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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Quantum Information Processing with Superconducting Qubits and Cavities

Andreas J. Wallraff, David Schuster, Alexandre Blais, Jay Gambetta, Andrew Houck, J. A. Schreier, B. Johnsson, Jerry M. Chow, Luigi Frunzio, Johannes Majer, Michel Devoret, S. M. Girvin, Robert J. Schoelkopf

Published Jun 1, 2007• 2 citations
Publisher

Abstract

In this paper, the coherent interaction of individual microwave photons with superconducting qubits is presented both for quantum information processing and for novel quantum optics experiments in the circuit quantum electrodynamics (QED) architecture. In the resonant regime we observe the vacuum Rabi mode splitting. In the non-resonant regime we use the dispersive coupling between the qubit and the cavity field to perform high visibility quantum non-demolition (QND) measurements of the qubit state. In the strong dispersive limit we also perform measurements of the cavity state from which the photon number statistics of the field can be extracted. Generally, the circuit QED architecture is attractive for quantum information processing and as an interface in hybrid quantum systems.

DOI
10.1109/cleoe-iqec.2007.4386783

Related papers

Quantum information processing and measurement in circuit quantum electrodynamics

Ferdinand Helmer

In this thesis, experimentally relevant aspects and open questions of quantum information processing and measurement in circuit quantum electrodynamics have been investigated theoretically. Circuit quantum electrodynamics is a relatively young field combining superconducting transmission line resonators on-chip with superconducting quantum bits which serve as artificial atoms. Remarkable experiments have underlined the prospects of circuit QED as a possible architecture for quantum information processing as well as a framework within which quantum optics experiments can be performed. In contrast to their optical counterparts, these experiments reach the ultra-strong coupling limit and allow e.g. the generation of Fock states, the study of decoherence and the observation of quantum jumps. We present the physics of superconducting circuits based on the Josephson junction as a non-linear circuit element. We discuss the various types of quantum bits (qubits) before turning to an introduction on cavity QED and conclude the introduction with a brief presentation of the most relevant experiments and a short introduction to the principles and prospects of quantum information processing. Building on the pioneering theoretical and experimental work in which up to three qubits have been integrated on a chip and successfully coupled via a cavity mode, we propose a scheme to overcome the natural limits concerning scalability in these systems. Usually, scalability is severely limited by the resonance width of the qubit transitions and the attainable frequency range for both qubit transition and cavity resonance frequencies. This limits the present setups to at most ten qubits. As a possible solution, we propose and investigate a cross-bar grid layout of cavities with qubits at the intersections. It turns out that this setup, allowing for up to about 1000 qubits, offers significant advantages over e.g. nearest-neighbor coupling schemes. In addition, it can serve as a building block for a truly scalable scheme for fault-tolerant quantum information processing with superconducting circuits by combining 7x7 arrays in a staircase manner. Furthermore, we discuss and simulate different possibilities to improve upon the suggested scheme by e.g. using resonant gates and optimal control theory. Another focus of the present thesis is measurement physics. In order to investigate e.g. the possibilities of using a circuit QED system to dispersively detect single microwave photons or to generate multi-qubit entangled states, we introduce in a pedagogical manner the basics of stochastic master equations which generate quantum trajectories before turning to concrete applications. Quantum trajectories have proven to be a state-of-the-art tool to analyze measurement situations in a very realistic manner by giving access to both the measurement record as well as the internal quantum dynamics conditioned on this record. Using the method of quantum trajectories as generated by stochastic master equations, we discuss a scheme to efficiently generate multi-qubit entangled states in a very flexible way. The method is based on a collective, dispersive qubit readout. By this measurement, a suitable product state of N qubits can be reliably converted into e.g. an N-qubit Greenberger-Horne-Zeilinger or W state. We propose and discuss the scheme and investigate the effects of decoherence and parameter spread as they would be encountered in experiment. Last but not least, we propose and fully analyze a scheme to dispersively detect single itinerant microwave photons. While experiments to generate single microwave photons have already been successfully performed, their single-shot quantum non-demolition detection has not been possible so far. The scheme presented in this thesis closes this gap in the circuit QED toolbox and reaches detection efficiencies of 30% only limited by fundamental quantum mechanics in this case the Quantum Zeno effect. This detection scheme could be used in quantum communication or quantum cryptography applications.

