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At this point, the squid ramp can be executed and the switching time t Switch will indicate whether the qubit state remained in the operating branch during the tunneling measurement (here: t Switch ≈ 12.4 µs) or whether it tunneled to the neighboring branch (here: t Switch ≈ 16.2 µs). This completes the DC part of the biasing sequence as shown in Figure 8.4a. If the qubit’s ciritical current is too high and the qubit potential always has many stable minima, i.e. three or more overlaps, the qubit can not be reset into the operating branch as described above. In that case, the qubit is reset by alternatingly biasing it to the points where the operating branch is the left-most or right-most stable branch. This will dynamically destabilize all branches other than the operating branch and leads to a probability for finding the qubit in the target branch that increases with the number of reset cycles. Usually 3 to 5 cycles are sufficient to bring this probability to above 99.99%. 8.3 Step Edge To maximize the non-linearity and thus the speed at which operations can be performed on the qubit without driving unwanted transitions, it is desirable to bias the qubit such that the operating minimum is as shallow as possible. We call the point at which the qubit ground-state (| 0 〉) in the operating minimum 182
Figure 8.4: Step Edge – a) Bias sequence: The qubit is reset into the operating minimum and moved to the operating bias V Operate for a few µs to allow for any tunneling. After, the qubit is biased at the readout point and the squid is ramped to measure I c . This sequence is repeated many times for each value of V Operate . b) Switching data: As V Operate is increased, the qubit state tunnels from the operating minimum (lower branch) to the neighboring minimum (higher branch). c) Probability: If the switching times are sorted using a cutoff time between the switching distributions, the probability for the state to tunnel can be extracted as a function of V Operate . 183
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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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Page 164 and 165: 7.3.4 Performance Addressing the Pe
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Page 168 and 169: Table 7.3: LabRAD Type Annotations
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Page 180 and 181: Since the API guarantees that all R
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Page 184 and 185: 7.5.3 DC Rack Server The DC Rack Se
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Page 194 and 195: efore the execution of the sequence
Page 196 and 197: 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
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Page 208 and 209: Figure 8.3: Squid Steps Failure Mod
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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 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
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Page 250 and 251: Figure 9.11: Resonator T 1 - a) Seq
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For a measurement of two particles
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10.2.1 Photons The first and most n
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10.2.3 Ion and Photon In the attemp
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238
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11.1 State Preparation Since the ab
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Figure 11.1: Bell State Preparation
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Table 11.1: Entangled State Density
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Figure 11.2: Bell Measurements - a)
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11.2.3 Statistical Analysis For the
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11.3 Calibration The most difficult
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Table 11.4: Sequence Parameters - R
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ally determine an optimal value for
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ages are based on this method, incl
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equires to converge. Since the algo
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Table 11.7: Bell Violation Results
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Table 11.9: Error Budget - Capaciti
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Bell inequality. To make this claim
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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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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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