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Figure 8.3: Squid Steps Failure Modes: Insets indicate problem (red) and correction (green). – a) Low SQ cutoff : The voltage cutoff detecting the switching is set too low leading to false positives. b) High SQ cutoff : The voltage cutoff is too high to detect the switch; instead it is crossed when the squid moves along the resistive part of the voltage branch. c) High V Start : The bias crosses I c during the ramp to V Start . d) Low V End : The bias barely/never crosses I c . e) Large ramp: The bias is ramped too quickly through I c . f) Functional squid: Perfect at last. 180
picking the “operating branch”, i.e. the potential minimum in which the qubit state will reside during operations. Here, for example, we can choose the branch that extends from V Bias ≈ −2.4 V to V Bias ≈ −0.3 V. The qubit is reset into this branch by biasing it to a point V Reset at which the operating branch is the only minimum of the potential, e.g. V Reset = −1.35 V. If the qubit is held at this bias for a time t Reset ≫ T 1 , its state will decay into the operating branch with certainty. To maximize the non-linearity during operation, i.e. the difference in energy spacing of the lowest levels in the operating minimum, the qubit is biased close to the “end” of the operating branch, i.e. to a point where the operating minimum becomes very shallow, for example around V Operate ≈ −0.3 V. This is necessary so that the lowest two energy levels in the minimum can be addressed exclusively as described in Chapter 3.3. To measure the qubit, the excited state (| 1 〉) will be selectively tunneled out of the operating branch as described in Section 8.5 into the neighboring branch – here, the branch that extends from V Bias ≈ −1.2 V to V Bias ≈ −1.0 V. The qubit is then biased to the point V Readout where the depth of the two potential minima is maximized, e.g. V Readout = −0.75 V. This maximizes the barrier height between the two minima to reduce the chance of the qubit state tunneling between the minima by accident. 181
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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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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 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 210 and 211: At this point, the squid ramp can b
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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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of E xy is measured by expressing i
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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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