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9.2.5 Phase Calibration . . . . . . . . . . . . . . . . . . . . . . . 213 9.2.6 “Controllable Coupling” via Bias Changes . . . . . . . . . 214 9.3 Resonator Based Coupling . . . . . . . . . . . . . . . . . . . . . . 215 9.3.1 2D-Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . 217 9.3.2 Swapping a Photon into the Resonator . . . . . . . . . . . 217 9.3.3 Retrieving the Photon from the Resonator . . . . . . . . . 218 9.3.4 Timing Calibration . . . . . . . . . . . . . . . . . . . . . . 220 9.3.5 Swaps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 9.3.6 Resonator T 1 and T 2 . . . . . . . . . . . . . . . . . . . . . 222 10 Hidden Variable Theories versus Quantum Mechanics 225 10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 10.1.1 Is Quantum Mechanics Incomplete? . . . . . . . . . . . . . 225 10.1.2 Is Quantum Mechanics Wrong? . . . . . . . . . . . . . . . 226 10.1.3 Settling the Question Experimentally . . . . . . . . . . . . 226 10.2 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . 233 10.2.1 Photons . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233 10.2.2 Ions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234 10.2.3 Ion and Photon . . . . . . . . . . . . . . . . . . . . . . . . 235 10.3 The Bell Inequality versus Phase Qubits? . . . . . . . . . . . . . . 236 11 Implementing the Bell Test 239 11.1 State Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . 240 11.1.1 Initialization in the | 10 〉 state . . . . . . . . . . . . . . . . 240 11.1.2 Entangling the Qubits – Capacitive Coupling . . . . . . . 240 11.1.3 Entangling the Qubits – Resonator Coupling . . . . . . . . 241 11.1.4 Verifying Entanglement – State Tomography . . . . . . . . 244 11.2 Correlation Measurements . . . . . . . . . . . . . . . . . . . . . . 246 11.2.1 Bell Rotations . . . . . . . . . . . . . . . . . . . . . . . . . 247 11.2.2 Tunneling Measurement . . . . . . . . . . . . . . . . . . . 247 11.2.3 Statistical Analysis . . . . . . . . . . . . . . . . . . . . . . 248 11.3 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250 11.3.1 Global Optimization . . . . . . . . . . . . . . . . . . . . . 250 11.3.2 Manual Search . . . . . . . . . . . . . . . . . . . . . . . . 251 11.3.3 Nelder-Mead Simplex Algorithm . . . . . . . . . . . . . . . 255 11.3.4 Particle Swarm Optimization . . . . . . . . . . . . . . . . 256 11.4 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . 258 11.4.1 Capacitive Coupling . . . . . . . . . . . . . . . . . . . . . 259 11.4.2 Resonator Coupling . . . . . . . . . . . . . . . . . . . . . . 263 xxii
11.5 Analysis and Verification . . . . . . . . . . . . . . . . . . . . . . . 267 11.5.1 Standard Error of the S-Value . . . . . . . . . . . . . . . . 267 11.5.2 Dependence of S on Sequence Parameters . . . . . . . . . 270 11.5.3 Microwave and Measurement Crosstalk . . . . . . . . . . . 272 11.5.4 Numerical Simulation . . . . . . . . . . . . . . . . . . . . . 275 11.5.5 Measurement Correction . . . . . . . . . . . . . . . . . . . 280 12 Conclusion 283 12.1 Claim of Violation of Bell’s Inequality . . . . . . . . . . . . . . . . 283 12.2 S-Value as Qubit Pair Benchmark . . . . . . . . . . . . . . . . . . 284 12.3 Josephson Phase Qubit Performance . . . . . . . . . . . . . . . . 285 12.4 Future Direction . . . . . . . . . . . . . . . . . . . . . . . . . . . 286 xxiii
Page 1: UNIVERSITY of CALIFORNIA Santa Barb
Page 5: Benchmarking the Superconducting Jo
Page 8 and 9: viii
Page 11 and 12: Curriculum Vitæ Markus Ansmann Edu
Page 13 and 14: 99:187006 Lisenfeld, J., Lukashenko
Page 15 and 16: Abstract Benchmarking the Supercond
Page 17 and 18: Contents Contents List of Figures L
Page 19 and 20: 4.1.3 Readout Squid Parameters . .
Page 21: 7.5.5 Grapher . . . . . . . . . . .
Page 25 and 26: List of Figures 2.1 Inductor-Capaci
Page 27 and 28: List of Tables 3.1 Transition Matri
Page 29 and 30: Chapter 1 Quantum Computation 1.1 M
Page 31 and 32: for such problems include factoring
Page 33 and 34: if present encrypted data will rema
Page 35 and 36: In terms of quantum bits, this mean
Page 37 and 38: 1.2.3 Implications - The EPR Parado
Page 39 and 40: proposed architecture of quantum bi
Page 41 and 42: “coherence times”, i.e. the tim
Page 43 and 44: Chapter 2 Superconducting Josephson
Page 45 and 46: of the glue-circuitry needed to con
Page 47 and 48: Figure 2.1: Inductor-Capacitor Osci
Page 49 and 50: • The circuit needs to be cooled
Page 51 and 52: Figure 2.2: Josephson Tunnel Juncti
Page 53 and 54: the trace along the V-axis, gives c
Page 55 and 56: Figure 2.4: Josephson Qubits: Sligh
Page 57 and 58: the cosine forms a local minimum al
Page 59 and 60: Figure 2.5: Example Qubit Coupling
Page 61 and 62: Readout schemes can further be cate
Page 63: states in the qubit’s inductor, t
Page 66 and 67: at time t. r is not restricted to b
Page 68 and 69: 3.1.2 Effects of a Time Dependent P
Page 70 and 71: 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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esonator. The latter calibration is
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Figure 9.11: Resonator T 1 - a) Seq
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224
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He does not throw dice” [Einstein
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(independent of which axis it is),
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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
Page 320:
Matthias Steffen, M. Ansmann, Rados
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