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seems to be a box machined out of solid aluminum with coaxial feeds for the microwave lines. This allows the entire box to become superconducting and shield the sample from external magnetic fields. The box needs to support the chip with minimal contact above a cavity to not form a ground-plane underneath the chip that capacitively disperses microwaves across the chip. Nevertheless, the chip needs to be very well grounded to the box, which is achieved by hundreds of closely spaced wire bonds (see Section 6.3.3) that reduce the overall inductance in the grounding. The microwave lines should maintain their 50 Ω impedance throughout the box to minimize pulse distortion caused by reflections. This makes the sample mount one of the few parts that we have not been able to just buy off the shelf. But after the box was designed in a CAD program, it was very straightforward to have it machined to sufficient accuracy by the university’s machine shop. 6.3.3 Wire Bonding To be able to wire the qubit into the DR, the sub-millimeter traces of the qubit chip need to be connected to macroscopic coaxial cables that can be managed by hand. This can be done with a device called a “Wire Bonder”. Wire bonding works by feeding a thin (∼ 1 mil) aluminum wire through a tip such that the tip can push the wire down onto the surface that it is meant to adhere to. While applying pressure to the wire, the tip is vibrated rapidly with ultrasonic waves. 114
This melts the aluminum wire and bonds it to the surface. This allows the system to run wires between pads without the use of solder. This technique makes it possible to make contact to pads that are only a few hundred µm wide. 6.3.4 Dilution Refrigerator Wiring The other non-off-the-shelf component needed is the wiring inside the DR (see Figure 6.2). It consists of several different parts that have to be chosen/built to manage heat loads, noise, and cryogenic properties. Starting at the outside of the qubit box, the squid is connected immediately to a ∼ 30 Ω shunting resistor. This resistor is needed to limit the voltage generated in the squid when it switches to the voltage state as explained in Chapter 4.1.3. If this resistor is omitted, the squid switching generates a large amount of quasiparticle excitations in the qubit circuit which reduce qubit performance. The next component along the squid line is a copper powder filter (Cu). This device consists of a wire wound into a spiral that is sitting in a cavity filled with copper powder and epoxy for thermal contact. Electrically, it functions as a very quiet low-pass filter that absorbs most noise coming down the squid line. The ∼ 30 Ω resistor and the copper powder filter are both mounted at the 25 mK stage of the DR to prevent them from creating noise due to their temperature. Along the squid line, at the 4 K stage of the DR is a resistor network that splits the line into a bias and 115
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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
Page 92 and 93: Decoherence consists of two parts:
Page 94 and 95: 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
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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 144 and 145: Figure 6.2: Dilution Refrigerator W
Page 146 and 147: cessing data. This protects the vol
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
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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
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Matthias Steffen, M. Ansmann, Rados
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