PDF (double-sided) - Physics Department, UCSB - University of ...

More documents

Recommendations

Info

11.3 Calibration The most difficult part of implementing any qubit experiment is that of calibrating the different control signals. The beauty of the Bell inequality used in this experiment is that its derivation is independent of almost all of these calibrations. If a hidden variable theory existed, the inequality would have to hold for any prepared state of the qubit pair as long as the preparation is entirely independent of the choice of measurement axes. It would also have to hold for any choice of measurement axes a, a ′ , b, and b ′ . It would even have to hold in the presence of energy relaxation, dephasing, and reduced measurement visibility as long as these effects are uncorrelated with the choice of measurement axes and do not introduce artificial correlations into the qubit pair’s state [Kofman and Korotkov, 2008a]. 11.3.1 Global Optimization This implies that it is not necessary to calibrate the relevant experimental parameters in detail independently, but instead gives the freedom to include most of them in a global optimization that maximizes (minimizes) the measured value of S. The parameters that can be included in this optimization are given in Tables 11.3, 11.4, and 11.5. For the optimization, the experiment is simply viewed as an oracle that evalu- 250
Table 11.3: Sequence Parameters – Capacitive State Preparation Name Description Comments Φ A Qubit A flux bias Places qubit far from TLS’s Φ B Qubit B flux bias Places qubits on resonance t π Length of π-pulse Much less than t √ i−Swap A π Amplitude of π-pulse Sufficiently small to avoid | 2 〉-state errors f π Frequency of π-pulse Corrects for AC stark shift → function of A π φ π Phase of π-pulse Shouldn’t matter t √ i−Swap Swap time Can be absorbed into rotation pulse delay ates S as a function of all free parameters. Since it is not possible to measure the derivative of S, the optimization is limited to “Direct Search” methods that do not rely on the knowledge of such derivatives. The algorithms to be used need to further be evaluated with respect to their tolerance for noisy data. Three algorithms seem to be good candidates for this optimization: Manual search, Nelder-Mead Simplex Optimization [Nelder and Mead, 1965], and Particle Swarm Optimization [Eberhart and Kennedy, 1995]. 11.3.2 Manual Search Manual search, as the name suggests, involves the experimenter probing the oracle manually in order to gain an understanding of the behavior of S to eventu- 251
Page 1:
UNIVERSITY of CALIFORNIA Santa Barb
Page 5:
Benchmarking the Superconducting Jo
Page 8 and 9:
viii
Page 11 and 12:
Curriculum Vitæ Markus Ansmann Edu
Page 13 and 14:
99:187006 Lisenfeld, J., Lukashenko
Page 15 and 16:
Abstract Benchmarking the Supercond
Page 17 and 18:
Contents Contents List of Figures L
Page 19 and 20:
4.1.3 Readout Squid Parameters . .
Page 21 and 22:
7.5.5 Grapher . . . . . . . . . . .
Page 23 and 24:
11.5 Analysis and Verification . .
Page 25 and 26:
List of Figures 2.1 Inductor-Capaci
Page 27 and 28:
List of Tables 3.1 Transition Matri
Page 29 and 30:
Chapter 1 Quantum Computation 1.1 M
Page 31 and 32:
for such problems include factoring
Page 33 and 34:
if present encrypted data will rema
Page 35 and 36:
In terms of quantum bits, this mean
Page 37 and 38:
1.2.3 Implications - The EPR Parado
Page 39 and 40:
proposed architecture of quantum bi
Page 41 and 42:
“coherence times”, i.e. the tim
Page 43 and 44:
