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Table 11.9: Error Budget – Capacitive Coupling Implementation Error Contribution New S Theoretical 2.828 Ideal simulation 0.000 2.828 T 1 decay 0.133 2.695 Visibility 0.512 2.183 Finite pulses during always-on coupling 0.116 2.067 Measurement crosstalk 0.240 1.827 Experimental result (T 2 , calibrations, . . . ) 1.816 useful primarily as a tool for understanding the error mechanisms that led to the lower number. With the help of the numerical simulations described in Chapter 3.3 it is possible to create an error budget that identifies the contributions of different imperfections to the reduction of the S-value. The results of this analysis are shown in Table 11.9. Even though T 1 decay is commonly cited as the biggest challenge faced by the field, for this experiment it has a relatively small effect since the overall sequence is fairly short. The biggest reduction results from the problems associated with the measurement, specifically the low visbilities and high crosstalk. Measurement crosstalk affects the experiment in an additional way since it actively introduces correlations into the result. It can be shown that 262
this leads to a modification of the inequality that raises the bound on the value of S that can be achieved with a locally realistic hidden variable theory [Kofman et al., 2007]: −2 + 4 min{p a c, p b c} ≤ S ≤ 2 + 2 ∣ ∣p a c − p b ∣ c (11.4) Here, p a c (p b c) is the classical probability that a tunneling of qubit A (B) causes a tunneling of qubit B (A), i.e. the probability that the state | 10 〉 (| 01 〉) is measured as | 11 〉 for reasons other than the non-ideal measurement fidelity of qubit B (A). This effect on the inequality itself makes measurement crosstalk very undesirable as it significantly complicates the justification of a claimed violation. To address this issue, a different coupling scheme can be used that allows the qubits to be decoupled during the measurement. Since controllable coupling was not available at the time of the implementation of this experiment, a temporary solution can be found by coupling the qubits through a coplanar resonator. 11.4.2 Resonator Coupling Resonant buses are frequently used in other qubit designs (like the charge qubit) to enable coupling despite the qubits’ high impedance [Majer et al., 2007]. Here, the purpose of the resonator instead is to act as a band-pass filter for the coupling. Since the qubits are far off resonance from the pass-band during 263
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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
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 254 and 255: He does not throw dice” [Einstein
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Page 264 and 265: 10.2.3 Ion and Photon In the attemp
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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 284 and 285: ages are based on this method, incl
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Page 288 and 289: Table 11.7: Bell Violation Results
Page 294 and 295: Bell inequality. To make this claim
Page 298 and 299: 11.5.2 Dependence of S on Sequence
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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 314 and 315: educe energy decay and dephasing an
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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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