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S. M. Girvin, Ren-Shou Huang, Alexandre Blais +2 more

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CIRCUIT QUANTUM ELECTRODYNAMICS

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Hybrid circuit QED with spin ensembles and carbon-nanotube-based superconducting qubits

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Circuit quantum electrodynamics has received an increasing amount of attention over the last decade in light of its potential use in quantum information processing. The underlying principle of this architecture is the coherent coupling between microwave photons stored in superconducting resonators and superconducting qubits made from non-linear, non-dissipative electrical circuits. This architecture can be extended to other solid-state systems with transition frequencies in the microwave regime, such as nuclear and electron spins or Andreev bound states. These hybrid devices would allow the coherent exchange of information between such systems and superconducting qubits mediated by a microwave resonator. This could lead to advances in quantum information processing and new insights in the physics governing these interacting systems. In this dissertation experimental work with different types of hybrid quantum circuits is presented. A first experiment investigates the coherent coupling of microwave photons with a spin ensemble in a correlated and uncorrelated state. The coupling strength and magnetic resonance is studied as a function of temperature and magnetic field direction. A pronounced temperature dependent anisotropy of the magnetic resonance is observed, which can be attributed to the onset of antiferromagnetic correlations in the spin ensemble when cooled below T=4 K. A simple one-dimensional model gives a good description of this anisotropy. A next experiment studies the transport characteristics of carbon nanotubes electrically accessed with normal and superconducting contacts. These devices were characterised using both DC and RF reflectometry techniques. The carbon nanotube devices with superconducting contacts exhibit transport characteristics of Josephson junctions with critical currents of up to Ic~18 nA, as well as multiple Andreev reflections. These semiconductor-superconductor hybrid Josephson junctions are then used to realise a carbon-nanotube-based superconducting qubit with voltage tunable transition frequency using a local electrostatic gate. Strong coupling (g~100 MHz) to a coplanar waveguide resonator is demonstrated via a resonator frequency shift dependent on applied gate voltage. Qubit parameters are extracted from spectroscopy and correspond well to the DC measurements of the carbon nanotube Josephson junctions. Qubit relaxation and coherence times in the range 10-100 ns are observed. The hybrid devices investigated in this work present potential building blocks for more extensive hybrid architectures for quantum information processing.

•Jan 1, 2018•0 citations

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S. M. Girvin

A revolution is underway in the construction of ‘artificial atoms’ out of superconducting electrical circuits. ‘Circuit QED’ permits strong-coupling non-linear optics at the single-photon level and gives an architecture for novel quantum information processing. The dispersive coupling between a qubit and a microwave cavity can be orders of magnitude larger than the line widths of both qubit and cavity. This yields a new ‘quantum toolbox’ which permits arbitrary control of the entangled quantum state of the system. For example one can flip the state of the qubit conditioned on there being exactly n photons in the cavity or one can displace the cavity oscillation amplitude conditioned on the state of the qubit. Using these tools it is now possible to create large ‘Schrödinger cat’ states containing more than 100 photons. An introduction to circuit QED and a review of recent experimental results will be presented.

