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small scales of these barriers, it is fairly hard to use anything but an oxide of the superconductor. For this experiment, the junctions’ tunnel barriers will therefore be formed by amorphous aluminum oxide. Unfortunately, the quality of the junction dielectric is one of the crucially important details that will determine the final device performance. This is due to the very small thickness of these junctions as it will causes large oscillating electric fields to form across the dielectric during device operation. These fields can easily couple to individual defect states in the tunnel barrier provided they resonate at the qubit’s operating frequency [Neeley et al., 2008a]. Therefore, a crystalline barrier would be a very desirable achievement. 4.3.3 Crossover Dielectric Another material of great concern is that used for general insulating layers like in the external parallel plate capacitor or the wiring crossovers. Even though the fields formed across these during operation are much smaller, their larger bulk more than makes up for this by providing a greater number of defects. According to our current understanding, it is this bath of defect states that is the predominant cause for qubit energy relaxation [Martinis et al., 2005]. Thus, it is necessary to pay close attention to the development of a material with as low a defect density as possible. Again, crystalline dielectrics would be the preferred solution, but for 86
now, amorphous silicon seems to provide a reasonable and much more obtainable alternative. 4.3.4 Wafer The last choice is the wafer to be used: Since electric fields created by amorphous dielectrics can polarize a 2D electron gas in silicon, we choose sapphire (crystalline Al 2 O 3 ). 87
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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
Page 63: states in the qubit’s inductor, t
Page 66 and 67: at time t. r is not restricted to b
Page 68 and 69: 3.1.2 Effects of a Time Dependent P
Page 70 and 71: In some cases, it is possible to so
Page 72 and 73: Figure 3.1: Examples of Numerical S
Page 74 and 75: • The energy difference between t
Page 76 and 77: like this: V = ( V (−1, −1), V
Page 78 and 79: Figure 3.2: Simulation of LC Oscill
Page 80 and 81: Table 3.1: Transition Matrix Elemen
Page 82 and 83: with ω mn = Em−En . Multiplying
Page 84 and 85: α, it can be ignored. Thus, the in
Page 86 and 87: e solved exactly: A(t + ∆t) = e
Page 88 and 89: qubits would be simulated using: A(
Page 90 and 91: 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: squid loop. Thus, this tool can be
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 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
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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
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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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