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Benchmarking the Superconducting Josephson Phase Qubit: The Violation <strong>of</strong> Bell’s Inequality Copyright 2009 by Markus Ansmann v
Page 1: UNIVERSITY of CALIFORNIA Santa Barb
Page 7 and 8: To my parents, Klaus and Ulrike Ans
Page 9: Acknowledgements This work would no
Page 12 and 13: Katz, N., Neeley, M., Ansmann, M.,
Page 14 and 15: A., Lubin, P., Marvil, J., McCreary
Page 16 and 17: a stronger correlation than possibl
Page 18 and 19: 2 Superconducting Josephson Qubits
Page 20 and 21: 6.1.3 Atomic Force Microscopy . . .
Page 22 and 23: 9.2.5 Phase Calibration . . . . . .
Page 24 and 25: xxiv
Page 26 and 27: 8.1 Squid I/V . . . . . . . . . . .
Page 28 and 29: xxviii
Page 30 and 31: hours by 2010 [Coles et al., 2006].
Page 32 and 33: any possible classical computer for
Page 34 and 35: 1.2 The Power of Quantum Computers
Page 36 and 37: states, effectively giving it 2 n+1
Page 38 and 39: Podolsky, and Rosen [Einstein et al
Page 40 and 41: 1.3.1 Scalable Physical System with
Page 42 and 43: this, but must still be universal.
Page 44 and 45: While the underlying technology pro
Page 46 and 47: The specifics of implementing the i
Page 48 and 49: Equation 2.2 can be rewritten as: C
Page 50 and 51: other states using a classical exci
Page 52 and 53: • The horizontal line along the V
Page 54 and 55:
Figure 2.3: Modified Inductor-Capac
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If the inductor is removed from the
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a constant bias at which the potent
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ground of a wire of any usable leng
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Figure 2.6: Squid Readout Scheme -
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Chapter 3 Understanding Qubits Nume
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Equation 3.6, also called the “ti
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As the eigenstates are ortho-normal
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This can be expressed as a tri-diag
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pecially for the higher levels, for
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• The x-range over which the pote
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This will most likely take forbiddi
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Figure 3.3: Simulation of Mock-Qubi
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| 12 〉 and | 14 〉 (desired tran
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Figure 3.4: Bloch Sphere - a) Bloch
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safely ignored. This step is called
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3.3.3 Single Qubit Operations in a
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To couple qubits 2 and 3 out of fiv
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P ′′ | 01 〉(t) = (1 − X 21
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sphere. Instead, it corresponds to
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[ ] 1 0 K ϕa (∆t) = 0 e −∆t/
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Figure 4.1: Qubit Circuit: The qubi
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obtain control electronics that can
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will focus only on the integrated c
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Figure 4.2: Readout Squid - a) Circ
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the qubit to dissipate energy and t
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Figure 4.4: Spice Coupler Design -
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4.2.1 Qubit When designing the indu
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4.2.2 Bias Coil The design of the b
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small scales of these barriers, it
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Chapter 5 Phase Qubit Fabrication T
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that will be used in the later fabr
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the sapphire wafer is positioned cl
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5.3.3 ICP Etch Next, the wafer is l
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quality of the film deposited in th
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During this step, argon ions are ac
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Figure 5.5: 3D View of Junction: Th
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5.9 Top Wiring Layer - Part III Sin
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Chapter 6 Device Testing Equipment
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6.1.2 Scanning Electron Microscopy
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6.2 Electrical Screening after Fabr
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down to temperatures around 4 K. Th
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happens continuously, the DR can th
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This melts the aluminum wire and bo
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a readout line. These two lines are
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described in Chapter 8 (specificall
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Filters selectively attenuate certa
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Chapter 7 Control Software - LabRAD
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Requirement. Second, as the control
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7.2.3 Efficiency To promote accepta
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dent modules, but it also provides
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Another benefit of this hard separa
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different angles simultaneously, if
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7.3.3 Cross-Language and Cross-Plat
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useful to us in the future. Beyond
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Table 7.1: Basic LabRAD Types Type
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Table 7.5: LabRAD Packet Structure
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7.4.2 LabRAD Manager The LabRAD Man
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process. The SI conversion factors
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languages like Python it should be
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structure kept in the Server that h
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This is especially useful if second
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Figure 7.1: Control Layout: The con
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The next layers correspond to the
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7.5.5 Grapher At the far left of th
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hard drive. Having a central author
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which it prepends with the current
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system that needs to be changed in
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are involved in the experiment and
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to the “Sampling Scope Server”,
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eception of packets, and return the
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7.5.18 IPython In addition to using
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Chapter 8 Single Qubit Bring-Up and
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Figure 8.1: Squid I/V: Axis scales
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Figure 8.2: Squid Steps - a) Bias s
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where the potential has two stable
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picking the “operating branch”,
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Figure 8.4: Step Edge - a) Bias seq
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Plotting P T unnel versus the qubit
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Figure 8.6: S-Curve - a) Bias seque
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8.6 Spectroscopy Using this prelimi
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wave pulse at the qubit resonance f
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Figure 8.9: Visibility - a) Bias se
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as a function of the delay between
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Figure 8.12: Spin Echo - a) Bias se
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Figure 8.13: Fine Spectroscopy - a)
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Chapter 9 Coupled Qubit Bringup The
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is of significant concern for relia
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Figure 9.1: Effect of Squid Crossta
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Figure 9.2: Measure Pulse Timing -
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Figure 9.3: Spectroscopy of Coupled
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Figure 9.5: Capacitive Coupling Res
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9.2.5 Phase Calibration The trickie
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9.3 Resonator Based Coupling The me
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9.3.1 2D-Spectroscopy To couple a s
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Figure 9.9: Swapping Photon out of
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Figure 9.10: Resonator Swaps - a) S
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a Ramsey-type experiment needs to b
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Chapter 10 Hidden Variable Theories
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10.1.3 Settling the Question Experi
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Table 10.1: Possible Populations fo
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This restriction is called the Bell
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This leads to the correlation value
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“choosing” between polarization
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croscopic quantum systems like atom
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Chapter 11 Implementing the Bell Te
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singlet state due to the extra fact
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process of the qubits in two ways:
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[Steffen et al., 2006] (the details
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11.2.1 Bell Rotations The first ste
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P | 11 〉 (a ′ b ′ )) estimate
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Table 11.3: Sequence Parameters - C
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Table 11.5: Sequence Parameters - C
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the data taking can lead to thermal
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and back towards the position of th
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Table 11.6: Qubit Sample Parameters
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Table 11.8: Optimization Results -
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this leads to a modification of the
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Table 11.11: Optimization Results -
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Figure 11.3: Standard Error Analysi
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20 minutes worth of data. Within ea
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Figure 11.4: Behavior of S: Examini
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Figure 11.5: Quantifying Measuremen
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11.5.4 Numerical Simulation To unde
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Table 11.13: Qubit Sample Parameter
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Figure 11.7: Visibility Analysis -
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pair, independent of the measuremen
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Chapter 12 Conclusion 12.1 Claim of
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information about the quality of th
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Bibliography J. Altepeter, E. Jeffr
Page 317 and 318:
Max Hofheinz, E. M. Weig, M. Ansman
Page 319 and 320:
Matthew Neeley, M. Ansmann, Radosla
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