The Rochester Conferences on Coherence and Quantum Optics and the Quantum Information and Measurement meeting•Jan 1, 2013•0 citations
In this paper, the coherent interaction of individual microwave photons with superconducting qubits is presented both for quantum information processing and for novel quantum optics experiments in the circuit quantum electrodynamics (QED) architecture. In the resonant regime we observe the vacuum Rabi mode splitting. In the non-resonant regime we use the dispersive coupling between the qubit and the cavity field to perform high visibility quantum non-demolition (QND) measurements of the qubit state. In the strong dispersive limit we also perform measurements of the cavity state from which the photon number statistics of the field can be extracted. Generally, the circuit QED architecture is attractive for quantum information processing and as an interface in hybrid quantum systems.
In this thesis, experimentally relevant aspects and open questions of quantum information processing and measurement in circuit quantum electrodynamics have been investigated theoretically. Circuit quantum electrodynamics is a relatively young field combining superconducting transmission line resonators on-chip with superconducting quantum bits which serve as artificial atoms. Remarkable experiments have underlined the prospects of circuit QED as a possible architecture for quantum information processing as well as a framework within which quantum optics experiments can be performed. In contrast to their optical counterparts, these experiments reach the ultra-strong coupling limit and allow e.g. the generation of Fock states, the study of decoherence and the observation of quantum jumps. We present the physics of superconducting circuits based on the Josephson junction as a non-linear circuit element. We discuss the various types of quantum bits (qubits) before turning to an introduction on cavity QED and conclude the introduction with a brief presentation of the most relevant experiments and a short introduction to the principles and prospects of quantum information processing. Building on the pioneering theoretical and experimental work in which up to three qubits have been integrated on a chip and successfully coupled via a cavity mode, we propose a scheme to overcome the natural limits concerning scalability in these systems. Usually, scalability is severely limited by the resonance width of the qubit transitions and the attainable frequency range for both qubit transition and cavity resonance frequencies. This limits the present setups to at most ten qubits. As a possible solution, we propose and investigate a cross-bar grid layout of cavities with qubits at the intersections. It turns out that this setup, allowing for up to about 1000 qubits, offers significant advantages over e.g. nearest-neighbor coupling schemes. In addition, it can serve as a building block for a truly scalable scheme for fault-tolerant quantum information processing with superconducting circuits by combining 7x7 arrays in a staircase manner. Furthermore, we discuss and simulate different possibilities to improve upon the suggested scheme by e.g. using resonant gates and optimal control theory. Another focus of the present thesis is measurement physics. In order to investigate e.g. the possibilities of using a circuit QED system to dispersively detect single microwave photons or to generate multi-qubit entangled states, we introduce in a pedagogical manner the basics of stochastic master equations which generate quantum trajectories before turning to concrete applications. Quantum trajectories have proven to be a state-of-the-art tool to analyze measurement situations in a very realistic manner by giving access to both the measurement record as well as the internal quantum dynamics conditioned on this record. Using the method of quantum trajectories as generated by stochastic master equations, we discuss a scheme to efficiently generate multi-qubit entangled states in a very flexible way. The method is based on a collective, dispersive qubit readout. By this measurement, a suitable product state of N qubits can be reliably converted into e.g. an N-qubit Greenberger-Horne-Zeilinger or W state. We propose and discuss the scheme and investigate the effects of decoherence and parameter spread as they would be encountered in experiment. Last but not least, we propose and fully analyze a scheme to dispersively detect single itinerant microwave photons. While experiments to generate single microwave photons have already been successfully performed, their single-shot quantum non-demolition detection has not been possible so far. The scheme presented in this thesis closes this gap in the circuit QED toolbox and reaches detection efficiencies of 30% only limited by fundamental quantum mechanics in this case the Quantum Zeno effect. This detection scheme could be used in quantum communication or quantum cryptography applications.
We propose a realizable architecture using one-dimensional transmission line resonators to reach the strong-coupling limit of cavity quantum electrodynamics in superconducting electrical circuits. The vacuum Rabi frequency for the coupling of cavity photons to quantized excitations of an adjacent electrical circuit (qubit) can easily exceed the damping rates of both the cavity and qubit. This architecture is attractive both as a macroscopic analog of atomic physics experiments and for quantum computing and control, since it provides strong inhibition of spontaneous emission, potentially leading to greatly enhanced qubit lifetimes, allows high-fidelity quantum nondemolition measurements of the state of multiple qubits, and has a natural mechanism for entanglement of qubits separated by centimeter distances. In addition it would allow production of microwave photon states of fundamental importance for quantum communication.
