open Problems]] #<big>[[Chapter 5 - Quantum Information: Basics and Simple Examples]]</big> ##[[Chapter 5 - Quantum Information: Basics and Simple Examples#Introduction|Introduction]] ##[[Chapter 5 - Quantum Information: Basics and Simple Examples#No Cloning!|No Cloning!]] ##[[Chapter 5 - Quantum Information: Basics and Simple Examples#Uncertainty Principle|Uncertainty Principle]] ##[[Chapter 5 - Quantum Information: Basics and Simple Examples#Quantum Dense Coding|Quantum Dense Coding]] ##[[Chapter 5 - Quantum Information: Basics and Simple Examples#Teleporting a Quantum State|Teleporting a Quantum State]] ##[[Chapter 5 - Quantum Information: Basics and Simple Examples#QKD: BB84|QKD: BB84]] #<big>[[Chapter 6 - Noise in Quantum Systems]]</big> ##[[Chapter 6 - Noise in Quantum Systems#Introduction|Introduction]] ##[[Chapter 6 - Noise in Quantum Systems#SMR Representation or Operator-Sum Representation|SMR Representation or Operator-Sum Representation]] ##[[Chapter 6 - Noise in Quantum Systems#Modelling Open System Evolution|Modelling Open System Evolution]] ##[[Chapter 6 - Noise in Quantum Systems#Unitary Degree of Freedom in the OSR|Unitary Degree of Freedom in the OSR]] ##[[Chapter 6 - Noise in Quantum Systems#Examples|Examples]] ##[[Chapter 6 - Noise in Quantum Systems#Notes|Notes]] #<big>[[Chapter 7 - Quantum Error Correcting Codes]]</big> ##[[Chapter 7 - Quantum Error Correcting Codes#Introduction|Introduction]] ##[[Chapter 7 - Quantum Error Correcting Codes#Shor's Nine-Qubit Quantum Error Correcting Code|Shor's Nine-Qubit Quantum Error Correcting Code]] ##[[Chapter 7 - Quantum Error Correcting Codes#Quantum Error Correcting Codes: General Properties|Quantum Error Correcting Codes: General Properties]] ##[[Chapter 7 - Quantum Error Correcting Codes#Stabilizer Codes|Stabilizer Codes]] ##[[Chapter 7 - Quantum Error Correcting Codes#CSS Codes|CSS codes]] ##[[Chapter 7 - Quantum Error Correcting Codes#Steane's Seven Qubit Code|Steane's Seven Qubit Code]] #<big>[[Chapter 8 - Decoherence-Free/Noiseless Subsystems]]</big> ##[[Chapter 8 - Decoherence-Free/Noiseless Subsystems#Introduction|Introduction]] ##[[Chapter 8 - Decoherence-Free/Noiseless Subsystems#General Considerations|General Considerations]] ##[[Chapter 8 - Decoherence-Free/Noiseless Subsystems#DNS Examples|DNS Examples]] ##[[Chapter 8 - Decoherence-Free/Noiseless Subsystems#Quantum Computing on a DNS|Quantum Computing on a DNS]] ##[[Chapter 8 - Decoherence-Free/Noiseless Subsystems#QC Examples|QC Examples]] #<big>[[Chapter 9 - Dynamical Decoupling Controls]]</big> ##[[Chapter 9 - Dynamical Decoupling Controls#Introduction|Introduction]] ##[[Chapter 9 - Dynamical Decoupling Controls#General Conditions|General Conditions]] ##[[Chapter 9 - Dynamical Decoupling Controls#The Magnus Expansion|The Magnus Expansion]] ##[[Chapter 9 - Dynamical Decoupling Controls#First-Order Theory|First-Order Theory]] ##[[Chapter 9 - Dynamical Decoupling Controls#The Single Qubit Case|The Single Qubit Case]] ##[[Chapter 9 - Dynamical Decoupling Controls#Extensions|Extensions]] #<big>[[Chapter 10 - Fault-Tolerant Quantum Computing|Chapter 10 - Fault-Tolerant Quantum Computing]]</big> ##[[Chapter 10 - Fault-Tolerant Quantum Computing|Introduction]] ##[[Chapter 10 - Fault-Tolerant Quantum Computing|Requirements for Fault-Tolerance]] ##[[Chapter 10 - Fault-Tolerant Quantum Computing|Concatenated Codes]] ##[[Chapter 10 - Fault-Tolerant Quantum Computing|Fault-Tolerant Quantum Computing for the Steane Code]] #<big>[[Chapter 11 - Hybrid Methods of Quantum Error Prevention]]</big> ##[[Chapter 11 - Hybrid Methods of Quantum Error Prevention|Introduction]] ##[[Chapter 11 - Hybrid Methods of Quantum Error Prevention|General Principles for Combining Error