Companion to Quantum Computation and Communication

This is a timely, self-contained introduction to the rapidly expanding field of quantum information and computation that avoids detailed mathematical proofs wherever possible. The author uses a mixed exposition between a popular and technical approach, connecting the standard results of the field with more recent developments. A complete but not highly technical textbook for students of physics, mathematics, and computer science.

Mladen Pavicic is a physics professor at the University of Zagreb, Croatia, where he also holds the physics chair at the Faculty of Civil Engineering. After taking his Ph.D. degree in Belgrade in 1986, he stayed at various universities in Germany (Humboldt University, Berlin, Technical University, Berlin, University of Cologne) and the United States (University of Maryland, Baltimore) as a visiting professor. Professor Pavicic has published over 100 articles and several books. He has received the Alexander von Humboltd Research Award several times.

1 Making Computation Faster and Communication Secure: Quantum Solution
1.1 Turing Machine: a Real Machine or . . .
1.2 . . . a Mathematical Procedure
1.3 Faster SuperTuring Computation
1.4 Digital Computers Do not Run on Logic
1.5 Speeding up Computation: Classical Analog Computation . . .
1.6 . . . versus Quantum Physical Computation
1.7 Complexity Limits: Exponential Time
1.8 Energy Limits . . .
1.9 . . . and Reversible Gates
1.10 Ultimate Efficiency: Quantum Computers and Qubits
1.11 Combining andMeasuringQubits: QuantumSuperposition?Qubit Primer
1.15 Generating Qubits: Sources of Photons?Polarization Primer
1.16 Correlating Unpolarized Qubits: Quantum Entanglement
1.17 Separating and Transforming Entanglements: Bell States at a Beam Splitter
1.18 Manipulating and Verifying Entanglements: Superdense Coding
1.19 Copying Qubits? No. Teleporting Qubits!
1.20 Unperformed Measurements Have no Values: KochenSpecker Sets
1.21 Controlling Qubits: Quantum Gates and Circuits
1.22 Self-Sustaining Qubits: Quantum Error Correction
1.23 Flying Qubits Connecting Quantum Chips and Computers: Quantum Repeaters
1.24 Why Classical Cryptography Cannot Keep Secrets for Long . . .
1.25 . . . and why Quantum Cryptography Can?
1.25.1 Entanglement in Action: Deterministic Communication
1.25.2 NoCloning in Action: Probabilistic BB84 Protocol
1.26 WhyThereCanBe noQuantumEavesdroppers? Unconditional Security

2 Quantum Computation and Communication Hardware
2.1 Technological Candidates for Quantum Computation Implementation
2.2 All-Optical Scalable Quantum Computation
2.2.1 Probabilistic Parity Check Gate with a Quantum Encoder
2.2.2 Destructive CNOT Gate
2.2.3 Nondestructive Probabilistic Full CNOT Gate
2.2.4 The Teleportation Trick
2.2.5 Scalable Computation
2.3 Trapped Ions
2.4 Nuclear Magnetic Resonance
2.5 SiliconBased Nuclear Spins?Kane?s Computer
2.6 Quantum Dots
2.6.1 EnergyLevel Design;
Quantum Dots in a Microcavity
2.6.2 Atom-Cavity Interaction between Levels |0> and |1>
2.6.3 Laser-Atom Interaction between |0> and |1>
2.6.4 Atom-Cavity and Laser-Atom Interactions between |0> and |2>
2.6.5 Implementation of a CNOT gate
2.6.6 Reading out the Results;
Perspectives
2.6.7 Spinlevel design; array of coupled quantum dots
2.7 Superconducting Devices
2.7.1 Josephson Junction
2.7.2 Josephson Junction Circuit and Hamiltonian
2.7.3 Josephson Junction Cooper-Pair Box
2.7.4 Superconducting Quantum Interference Device?SQUID
2.7.5 Cooper Pairs
2.7.6 Quantum Gates for Single Qubits
2.7.7 Quantum Gates for Two Qubits?CNOT Gate
2.7.8 Reading out the results

3 Melting Theory with Implementation
3.1 Quantum Network
3.1.1 One-Atom Laser and Atom-Cavity Coupling
3.1.2 Single Photons on Demand
3.1.3 Dark States
3.1.4 Quantum Repeaters Revisited
3.2 Quantum-Classical Coupling: Interaction-Free Computation
3.3 Quantum Algorithms: Quantum or Classical Problems?
3.3.1 Are there Universal Quantum Algorithms?
3.3.2 Quantum Coin?Deutsch?s Algorithm
3.3.3 Deutsch-Jozsa and Bernstein-Vazirani Algorithms
3.3.4 Shor?s Algorithm
3.3.5 Quantum Simulators
4 Beyond Standard Qubit Computation
4.1 Persistent Entanglement
4.2 One-Way Computing and Cluster States
4.2.1 Dumping Reversibility and Unitarity?
4.2.2 Irreversible Measurement Setup
4.2.3 Reversibility and Unitarity Revisited
4.3 Continuous Variables
4.3.1 Continuous Entanglement
4.3.2 Second-Order (One-Photon) vs. Fourth-Order (Two-Photon) Interference
4.3.3 Qubits with Continuous Spatial Degree of Freedom
4.3.4 Universal Quantum Computation with Continuous-Variable Cluster States
5 Epilogue?Hybrid Systems