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He does not throw dice” [Einstein et al., 1971], which is commonly paraphrased as “God does not play dice with the universe”. The fact that quantum mechanics does not provide a way to predict outcomes of all possible measurements with certainty lead to the suspicion that quantum mechanics had to be incomplete [Einstein et al., 1935], i.e. the wave-function representation of a system’s state does not contain all relevant information about the system. To complete the theory, a way must be found to capture the missing information in extra variables, often called “hidden variables” as they could not be measured. A deterministic alternate theory to quantum mechanics would therefore be called a “Hidden Variable Theory” (HVT). 10.1.2 Is Quantum Mechanics Wrong? In 1964, John S. Bell investigated the theoretical implications of a possible local HVT and showed that quantum mechanics could not be derived from such a theory to arbitrary accuracy [Bell, 1964]. With this, a hidden variable theory could no longer be a compatible extension to quantum mechanics, but would instead refute quantum mechanics altogether. 226
10.1.3 Settling the Question Experimentally J.F. Clauser, M.A. Horne, A. Shimony, and R.A. Holt later formulated one example of an incompatibility between a hidden variable theory and quantum mechanics into an experiment that could test whether quantum mechanics was indeed incomplete [Clauser et al., 1969]. In the proposed experiment a source is used that produces pairs of particles (e.g. photons or ions) in a perfectly anticorrelated state (e.g. opposite polarization or spin). For the purposes of illustration, the state of the entangled pair (particle A and B) can be taken to be the Bell singlet state | 01 〉−| 10 〉 √ 2 . These particles are then physically separated by a large enough distance to disallow any classical transfer of information between them throughout the remainder of the experiment, i.e. d AB ≫ c t expt . At those remote locations the particles are then measured along random axes (e.g. projected onto the X, Y, or Z-axis of the Bloch sphere). If the singlet state is re-expressed in the basis of the measurement axes, it will still show perfect anti-correlation if the axes are equal, e.g.: | X − X + 〉 − | X + X − 〉 √ 2 = = = | 0 〉−| 1 〉 √ 2 ⊗ | 0 〉+| 1 〉 √ 2 − | 0 〉+| 1 〉 √ 2 ⊗ | 0 〉−| 1 〉 √ 2 √ 2 | 00 〉+| 01 〉−| 10 〉−| 11 〉 − 2 | 00 〉−| 01 〉+| 10 〉−| 11 〉 2 √ 2 | 01 〉 − | 10 〉 √ (10.1) 2 Thus, every time both particles happen to be measured along the same axis 227
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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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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 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 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
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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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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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