0198506961.pdf

286 Quantum computing of such measurements looks like: 1 0, 10 , 01 , 10 , 10 ,.... Each ion gives a random sequence of 0s and 1 ...

13.2 A quantum logic gate 287 13.2 A quantum logic gate Quantum computing uses nothing more than standard quantum mechan- ics bu ...

288 Quantum computing (a) (b) Energy Fig. 13.4(a) The energy levels of two spin-1/2 particles which do not interact with each ot ...

13.3 Parallelism in quantum computing 289 qubit| 0 〉↔| 1 〉, i.e.a| 0 〉+b| 1 〉→a| 1 〉+b| 0 〉. Similarly, pulses at angular frequ ...

290 Quantum computing to 7 in decimals, the quantum computation does all eight calculations simultaneously. Herein lies the grea ...

13.5 Decoherence and quantum error correction 291 13.4 Summary of quantum computers Qubits are quantum objects that store inform ...

292 Quantum computing a few qubits to demonstrate the principle of some elementary opera- tions. These experiments all use state ...

13.6 Conclusion 293 desired energy level. (3) Ion traps confined the ions for long periods with buffer gas cooling. (4) The adve ...

294 Quantum computing The theoretical principles of quantum computing are well understood but there are many practical difficult ...

Exercises for Chapter 13 295 (a) WriteUˆCROTas a 4×4 matrix and show that it is unitary. (b) Equation 13.3 defines the Hadamard ...

296 Quantum computing (d) The operatorUˆZcorresponds to| 0 〉→| 0 〉and | 1 〉→−| 1 〉, for each qubit. Write down the resulting s ...

Exercises for Chapter 13 297 The above figure shows a particular QEC scheme. On the left-hand side, Qubit 1 starts in|x〉and Qubi ...

Appendix A: Perturbation theory A A.1 Mathematics of perturbation theory 298 A.2 Interaction of classical oscillators of similar ...

A.2 Interaction of classical oscillators of similar frequencies 299 When= 0 this leads to a matrix eigenvalue equation similar ...

300 Appendix A: Perturbation theory Fig. A.1An illustration of degener- ate perturbation theory in classical me- chanics, closel ...

A.2 Interaction of classical oscillators of similar frequencies 301 The determinantal equation yields ( ω 12 −ω^2 )( ω 12 +2ω^22 ...

Appendix B: The calculation of electrostatic energies B This appendix describes a method of dealing with the integrals that aris ...

Appendix B: The calculation of electrostatic energies 303 ∫∞ 0 dr 1 r^21 ρ 1 (r 1 ) ∫r 1 0 dr 2 r^22 ρ 2 (r 2 ) e^2 4 πε 0 r 12 ...

304 Appendix B: The calculation of electrostatic energies by electron 2 owing to the presence of electron 1. Whenρ(r 1 )=ρ(r 2 ) ...

Appendix C: Magnetic dipole transitions C The electric dipole transitions that lead to the emission and absorption of light by a ...