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11.5.2 Dependence of S on Sequence Parameters Since, for example, an experiment without measurement pulses yields an S- value of 2.0 as all states are read as | 00 〉, it is possible for the optimization process to get stuck in a local maximum that shows a maximized classical correlation but little or no quantum entanglement. Any artificially introduced correlations during the measurement might then yield a value of S > 2.0 and thus a false claim of a violation. A simple check of the behavior of S versus one of the sequence parameters is useful to quickly expose such major problems in the experiment. Figure 11.4a plots the dependence of S on the phase of the Bell rotation pulses (the plane in which the qubit is measured) on the second qubit. The data shows the sinusoidal response predicted by quantum mechanics, and thus provides strong evidence that the experiment is implemented in the expected way. Due to the short coherence times of the involved qubits, it was necessary to minize the overall sequence length as much as possible. This included moving the Bell rotations and measurement on the second qubit forward to place them right after the pulse that entangles the qubit with the resonator. Even though the short distance between the qubits relative to the time-scales of measurement makes it impossible to close the locality loophole in this experimental setup anyway, 270
Figure 11.4: Behavior of S: Examining the behavior of S versus sequence parameters can verify a trustworthy implementation – a) S versus phase b, b ′ : As the phase of the rotation pulses on the second qubit is varied, S shows the expected sinusoidal response. b) S versus measurement delay: The fact that S shows only the expected T 1 and T 2 decay, but no other features indicating a dependence on the relative timing of the measurements, is strong evidence that the qubits are truly decoupled during measurement. the early measurement of one qubit might still prompt criticism as it opens the locality loophole even wider by giving the qubits even more time to interact via the unknown processes postulated by the loophole. To counter this criticism, it can be shown that the relative timing of the measurement does not influence the resulting S-value in a way that suggests the existence of an additional interaction allowed by the time difference. Figure 11.4b shows the dependence of S on the delay of the Bell rotations and measurement on the second qubit. As expected from the additional qubit decoherence, S decreases as the measurement is delayed. But the plot shows no features that correlate with the relative timing of the measurements on the two qubits. Specifically, there is no reduction in S around t = −1 ns, the 271
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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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172
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8.1 Squid I/V Response As explained
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a digital signal via the use of a c
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energy landscape (see Chapter 2.2.3
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Figure 8.3: Squid Steps Failure Mod
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At this point, the squid ramp can b
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starts to tunnel to the neighboring
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Figure 8.5: General Bias Sequence -
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Figure 8.7: Spectroscopy - a) Bias
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Figure 8.8: Rabi Oscillation - a) B
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ensemble with respect to each other
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Figure 8.10: T 1 - a) Bias sequence
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Figure 8.11: Ramsey - a) Bias seque
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phase shift into the middle of the
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photon excitation behaves similarly
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is desirable to modularize the cont
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sequence was run. This allows for t
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possible to read out all qubits cor
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simultaneous application of such me
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Figure 9.4: Capacitive Coupling Swa
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Figure 9.6: Capacitive Coupling Pha
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a phase difference of 0 ◦ rather
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Figure 9.7: Fine Spectroscopy of Re
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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 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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Page 304 and 305: Figure 11.6: Resonator Coupled Samp
Page 306 and 307: From the resulting states, the 16 p
Page 308 and 309: Table 11.14: Error Budget - Resonat
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Page 318 and 319: J. Majer, J. M. Chow, J. M. Gambett
Page 320: Matthias Steffen, M. Ansmann, Rados
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