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Bulletin of the American Physical Society

Coherent manipulation of quantum information using two Josephson phase qubits coupled to a resonant cavity

Mika Sillanpää

Published Mar 10, 2008• 0 citations
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We describe the design for a scalable, solid-state quantum-information-processing architecture based on the integration of GHz-frequency nanomechanical resonators with Josephson tunnel junctions, which has the potential for demonstrating a variety of single- and multiqubit operations critical to quantum computation. The computational qubits are eigenstates of large-area, current-biased Josephson junctions, manipulated and measured using strobed external circuitry. Two or more of these phase qubits are capacitively coupled to a high-quality-factor piezoelectric nanoelectromechanical disk resonator, which forms the backbone of our architecture, and which enables coherent coupling of the qubits. The integrated system is analogous to one or more few-level atoms (the Josephson junction qubits) in an electromagnetic cavity (the nanomechanical resonator). However, unlike existing approaches using atoms in electromagnetic cavities, here we can individually tune the level spacing of the ``atoms'' and control their ``electromagnetic'' interaction strength. We show theoretically that quantum states prepared in a Josephson junction can be passed to the nanomechanical resonator and stored there, and then can be passed back to the original junction or transferred to another with high fidelity. The resonator can also be used to produce maximally entangled Bell states between a pair of Josephson junctions. Many such junction-resonator complexes can be assembled in a hub-and-spoke layout, resulting in a large-scale quantum circuit. Our proposed architecture combines desirable features of both solid-state and cavity quantum electrodynamics approaches, and could make quantum-information processing possible in a scalable, solid-state environment.

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Quantum computing & quantum information

Tommy Andersson, Håkan Carlsson, Anders Martinsson +2 more

This report is an introduction to quantum computation and quantum information.\nWe present a two-part theory section followed by data analysis of a transmon qubit.\nThe ¯rst theory part, needed for the analysis, introduces fundamental properties of\nqubit states and the Bloch sphere description. The qubit manipulation, interaction\nwith a electromagnetic ¯eld, is then studied in the Rabi model (semi-classical) and the\nJaynes-Cummings model (fully quantized). The second theory part is a qualitative\npresentation of the density matrix representation, decoherence (e®ects of noise) and\nread-out, which are useful topics in more advanced analysis.\nWe also present a summary of qubit realizations, with focus on the superconduct-\ning qubits: charge, phase and transmon.\nIn the last part of the report, we analyze spectroscopic measurements on a trans-\nmon qubit in a cavity resonator, performed atMC2 Chalmers. The data was compared\nto the expected behavior from the Jaynes-Cummings Hamiltonian and then the full\nHamiltonian for the transmon. The comparison enabled us to extract the parame-\nters of the transmon. The ratio of the Josephson energy and the charge energy was\ndetermined to be EJ=EC = 34:5644 § 0:9456 GHz, which is in the transmon regime.\nFurthermore, the coupling strength between the cavity resonator and the qubit was\ndetermined to be 2¯eV 0\nrms = 0:1301 § 0:00095 GHz, with a 68% con¯dence interval.

•Jan 1, 2010•3 citations
We describe the design for a scalable, solid-state quantum-information-processing architecture based on the integration of GHz-frequency nanomechanical resonators with Josephson tunnel junctions, which has the potential for demonstrating a variety of single- and multiqubit operations critical to quantum computation. The computational qubits are eigenstates of large-area, current-biased Josephson junctions, manipulated and measured using strobed external circuitry. Two or more of these phase qubits are capacitively coupled to a high-quality-factor piezoelectric nanoelectromechanical disk resonator, which forms the backbone of our architecture, and which enables coherent coupling of the qubits. The integrated system is analogous to one or more few-level atoms (the Josephson junction qubits) in an electromagnetic cavity (the nanomechanical resonator). However, unlike existing approaches using atoms in electromagnetic cavities, here we can individually tune the level spacing of the ``atoms'' and control their ``electromagnetic'' interaction strength. We show theoretically that quantum states prepared in a Josephson junction can be passed to the nanomechanical resonator and stored there, and then can be passed back to the original junction or transferred to another with high fidelity. The resonator can also be used to produce maximally entangled Bell states between a pair of Josephson junctions. Many such junction-resonator complexes can be assembled in a hub-and-spoke layout, resulting in a large-scale quantum circuit. Our proposed architecture combines desirable features of both solid-state and cavity quantum electrodynamics approaches, and could make quantum-information processing possible in a scalable, solid-state environment.
We propose an active mechanism for coupling the quantized mode of a nanomechanical resonator to the persistent current in the loop of a superconducting Josephson junction (or phase slip) flux qubit. This coupling is independently controlled by an external coupling magnetic field. The whole system forms a novel solid-state cavity quantum electrodynamics (QED) architecture in the strong coupling limit. This architecture can be used to demonstrate quantum optics phenomena and coherently manipulate the qubit for quantum information processing. The coupling mechanism is applicable for more generalized situations where the superconducting Josephson junction system is a multi-level system. We also address the practical issues concerning experimental realization.
This report is an introduction to quantum computation and quantum information.\nWe present a two-part theory section followed by data analysis of a transmon qubit.\nThe ¯rst theory part, needed for the analysis, introduces fundamental properties of\nqubit states and the Bloch sphere description. The qubit manipulation, interaction\nwith a electromagnetic ¯eld, is then studied in the Rabi model (semi-classical) and the\nJaynes-Cummings model (fully quantized). The second theory part is a qualitative\npresentation of the density matrix representation, decoherence (e®ects of noise) and\nread-out, which are useful topics in more advanced analysis.\nWe also present a summary of qubit realizations, with focus on the superconduct-\ning qubits: charge, phase and transmon.\nIn the last part of the report, we analyze spectroscopic measurements on a trans-\nmon qubit in a cavity resonator, performed atMC2 Chalmers. The data was compared\nto the expected behavior from the Jaynes-Cummings Hamiltonian and then the full\nHamiltonian for the transmon. The comparison enabled us to extract the parame-\nters of the transmon. The ratio of the Josephson energy and the charge energy was\ndetermined to be EJ=EC = 34:5644 § 0:9456 GHz, which is in the transmon regime.\nFurthermore, the coupling strength between the cavity resonator and the qubit was\ndetermined to be 2¯eV 0\nrms = 0:1301 § 0:00095 GHz, with a 68% con¯dence interval.