Chapter 2 Superconducting Josephson
Page 45 and 46:
of the glue-circuitry needed to con
Page 47 and 48:
Figure 2.1: Inductor-Capacitor Osci
Page 49 and 50:
• The circuit needs to be cooled
Page 51 and 52:
Figure 2.2: Josephson Tunnel Juncti
Page 53 and 54:
the trace along the V-axis, gives c
Page 55 and 56:
Figure 2.4: Josephson Qubits: Sligh
Page 57 and 58:
the cosine forms a local minimum al
Page 59 and 60:
Figure 2.5: Example Qubit Coupling
Page 61 and 62:
Readout schemes can further be cate
Page 63:
states in the qubit’s inductor, t
Page 66 and 67:
at time t. r is not restricted to b
Page 68 and 69:
3.1.2 Effects of a Time Dependent P
Page 70 and 71:
In some cases, it is possible to so
Page 72 and 73:
Figure 3.1: Examples of Numerical S
Page 74 and 75:
• The energy difference between t
Page 76 and 77:
like this: V = ( V (−1, −1), V
Page 78 and 79:
Figure 3.2: Simulation of LC Oscill
Page 80 and 81:
Table 3.1: Transition Matrix Elemen
Page 82 and 83:
with ω mn = Em−En . Multiplying
Page 84 and 85:
α, it can be ignored. Thus, the in
Page 86 and 87:
e solved exactly: A(t + ∆t) = e
Page 88 and 89:
qubits would be simulated using: A(
Page 90 and 91:
This calculation assumes that the s
Page 92 and 93:
Decoherence consists of two parts:
Page 94 and 95:
Note the difference in signs of the
Page 97 and 98:
Chapter 4 Designing the Phase Qubit
Page 99 and 100:
mutual inductance between the qubit
Page 101 and 102:
During the measurement, the | 1 〉
Page 103 and 104:
the right impedance transformation
Page 105 and 106:
excitations. Since these are a pote
Page 107 and 108:
Figure 4.3: Squid I/V Traces - a) L
Page 109 and 110:
Figure 4.5: Qubit Integrated Circui
Page 111 and 112:
The geometry of the qubit junction
Page 113 and 114:
squid loop. Thus, this tool can be
Page 115:
now, amorphous silicon seems to pro
Page 118 and 119:
Figure 5.1: L-Edit Mask Layout Tool
Page 120 and 121:
Figure 5.2: Fabrication Building Bl
Page 122 and 123:
Figure 5.3: Photolithography and Et
Page 124 and 125:
times the removal can be a bit tric
Page 126 and 127:
Figure 5.4: Clearing Vias from Nati
Page 128 and 129:
5.6 Junction Layers 5.6.1 Oxidation
Page 130 and 131:
top wiring layer to protect all low
Page 132 and 133:
104
Page 134 and 135:
6.1 Physical Quality Control during
Page 136 and 137:
6.1.3 Atomic Force Microscopy To re
Page 138 and 139:
Figure 6.1: 4-Wire Measurement - a)
Page 140 and 141:
6.3 Quantum Measurements at 25 mK 6
Page 142 and 143:
seems to be a box machined out of s
Page 144 and 145:
Figure 6.2: Dilution Refrigerator W
Page 146 and 147:
cessing data. This protects the vol
Page 148 and 149:
6.3.9 Anritsu Microwave Source The
Page 150 and 151:
122
Page 152 and 153:
ment, the scalability requirements,
Page 154 and 155:
people without any formal training
Page 156 and 157:
7.2.4 Performance Last, but certain
Page 158 and 159:
or a Client Module. Client Modules
Page 160 and 161:
second Module talks to all these an
Page 162 and 163:
puters to talk to each other. Usual
Page 164 and 165:
7.3.4 Performance Addressing the Pe
Page 166 and 167:
is designed such that the LabRAD Ma
Page 168 and 169:
Table 7.3: LabRAD Type Annotations
Page 170 and 171:
listed in Table 7.3. For transmissi
Page 172 and 173:
Architecture to manage network conn
Page 174 and 175:
Manager. In fact, in our lab, the o
Page 176 and 177:
waiting for their completion. The C
Page 178 and 179:
mentation of pipelining and certain
Page 180 and 181:
Since the API guarantees that all R
Page 182 and 183:
one microwave line for X/Y-rotation
