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Figure 8.11: Ramsey – a) Bias sequence: A π -pulse excites the qubit into the 2 equator of the Bloch sphere where it is allowed to dephase for a time t Delay . A second π -pulse continues the rotation of the qubit state (ideally) to the | 1 〉 state. 2 b) On resonance: As the qubit dephases its chance of making it to the | 1 〉 state decreases. c) Off resonance: If the qubit and the pulses are not at the same frequency, the qubit state spins around the equator of the Bloch sphere during the delay. Depending on the angle at which the second pulse “catches” the state, it either continues its rotation towards the | 1 〉 state or reverses it back to the | 0 〉 state. The oscillation frequency of the data should match the detuning, here 20MHz. 196
Figure 8.12: Spin Echo – a) Bias sequence: A π-pulse around the Y-axis that is placed in the middle of the Ramsey delay reverses the qubit state’s precession angle causing it to undo the precession during the second half of the delay. This compensates for slow bias drifts and off-resonant pulses. b) Spin echo: The qubit’s phase information decays following a gaussian shape. of T 2 if the frequency of the microwave pulse is exactly on resonance with the transition frequency of the qubit. If the microwave drive is detuned, the qubit will not only dephase, but also precess in the equator of the Bloch sphere, leading to a trace like Figure 8.11c. The frequency of the oscillation is equal to the detuning of the microwaves from the qubit. Thus, it is not necessarily clear, how much of the “decay” in Figure 8.11b. is due to T 2 and how much is due to the beginning of a slow oscillation caused by a very slight detuning of the microwaves. 8.11 Spin-Echo The detuning effect on the measurement of the Ramsey trace can be eliminated by a trick called “Spin Echoing”. It works by inserting a π-pulse with a 90 ◦ 197
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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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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 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
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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
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Page 228 and 229: photon excitation behaves similarly
Page 230 and 231: is desirable to modularize the cont
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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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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 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
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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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