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cessing data. This protects the voltage output from the large amount of white noise that digital electronics always create during switching. The fiber-optic link was chosen to allow for electrical isolation of the DR from the control electronics. For the same reason, the FastBias and PreAmp cards are powered by a battery box rather than a power supply that plugs into a wall outlet. 6.3.6 PreAmp Card The PreAmp Card is used to detect the switching of the readout squid by monitoring it through the readout line. After optional low- and high-pass filtering, it amplifies the incoming signal by 1, 000× and then compares it to a digitally controlled cutoff voltage. The result of this comparison is made available via a binary fiber-optic line. Just like the FastBias card, the DAC that sets the cutoff voltage is controlled by an FPGA that turns off the card’s clock whenever it is not needed. 6.3.7 Bias Box Both the FastBias and the PreAmp card are designed to plug into a rack-mount bias box. This box supplies the cards with power from batteries and provides two analog and two digital buses that the cards can use to make signals available for monitoring. This is useful for the early stages of the qubit bring procedure 118
described in Chapter 8 (specifically the Squid I/V measurement). 6.3.8 GHz DACs The fiber-optical signals are sent to the FastBias and received from the PreAmp cards by another custom electronic device, the GHz DAC. It is a high-speed FPGA-based signal generator that uses two 14-bit DACs running at 1 GHz to synthesize waveforms with frequencies up to 500 MHz. These waveforms are used to control the RF portion of the qubit bias. This is done by compositing one waveform that is directly synthesized by a DAC and another that is the result of using the DACs to modulate a carrier microwave signal with an I/Q mixer. The first half of the waveform generates Z-rotations and the measure pulse. The second half of the waveform is used to generate X/Y-rotations. The GHz DAC boards are controlled by a computer via a 100 MBit Ethernet connection and can synchronize to each other via a 10 MHz reference clock and a daisy-chain trigger. The GHz DACs as well as the bias cards could easily be replaced by off-theshelf electronics, but the cost of the commercial equivalents would increase the price of adding one more qubit channel by a factor of more than 20. This, and the desire for exact control over the electronics’ performance, prompted us to design these modules ourselves. 119
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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
Page 97 and 98: Chapter 4 Designing the Phase Qubit
Page 99 and 100: mutual inductance between the qubit
Page 101 and 102: During the measurement, the | 1 〉
Page 103 and 104: the right impedance transformation
Page 105 and 106: excitations. Since these are a pote
Page 107 and 108: Figure 4.3: Squid I/V Traces - a) L
Page 109 and 110: Figure 4.5: Qubit Integrated Circui
Page 111 and 112: The geometry of the qubit junction
Page 113 and 114: squid loop. Thus, this tool can be
Page 115: now, amorphous silicon seems to pro
Page 118 and 119: Figure 5.1: L-Edit Mask Layout Tool
Page 120 and 121: Figure 5.2: Fabrication Building Bl
Page 122 and 123: Figure 5.3: Photolithography and Et
Page 124 and 125: times the removal can be a bit tric
Page 126 and 127: Figure 5.4: Clearing Vias from Nati
Page 128 and 129: 5.6 Junction Layers 5.6.1 Oxidation
Page 130 and 131: top wiring layer to protect all low
Page 132 and 133: 104
Page 134 and 135: 6.1 Physical Quality Control during
Page 136 and 137: 6.1.3 Atomic Force Microscopy To re
Page 138 and 139: Figure 6.1: 4-Wire Measurement - a)
Page 140 and 141: 6.3 Quantum Measurements at 25 mK 6
Page 142 and 143: seems to be a box machined out of s
Page 144 and 145: Figure 6.2: Dilution Refrigerator W
Page 148 and 149: 6.3.9 Anritsu Microwave Source The
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Page 152 and 153: ment, the scalability requirements,
Page 154 and 155: people without any formal training
Page 156 and 157: 7.2.4 Performance Last, but certain
Page 158 and 159: or a Client Module. Client Modules
Page 160 and 161: second Module talks to all these an
Page 162 and 163: puters to talk to each other. Usual
Page 164 and 165: 7.3.4 Performance Addressing the Pe
Page 166 and 167: is designed such that the LabRAD Ma
Page 168 and 169: Table 7.3: LabRAD Type Annotations
Page 170 and 171: listed in Table 7.3. For transmissi
Page 172 and 173: Architecture to manage network conn
Page 174 and 175: Manager. In fact, in our lab, the o
Page 176 and 177: waiting for their completion. The C
Page 178 and 179: mentation of pipelining and certain
Page 180 and 181: Since the API guarantees that all R
Page 182 and 183: one microwave line for X/Y-rotation
Page 184 and 185: 7.5.3 DC Rack Server The DC Rack Se
Page 186 and 187: data taking on the lab servers and
Page 188 and 189: keys and the ability to set Context
Page 190 and 191: a certain time. 7.5.9 Optimizer Cli
Page 192 and 193: ters read from different sub-direct
Page 194 and 195: 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
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Matthias Steffen, M. Ansmann, Rados
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