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esonator. The latter calibration is preferred as it simultaneously ensures that the excitation indeed was swapped into the resonator rather than a two-level state. For this, a second bias pulse is added to the sequence to sweep one of the other qubits onto resonance with the resonator. The amplitude and length of this second pulse can then be swept to maximize the excitation of the respective qubit. The data looks like Figure 9.9b. 9.3.4 Timing Calibration Due to the absence of measurement crosstalk, it is now no longer as straightforward to calibrate the timing of the bias channels for the different qubits. Instead, the coupling of the excitation through the resonator needs to be used. If the second pulse on the receiving qubit is placed progressively earlier, it will eventually happen before the excitation is fully swapped into the resonator. At this point, the measured final amplitude will decrease as more and more of the excitation remains in the resonator after the swap is over. Since the swaps take a finite time, though, this reduction in the final amplitude happens gradually and might show features resulting from complicated dynamics while both qubits are on resonance with the resonator. Therefore, this method only gives a rough calibration of the timing delay. If the final sequence only requires a single coupling operation in one direction, though, it does not matter too much if the excitation remains in the 220
Figure 9.10: Resonator Swaps – a) Sequence: The second qubit is excited into the | 1 〉 state with a π-pulse (X π ). The qubit is brought on resonance with the resonator for a time t Delay allowing it to swap the state back and forth between the qubit and the resonator. After, the first qubit is brought on resonance for the time needed for one full swap (S) to transfer the state from the resonator into the first qubit. Finally both qubits are measured (M). b) Swaps: The final coupled qubit state oscillates between the | 10 〉 and | 01 〉 state. The measurement error in identifying the | 0 〉 state causes a non-zero probability for measuring | 11 〉. As a function of time, T 1 decays the signal and relaxes the qubits into the | 00 〉 state. resonator for a while before it is retrieved, especially since the T 1 of our current coplanar resonators are much better (few µs) than the T 1 ’s of the qubits. 9.3.5 Swaps At this point it is possible to reproduce the time resolved swapping experiment described above. In this case, though, the oscillation will be either between the 221
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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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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
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Page 222 and 223: Figure 8.10: T 1 - a) Bias sequence
Page 224 and 225: Figure 8.11: Ramsey - a) Bias seque
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Page 228 and 229: photon excitation behaves similarly
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Page 238 and 239: Figure 9.4: Capacitive Coupling Swa
Page 240 and 241: Figure 9.6: Capacitive Coupling Pha
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Page 244 and 245: Figure 9.7: Fine Spectroscopy of Re
Page 246 and 247: Figure 9.8: Swapping Photon into Re
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
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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 288 and 289: Table 11.7: Bell Violation Results
Page 290 and 291: Table 11.9: Error Budget - Capaciti
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11.5.2 Dependence of S on Sequence
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point where the measurement happens
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The second qubit is not driven and
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Figure 11.6: Resonator Coupled Samp
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From the resulting states, the 16 p
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Table 11.14: Error Budget - Resonat
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Table 11.15: Bell Violation Results
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sponding to a violation by 244.0σ.
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educe energy decay and dephasing an
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John F. Clauser, Michael A. Horne,
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J. Majer, J. M. Chow, J. M. Gambett
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Matthias Steffen, M. Ansmann, Rados
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