Prevention Methods]] ##[[Chapter 11 - Hybrid Methods of Quantum Error Prevention|Examples of Hybrid Error Prevention]] #<big>[[Chapter 12 - Conclusions and Further Study]]</big> ===Table of Contents: Part II -- Advanced Topics=== #<big>[[Chapter 13 - Topological Quantum Error Correction]]</big> ##[[Chapter 13 - Topological Quantum Error Correction|Introduction]] ##[[Chapter 13 - Topological Quantum Error Correction|The Surface Code]] ===Appendices=== #<big>[[Appendix A - Basic Probability Concepts]]</big> #<big>[[Appendix B - Complex Numbers]]</big> #<big>[[Appendix C - Vectors and Linear Algebra]]</big> ##[[Appendix C - Vectors and Linear Algebra#Introduction|Introduction]] ##[[Appendix C - Vectors and Linear Algebra#Vectors|Vectors]] ##[[Appendix C - Vectors and Linear Algebra#Linear Algebra: Matrices|Linear Algebra: Matrices]] ##[[Appendix C - Vectors and Linear Algebra#More Dirac Notation|More Dirac Notation]] ##[[Appendix C - Vectors and Linear Algebra#Transformations|Transformations]] ##[[Appendix C - Vectors and Linear Algebra#Eigenvalues and Eigenvectors|Eigenvalues and Eigenvectors]] ##[[Appendix C - Vectors and Linear Algebra#Tensor Products|Tensor Products]] #<big>[[Appendix D - Group Theory]]</big> ##[[Appendix D - Group Theory#Introduction|Introduction]] ##[[Appendix D - Group Theory#Definitions and Examples|Definitions and Examples]] ##[[Appendix D - Group Theory#Comparing Groups: Homomorphisms and Isomorphisms|Comparing Groups: Homomorphisms and Isomorphisms]] ##[[Appendix D - Group Theory#Discussion|Discussion]] ##[[Appendix D - Group Theory#Applications to Physics|Applications to Physics]] ##[[Appendix D - Group Theory#A Little Representation Theory|A Little Representation Theory]] ##[[Appendix D - Group Theory#Infinite Order Groups: Lie Groups|Infinite Order Groups: Lie Groups]] ##[[Appendix D - Group Theory#More Representation Theory|More Representation Theory]] #<big>[[Appendix E - Density Operator: Extensions]]</big> ##[[Appendix E - Density Operator: Extensions#Introduction|Introduction]] ##[[Appendix E - Density Operator: Extensions#An N-dimensional Generalization of the Polarization Vector|An N-dimensional Generalization of the Polarization Vector]] ##[[Appendix E - Density Operator: Extensions#The Density Matrix for Two Qubits|The Density Matrix for Two Qubits]] #<big>[[Appendix F - Classical Error Correcting Codes]]</big> ##[[Appendix F - Classical Error Correcting Codes#Introduction|Introduction]] ##[[Appendix F - Classical Error Correcting Codes#Binary Operations|Binary Operations]] ##[[Appendix F - Classical Error Correcting Codes#Definitions and Basics|Definitions and Basics]] ##[[Appendix F - Classical Error Correcting Codes#Linear Codes|Linear Codes]] ##[[Appendix F - Classical Error Correcting Codes#Errors|Errors]] ##[[Appendix F - Classical Error Correcting Codes#The Disjointness Condition and Correcting Errors|The Disjointness Condition and Correcting Errors]] ##[[Appendix F - Classical Error Correcting Codes#The Hamming Bound|The Hamming Bound]] #<big>[[Appendix G - NOTES and CREDITS]]</big> #<big>[[Appendix H: Topics in Quantum Mechanics]]</big> #<big>[[Vectors: A beginner's guide]]</big> #<big>[[Matrices: A beginner's guide]]</big> #<big>[[Binary]]</big> #<big>[[Testing]]</big> #<big>[[Simulation Testing]]</big> <!--#<big>[[Vectors and Matrices: A new beginning]]</big>--> ===Glossary=== <big>[[Glossary]]</big> ===Index=== <big>[[Index]]</big> ===Bibliography=== <big>[[Bibliography]]</big> ===Notation=== <big>[[Notation]]</big> ---- ''Much of this material is based upon work supported by the National Science Foundation under Grant No. 0545798. However, any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.'' 4gaebv45hcuuz8hnqm52u8k29662a8y