Ph.D. Thesis - Physics

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[DLC + 09b] N. Daniilidis, T. Lee, R. Clark, S. Narayanan, and H. Häffner. Wiring up trapped ions to study aspects of quantum information. J. Phys. B., to appear, 2009. [DOS + 06] L. Deslauriers, S. Olmschenk, D. Stick, W. K. Hensinger, J. Sterk, and C. Monroe. Scaling and suppression of anomalous heating in ion traps. Phys. Rev. Lett., 97, 103007, 2006. [DRS03] J. Dukelsky, J. M. Roman, and G. Sierra. Comment on “Polynomial-time simulation of pairing models on a quantum computer”. Phys. Rev. Lett., 90, 249803–1, 2003. [DS96] D. P. DiVincenzo and P. W. Shor. Fault-tolerant error correction with efficient quantum codes. Phys. Rev. Lett., 77, 3260, 1996. [DS99] J. Dukelsky and G. Sierra. A density matrix renormalization group study of ultrasmall superconducting grains. Phys. Rev. Lett., 83, 172, 1999. [EKN68] L. E. Estes, T. H. Keil, and L. M. Narducci. Quantum-mechanical description of two coupled harmonic oscillators. Physical Review, 175, 286–299, 1968. [ESL + 07] R. J. Epstein, S. Seidelin, D. Leibfried, J. H. Wesenberg, J. J. Bollinger, J. M. Amini, R. B. Blakestad, J. Britton, J. P. Home, W. M. Itano, J. D. Jost, E. Knill, C. Langer, R. Ozeri, N. Shiga, and D. J. Wineland. Simplified motional heating rate measurements of trapped ions. Phys. Rev. A, 76, 033411, 2007. [Fey82] R. Feynman. Simulating physics with computers. Int. J. Theor. Phys., 21, 467, 1982. [Fis76] J. R. Fisk. Helical-resonator design techniques. QST, p. 11, 1976. [FKW02] M. H. Freedman, A. Kitaev, and Z. Wang. Simulation of topological field theories by quantum computers. Comm. Math. Phys., 227, 587, 2002. [FSG + 08] A. Friedenauer, H. Schmitz, J. Glückert, D. Porras, and T. Schätz. Simulating a quantum magnet with trapped ions. Nature Physics, 4, 757, 2008. [GC97] N. Gershenfeld and I. L. Chuang. Bulk spin-resonance quantum computation. Science, 275, 350, 1997. [GC99] D. Gottesman and I. L. Chuang. Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations. Nature, 402, 390, 1999. [Gho95] P. K. Ghosh. Ion Traps. Oxford Science Publications, 1995. [GKK + 08] D. Gavinsky, J. Kempe, I. Kerenidis, R. Raz, and R. de Wolf. Exponential separation for one-way quantum communication complexity, with applications to cryptography. www.arxiv.org: quant-ph/0611209v3, 2008. [GL50] V. L. Ginzburg and L. D. Landau. Zh. Eksperim. i Teor. Fiz., 20, 1064, 1950. 220
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Page 1:
An Investigation of Precision and S
Page 5 and 6:
Acknowledgments What a long, strang
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should totally start a band. I also
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2.4 Conclusions and further questio
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7.6.1 Regular array of stationary q
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List of Figures 2-1 The CNOT gate i
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7-12 Magnetic fields due to a “tr
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Chapter 1 Introduction The growth o
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1.1 Quantum information The concept
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us whether the target system obeys
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Nevertheless, there are a number of
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Digital Analog Classical Quantum Sp
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electrodes [TKK + 99]. This heating
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Digital Analog Classical Quantum Sp
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2. Initialization to a simple fiduc
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qubits, and in Ref. [SGA + 05] in t
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the lattice architecture, we discov
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1.6 Contributions to this work In t
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5) Ref. [DLC + 09b] Wiring up trapp
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Chapter 2 Quantum simulation using
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µN the nuclear magneton, and B0 th
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⎡ ⎤ a 0 0 0 ⎢ ⎥ ⎢ ρ2 =
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The same effect as number 2 above i
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where V0 is the maximum signal stre
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actions that occur between nuclei i
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Figure 2-2: The 2,3-dibromothiophen
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detail how this was done with a sim
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and thus requires invocation of the
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Renormalization Group (DMRG), with
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3.3 The bounds on precision In this
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Figure 3-1: A schematic of a generi
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Figure 3-3: The 11.7 T, 500 MHz sup
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. Figure 3-4: The above probe is a
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Figure 3-5: The CHFBr2 molecule. Al
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Figure 3-6: Frequency-domain spectr
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used to extract the answer is irrel
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Chapter 4 Theory and history of qua
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GND RF r ENDCAP 0 z 0 ENDCAP Ring T
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where Q is the charge of the trappe
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angular momentum along the quantiza
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emission from the excited state |
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selection rule ∆m = ±1 is applie
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Figure 4-3: Schematic diagram of sp
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to address an ion in state |↑〉
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the vibrational temperature is low.
