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this, but must still be universal. To prove universality, it is sufficient to show how the actual set can be used to implement the gates mentioned above. Even though being able to directly implement operations involving more than two qubits might lead to a performance increase, they are not required since it has been shown that any n-qubit operation can be implemented with the above mentioned universal set, even though it only includes the two-qubit cNOT gate. 1.3.5 High Quantum Efficiency, Qubit-Specific Measurements To extract the result of the computation in a way that is compatible with the universality requirement, it is necessary to be able to measure the state of each qubit independently. This measurement needs to be sufficiently accurate, since it is a common part of error correcting schemes that are needed to overcome short qubit coherence times. 14
Chapter 2 Superconducting Josephson Qubits 2.1 Motivation Many factors contribute to the decision of which approach to follow in an effort to build a quantum computer. While some approaches, like NMR [Vandersypen et al., 2001] and Ion Traps [Benhelm et al., 2008], yield the immediate satisfaction of naturally good single qubit performance, scalability presents a major hurdle to these systems due to the difficulty of arranging a multitude of these qubits into a layout that allows them to be coupled and controlled in a useful way. Superconducting Josephson qubits fall at the almost opposite end of the spectrum. 15
Page 1: UNIVERSITY of CALIFORNIA Santa Barb
Page 5: Benchmarking the Superconducting Jo
Page 8 and 9: viii
Page 11 and 12: Curriculum Vitæ Markus Ansmann Edu
Page 13 and 14: 99:187006 Lisenfeld, J., Lukashenko
Page 15 and 16: Abstract Benchmarking the Supercond
Page 17 and 18: Contents Contents List of Figures L
Page 19 and 20: 4.1.3 Readout Squid Parameters . .
Page 21 and 22: 7.5.5 Grapher . . . . . . . . . . .
Page 23 and 24: 11.5 Analysis and Verification . .
Page 25 and 26: List of Figures 2.1 Inductor-Capaci
Page 27 and 28: List of Tables 3.1 Transition Matri
Page 29 and 30: Chapter 1 Quantum Computation 1.1 M
Page 31 and 32: for such problems include factoring
Page 33 and 34: if present encrypted data will rema
Page 35 and 36: In terms of quantum bits, this mean
Page 37 and 38: 1.2.3 Implications - The EPR Parado
Page 39 and 40: proposed architecture of quantum bi
Page 41: “coherence times”, i.e. the tim
Page 45 and 46: of the glue-circuitry needed to con
Page 47 and 48: Figure 2.1: Inductor-Capacitor Osci
Page 49 and 50: • The circuit needs to be cooled
Page 51 and 52: Figure 2.2: Josephson Tunnel Juncti
Page 53 and 54: the trace along the V-axis, gives c
Page 55 and 56: Figure 2.4: Josephson Qubits: Sligh
Page 57 and 58: the cosine forms a local minimum al
Page 59 and 60: Figure 2.5: Example Qubit Coupling
Page 61 and 62: 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
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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
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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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