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Figure 9.11: Resonator T 1 – 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 the time needed for one full swap (S) to transfer the excitation into the resonator. There, the excitation is allowed to decay for a time t Delay . After, the first qubit is brought on resonance for the time needed for one full swap (S) to transfer the resonator state into the first qubit. Finally both qubits are measured (M). b) T 1 : The excitation in the resonator decays exponentially. source qubit and the resonator or between the resonator and the target qubit. The former will reproduce the dataset from above more faithfully as the latter will lead to some of the excitation sometimes remaining in the resonator at the end. Varying the length of the first swap pulse in the last used sequence will yield the familiar plot shown in Figure 9.10. 9.3.6 Resonator T 1 and T 2 To fully characterize the coupling, it is desirable in this case to also measure the resonator’s T 1 and T 2 . The T 1 can be easily measured by delaying the retrieval of the excitation from the resonator as shown in Figure 9.11. To measure the T 2 , 222
a Ramsey-type experiment needs to be conducted where a π -pulse prepares the 2 source qubit in a state in the X/Y-plane of the Bloch sphere. This state is then swapped into the resonator. After a variable delay t Ramsey , the state is retrieved with another swap operation and the result is interfered with another π 2 -pulse. The same concerns apply to the resulting data of this experiment as described for the single qubit case. 223
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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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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
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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
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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
Page 282 and 283: ally determine an optimal value for
Page 284 and 285: ages are based on this method, incl
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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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Page 298 and 299: 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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