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Table 11.4: Sequence Parameters – Resonator State Preparation Name Description Comments Φ A Qubit A flux bias Places qubit far from TLS’s and resonator Φ B Qubit B flux bias Places qubit far from TLS’s, resonator, and other qubit t π Length of π-pulse Short A π Amplitude of π-pulse Sufficiently small to avoid | 2 〉-state errors f π Frequency of π-pulse Corrects for AC stark shift → function of A π φ π Phase of π-pulse Shouldn’t matter dt √ i−Swap Entangling pulse delay Ensures π-pulse is done t √ i−Swap Entangling time Maximizes entaglement A √ i−Swap Entangling pulse amplitude Brings qubit and resonator on resonance O √ i−Swap Entangling pulse overshoot Adds delta function to beginning and end of pulse to compensate for qubit slowly moving onto resonance dt i−Swap Swap pulse delay Ensures entangling is done t i−Swap Swap time Adjusted for maximal state transfer A i−Swap Swap pulse amplitude Brings qubit and resonator on resonance O i−Swap Swap pulse overshoot Compensates for qubit slowly moving onto resonance 252
Table 11.5: Sequence Parameters – Correlation Measurement Name Description Comments dt A Qubit A rotation delay Ensures state prep. is done t a Length of a-rotation pulse As short as possible A a Amplitude of a-rotation pulse Determines angle α f a Frequency of a-rotation pulse Corrects AC stark shift → fn of A a φ a Phase of a-rotation pulse Shouldn’t matter t a ′ Length of a ′ -rotation pulse As short as possible A a ′ Amplitude of a ′ -rotation pulse Determines angle α ′ f a ′ Frequency of a ′ -rotation pulse Corrects AC stark shift → fn of A a ′ φ a ′ Phase of a ′ -rotation pulse Should equal φ a dt MPA Qubit A meas. pulse delay Ensures rotation pulse is done A MPA Qubit A meas. pulse ampl. Maximizes visibility t MPA Qubit A meas. pulse length Maximizes visibility (cap. coupl.: Minimizes crosstalk) dt B Qubit B rotation delay Ensures state prep. is done t b Length of b-rotation pulse As short as possible A b Amplitude of b-rotation pulse Determines angle β f b Frequency of b-rotation pulse Corrects AC stark shift → fn of A b φ b Phase of b-rotation pulse Should result in same phase as φ a (corrects for cable lengths) t b ′ Length of b ′ -rotation pulse As short as possible A b ′ Amplitude of b ′ -rotation pulse Determines angle β ′ f b ′ Frequency of b ′ -rotation pulse Corrects AC stark shift → fn of A b ′ φ b ′ Phase of b ′ -rotation pulse Should equal φ b dt MPB Qubit B meas. pulse delay Ensures rotation pulse is done (cap. coupl.: Minimizes crosstalk) A MPB Qubit B meas. pulse ampl. Maximizes visibility t MPB Qubit B meas. pulse length Maximizes visibility (cap. coupl.: Minimizes crosstalk) 253
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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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Page 238 and 239: 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
Page 256 and 257: (independent of which axis it is),
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Page 260 and 261: For a measurement of two particles
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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 282 and 283: ally determine an optimal value for
Page 284 and 285: ages are based on this method, incl
Page 286 and 287: equires to converge. Since the algo
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 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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