Page 184 and 185:
7.5.3 DC Rack Server The DC Rack Se
Page 186 and 187:
data taking on the lab servers and
Page 188 and 189:
keys and the ability to set Context
Page 190 and 191:
a certain time. 7.5.9 Optimizer Cli
Page 192 and 193:
ters read from different sub-direct
Page 194 and 195:
efore the execution of the sequence
Page 196 and 197:
can achieve very-close-to hardware
Page 198 and 199:
type to provide a one-stop location
Page 200 and 201:
172
Page 202 and 203:
8.1 Squid I/V Response As explained
Page 204 and 205:
a digital signal via the use of a c
Page 206 and 207:
energy landscape (see Chapter 2.2.3
Page 208 and 209:
Figure 8.3: Squid Steps Failure Mod
Page 210 and 211:
At this point, the squid ramp can b
Page 212 and 213:
starts to tunnel to the neighboring
Page 214 and 215:
Figure 8.5: General Bias Sequence -
Page 216 and 217:
Figure 8.7: Spectroscopy - a) Bias
Page 218 and 219:
Figure 8.8: Rabi Oscillation - a) B
Page 220 and 221:
ensemble with respect to each other
Page 222 and 223:
Figure 8.10: T 1 - a) Bias sequence
Page 224 and 225:
Figure 8.11: Ramsey - a) Bias seque
Page 226 and 227:
phase shift into the middle of the
Page 228 and 229: photon excitation behaves similarly
Page 230 and 231: is desirable to modularize the cont
Page 232 and 233: sequence was run. This allows for t
Page 234 and 235: possible to read out all qubits cor
Page 236 and 237: simultaneous application of such me
Page 238 and 239: Figure 9.4: Capacitive Coupling Swa
Page 240 and 241: Figure 9.6: Capacitive Coupling Pha
Page 242 and 243: a phase difference of 0 ◦ rather
Page 244 and 245: Figure 9.7: Fine Spectroscopy of Re
Page 246 and 247: Figure 9.8: Swapping Photon into Re
Page 248 and 249: esonator. The latter calibration is
Page 250 and 251: Figure 9.11: Resonator T 1 - a) Seq
Page 252 and 253: 224
Page 254 and 255: He does not throw dice” [Einstein
Page 256 and 257: (independent of which axis it is),
Page 258 and 259: of E xy is measured by expressing i
Page 260 and 261: For a measurement of two particles
Page 262 and 263: 10.2.1 Photons The first and most n
Page 264 and 265: 10.2.3 Ion and Photon In the attemp
Page 266 and 267: 238
Page 268 and 269: 11.1 State Preparation Since the ab
Page 270 and 271: Figure 11.1: Bell State Preparation
Page 272 and 273: Table 11.1: Entangled State Density
Page 274 and 275: Figure 11.2: Bell Measurements - a)
Page 276 and 277: 11.2.3 Statistical Analysis For the
Page 280 and 281: Table 11.4: Sequence Parameters - R
Page 282 and 283: ally determine an optimal value for
Page 284 and 285: ages are based on this method, incl
Page 286 and 287: equires to converge. Since the algo
Page 288 and 289: Table 11.7: Bell Violation Results
Page 290 and 291: Table 11.9: Error Budget - Capaciti
Page 294 and 295: Bell inequality. To make this claim
Page 298 and 299: 11.5.2 Dependence of S on Sequence
Page 300 and 301: point where the measurement happens
Page 302 and 303: The second qubit is not driven and
Page 304 and 305: Figure 11.6: Resonator Coupled Samp
Page 306 and 307: From the resulting states, the 16 p
Page 308 and 309: Table 11.14: Error Budget - Resonat
Page 312 and 313: sponding to a violation by 244.0σ.
Page 314 and 315: educe energy decay and dephasing an
Page 316 and 317: John F. Clauser, Michael A. Horne,
Page 318 and 319: J. Majer, J. M. Chow, J. M. Gambett
Page 320: Matthias Steffen, M. Ansmann, Rados
show all

PDF (double-sided) - Physics Department, UCSB - University of ...

Create successful ePaper yourself

Delete template?

Save as template?