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to the design of the trap itself. M
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to the quantum-mechanical ground st
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Chapter 5 Lattice ion traps for qua
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Figure 5-1: Schematic of the lattic
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Figure 5-3: Fit to Eq. 5.2 of the C
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Figure 5-4: The vacuum chamber for
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weeks. Low pressures depend on choo
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Figure 5-5: Left: Level diagram for
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Figure 5-7: (a) Schematic of the cr
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(a) Lattice Trap Schematic TOP PLAT
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mix the microspheres evenly in the
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Using the expression for ωˆr deri
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Figure 5-15: Plot of the motional c
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Figure 5-17: Dependence of the trap
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Chapter 6 Surface-electrode PCB ion
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Figure 6-1: Schematic of a linear i
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Figure 6-2: Layout of the trap elec
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Figure 6-3: Above are the cross sec
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Figure 6-6: Photograph of the trap
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Figure 6-8: CCD image of a cloud of
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Figure 6-9: Measurement results sho
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Figure 6-11: Bastille mounted in th
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Figure 6-13: A diagram of the setup
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Figure 6-14: A plot of the trapped
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allows us to upper-bound the amount
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Chapter 7 Quantum simulation in sur
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Figure 7-1: Left: Uraniborg 1, as r
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Figure 7-3: Calculated secular freq
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Figure 7-5: Left: Structure of 2-D
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Figure 7-7: Scaling of the order of
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involved. Because ions near the cen
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Results Before presenting the numer
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Figure 7-10: Calculation results fo
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7.3 Magnetic gradient forces Now th
Page 169 and 170: Figure 7-13: Scaling of the J-coupl
Page 171 and 172: how are single-ion operations to be
Page 173 and 174: 250 psi, which increases to around
Page 175 and 176: Figure 7-18: At the center of this
Page 177 and 178: Figure 7-19: The plastic socket tha
Page 179 and 180: Figure 7-21: The two internal lense
Page 181 and 182: Figure 7-22: Measured secular frequ
Page 183 and 184: Along ˆy, the spacing is dˆy = 28
Page 185 and 186: of O2 to 2 × 10 −12 torr. Decohe
Page 187 and 188: Part III Toward ion-ion coupling ov
Page 189 and 190: Chapter 8 Motivation for and theory
Page 191 and 192: Figure 8-1: Schematic of the experi
Page 193 and 194: are in close agreement in the case
Page 195 and 196: 8.2.3 Simulated coupling rates We n
Page 197 and 198: Johnson noise We begin our discussi
Page 199 and 200: should suffice. Note that the above
Page 201 and 202: Chapter 9 Measuring the interaction
Page 203 and 204: Figure 9-2: Left: Level diagram for
Page 205 and 206: Figure 9-5: Photograph of the micro
Page 207 and 208: A fit of the resulting curve return
Page 209 and 210: Figure 9-9: Linear fit of the ωˆy
Page 211 and 212: Figure 9-12: Heating rate as determ
Page 213 and 214: Chapter 10 Conclusions and outlook
Page 215 and 216: traps, linking ions using photons,
Page 217 and 218: Bibliography [ADM05] Paul M. Alsing
Page 219: [CGB + 94] J. I. Cirac, L. J. Garay
Page 223 and 224: [LCL + 07] D. R. Leibrandt, R. J. C
Page 225 and 226: [PC04a] D. Porras and J. I. Cirac.
Page 227 and 228: [TBZ05] L. Tian, R. Blatt, and P. Z
Page 229 and 230: Appendix A Matlab code for Ising mo
Page 231 and 232: err_result = mean(theerr) 231
Page 233 and 234: J = J0; Jt(1) = J; Bt(1) = B; for k
Page 235 and 236: A.3 Simulation with constant force
Page 237 and 238: Appendix B Mathematica code for ion
Page 239 and 240: 2 crystal_shape_6uraniborg.nb Out[6
Page 241 and 242: Appendix C How to trap ions in a cl
Page 243 and 244: Finally, we note that the chilled w
Page 245 and 246: C.4 Laser alignment and imaging As
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