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A., Lubin, P., Marvil, J., McCreary, P., Villela, T., “A 31 pixel flared 100-GHz high-gain scalar corrugated nonbonded platelet antenna array”, IEEE Antennas and Wireless Propagation Letters (2005), 4:245-248 Honors and Awards 2003 Arnold Nordsieck Award, Physics Department, University of California, Santa Barbara, California 2003 Research Honors, Physics Department, University of California, Santa Barbara, California 2003 Dean’s Honors, University of California, Santa Barbara, California 1999 - 2001 Dean’s List, Stevens Institute of Technology, Hoboken, NJ xiv
Abstract Benchmarking the Superconducting Josephson Phase Qubit: The Violation of Bell’s Inequality by Markus Ansmann The concepts of entanglement and superpositions introduced by quantum mechanics promise to allow for the design of a new computing architecture, called a quantum computer, that can exponentially outperform any possible classical computer. Such a performance improvement would make presently intractable computational problems efficiently solvable. Such problems include optimizations, like the traveling salesman problem, factorization, and quantum simulations, e.g. for medical research. This thesis discusses one approach to implementing a quantum computer that is based on Superconducting Josephson Phase Qubits. An experiment is presented that shows a violation of Bell’s inequality using these qubits (quantum bits), i.e. it demonstrates that a pair of these qubits can be placed into a state that shows xv
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: 99:187006 Lisenfeld, J., Lukashenko
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 and 42: “coherence times”, i.e. the tim
Page 43 and 44: Chapter 2 Superconducting Josephson
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
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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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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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