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Table 11.12: Bell Violation Results By Section – Resonator Coupling Section S Violation 1 2.06952 ± 0.00138 50.3σ 2 2.07227 ± 0.00134 53.9σ 3 2.07003 ± 0.00139 50.3σ 4 2.07249 ± 0.00137 53.1σ 5 2.06769 ± 0.00141 48.0σ 6 2.06661 ± 0.00143 46.7σ 7 2.07200 ± 0.00144 50.1σ 8 2.07419 ± 0.00142 52.4σ 9 2.06758 ± 0.00144 46.8σ 10 2.06933 ± 0.00146 47.6σ 11 2.07177 ± 0.00138 52.1σ 12 2.07251 ± 0.00130 55.8σ 13 2.07573 ± 0.00144 52.6σ 14 2.07739 ± 0.00137 56.3σ 15 2.07413 ± 0.00142 52.1σ 16 2.07482 ± 0.00146 51.4σ 17 2.07679 ± 0.00138 55.7σ 18 2.07646 ± 0.00140 54.6σ 19 2.08055 ± 0.00135 59.5σ 20 2.07769 ± 0.00137 56.9σ 21 2.07438 ± 0.00138 54.0σ 22 2.07197 ± 0.00145 49.7σ All 2.07320 ± 0.00030 244.0σ 268
20 minutes worth of data. Within each section, the standard error can now be assumed to be dominated by statistical sampling noise, i.e. the errors on S are independent of each other. The standard analysis technique described in Section 11.2.3 then yields 22 S-values with their standard errors as shown in Table 11.12. With this, we can now claim a violation of the Bell inequality by 59.5σ with an S-value of 2.08055 ± 0.00135 based on section 19. Each section’s S i and σ i imply a probability (erfc S i−2.0 σ i ≈ 10 −1200 ) for the actual S-value of that section to be less than 2.0. The probability for the actual S-value of the combined dataset to be less than 2.0 is then the product of the probabilities for the individual sections: P S
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UNIVERSITY of CALIFORNIA Santa Barb
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Benchmarking the Superconducting Jo
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viii
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Curriculum Vitæ Markus Ansmann Edu
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99:187006 Lisenfeld, J., Lukashenko
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Abstract Benchmarking the Supercond
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Contents Contents List of Figures L
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4.1.3 Readout Squid Parameters . .
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7.5.5 Grapher . . . . . . . . . . .
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11.5 Analysis and Verification . .
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List of Figures 2.1 Inductor-Capaci
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List of Tables 3.1 Transition Matri
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Chapter 1 Quantum Computation 1.1 M
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for such problems include factoring
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if present encrypted data will rema
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In terms of quantum bits, this mean
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1.2.3 Implications - The EPR Parado
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proposed architecture of quantum bi
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“coherence times”, i.e. the tim
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Chapter 2 Superconducting Josephson
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of the glue-circuitry needed to con
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Figure 2.1: Inductor-Capacitor Osci
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• The circuit needs to be cooled
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Figure 2.2: Josephson Tunnel Juncti
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the trace along the V-axis, gives c
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Figure 2.4: Josephson Qubits: Sligh
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the cosine forms a local minimum al
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Figure 2.5: Example Qubit Coupling
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Readout schemes can further be cate
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states in the qubit’s inductor, t
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at time t. r is not restricted to b
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3.1.2 Effects of a Time Dependent P
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In some cases, it is possible to so
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Figure 3.1: Examples of Numerical S
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• The energy difference between t
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like this: V = ( V (−1, −1), V
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Figure 3.2: Simulation of LC Oscill
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Table 3.1: Transition Matrix Elemen
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with ω mn = Em−En . Multiplying
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α, it can be ignored. Thus, the in
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e solved exactly: A(t + ∆t) = e
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qubits would be simulated using: A(
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This calculation assumes that the s
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Decoherence consists of two parts:
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Note the difference in signs of the
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Chapter 4 Designing the Phase Qubit
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mutual inductance between the qubit
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During the measurement, the | 1 〉
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the right impedance transformation
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excitations. Since these are a pote
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Figure 4.3: Squid I/V Traces - a) L
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Figure 4.5: Qubit Integrated Circui
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The geometry of the qubit junction
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squid loop. Thus, this tool can be
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now, amorphous silicon seems to pro
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Figure 5.1: L-Edit Mask Layout Tool
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Figure 5.2: Fabrication Building Bl
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Figure 5.3: Photolithography and Et
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times the removal can be a bit tric
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Figure 5.4: Clearing Vias from Nati
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5.6 Junction Layers 5.6.1 Oxidation
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top wiring layer to protect all low
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104
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6.1 Physical Quality Control during
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6.1.3 Atomic Force Microscopy To re
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Figure 6.1: 4-Wire Measurement - a)
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6.3 Quantum Measurements at 25 mK 6
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seems to be a box machined out of s
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Figure 6.2: Dilution Refrigerator W
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cessing data. This protects the vol
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6.3.9 Anritsu Microwave Source The
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122
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ment, the scalability requirements,
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people without any formal training
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7.2.4 Performance Last, but certain
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or a Client Module. Client Modules
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second Module talks to all these an
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puters to talk to each other. Usual
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7.3.4 Performance Addressing the Pe
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is designed such that the LabRAD Ma
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Table 7.3: LabRAD Type Annotations
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listed in Table 7.3. For transmissi
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Architecture to manage network conn
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Manager. In fact, in our lab, the o
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waiting for their completion. The C
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mentation of pipelining and certain
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Since the API guarantees that all R
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one microwave line for X/Y-rotation
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7.5.3 DC Rack Server The DC Rack Se
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data taking on the lab servers and
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keys and the ability to set Context
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a certain time. 7.5.9 Optimizer Cli
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ters read from different sub-direct
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efore the execution of the sequence
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can achieve very-close-to hardware
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type to provide a one-stop location
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172
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8.1 Squid I/V Response As explained
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a digital signal via the use of a c
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energy landscape (see Chapter 2.2.3
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Figure 8.3: Squid Steps Failure Mod
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At this point, the squid ramp can b
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starts to tunnel to the neighboring
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Figure 8.5: General Bias Sequence -
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Figure 8.7: Spectroscopy - a) Bias
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Figure 8.8: Rabi Oscillation - a) B
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ensemble with respect to each other
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Figure 8.10: T 1 - a) Bias sequence
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Figure 8.11: Ramsey - a) Bias seque
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phase shift into the middle of the
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photon excitation behaves similarly
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is desirable to modularize the cont
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sequence was run. This allows for t
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possible to read out all qubits cor
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simultaneous application of such me
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Figure 9.4: Capacitive Coupling Swa
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Figure 9.6: Capacitive Coupling Pha
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a phase difference of 0 ◦ rather
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Figure 9.7: Fine Spectroscopy of Re
Page 246 and 247: Figure 9.8: Swapping Photon into Re
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Page 250 and 251: Figure 9.11: Resonator T 1 - a) Seq
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Page 254 and 255: He does not throw dice” [Einstein
Page 256 and 257: (independent of which axis it is),
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Page 260 and 261: For a measurement of two particles
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Page 264 and 265: 10.2.3 Ion and Photon In the attemp
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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 278 and 279: 11.3 Calibration The most difficult
Page 280 and 281: Table 11.4: Sequence Parameters - R
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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
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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
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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
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