We propose a realizable architecture using one-dimensional transmission line resonators to reach the strong coupling limit of cavity quantum electrodynamics in superconducting electrical circuits. The vacuum Rabi frequency for the coupling of cavity photons to quantized excitations of an adjacent electrical circuit (qubit) can easily exceed the damping rates of both the cavity and the qubit. This architecture is attractive for quantum computing and control, since it provides strong inhibition of spontaneous emission, potentially leading to greatly enhanced qubit lifetimes, allows high-fidelity quantum non-demolition measurements of the state of multiple qubits, and has a natural mechanism for entanglement of qubits separated by centimeter distances. In addition it would allow production of microwave photon states of fundamental importance for quantum communication.
Circuit Quantum Electrodynamics (cQED), the study of the interaction between superconducting circuits behaving as artificial atoms and 1-dimensional transmission-line resonators, has shown much promise for quantum information processing tasks.For the purposes of quantum computing it is usual to approximate the artificial atoms as 2-level qubits, and much effort has been expended on attempts to isolate these qubits from the environment and to invent ever more sophisticated control and measurement schemes.Rather than focussing on these technological aspects of the field, this thesis investigates the opportunities for using these carefully engineered systems for answering questions of fundamental physics.The low dissipation and small mode volume of the circuits allows easy access to the strong-coupling regime of quantum optics, where one can investigate the interaction of light and matter at the level of single atoms and photons.A signature of strong coupling is the splitting of the cavity transmission peak into a pair of resolvable peaks when a single resonant atom is placed inside the cavity-an effect known as vacuum Rabi splitting.The cQED architecture is ideally suited for going beyond this linear response effect.This thesis shows that increasing the drive power results in two unique nonlinear features in the transmitted heterodyne signal: the supersplitting of each vacuum Rabi peak into a doublet, and the appearance of additional peaks with the characteristic √ n spacing of the Jaynes-Cummings ladder.These constitute direct evidence for the coupling between the quantized microwave field and the anharmonic spectrum of a superconducting qubit acting as an artificial atom.This thesis also addresses the idea of Bell tests, which are experiments that aim to disprove certain types of classical theories, presenting a proposed method for preparing maximally entangled 3-qubit states via a 'preparation by measurement' scheme using an optimized filter on the time-dependent signal obtained via homodyne monitoring of the transmitted microwave field.
Circuit quantum electrodynamics has received an increasing amount of attention over the last decade in light of its potential use in quantum information processing. The underlying principle of this architecture is the coherent coupling between microwave photons stored in superconducting resonators and superconducting qubits made from non-linear, non-dissipative electrical circuits. This architecture can be extended to other solid-state systems with transition frequencies in the microwave regime, such as nuclear and electron spins or Andreev bound states. These hybrid devices would allow the coherent exchange of information between such systems and superconducting qubits mediated by a microwave resonator. This could lead to advances in quantum information processing and new insights in the physics governing these interacting systems. In this dissertation experimental work with different types of hybrid quantum circuits is presented. A first experiment investigates the coherent coupling of microwave photons with a spin ensemble in a correlated and uncorrelated state. The coupling strength and magnetic resonance is studied as a function of temperature and magnetic field direction. A pronounced temperature dependent anisotropy of the magnetic resonance is observed, which can be attributed to the onset of antiferromagnetic correlations in the spin ensemble when cooled below T=4 K. A simple one-dimensional model gives a good description of this anisotropy. A next experiment studies the transport characteristics of carbon nanotubes electrically accessed with normal and superconducting contacts. These devices were characterised using both DC and RF reflectometry techniques. The carbon nanotube devices with superconducting contacts exhibit transport characteristics of Josephson junctions with critical currents of up to Ic~18 nA, as well as multiple Andreev reflections. These semiconductor-superconductor hybrid Josephson junctions are then used to realise a carbon-nanotube-based superconducting qubit with voltage tunable transition frequency using a local electrostatic gate. Strong coupling (g~100 MHz) to a coplanar waveguide resonator is demonstrated via a resonator frequency shift dependent on applied gate voltage. Qubit parameters are extracted from spectroscopy and correspond well to the DC measurements of the carbon nanotube Josephson junctions. Qubit relaxation and coherence times in the range 10-100 ns are observed. The hybrid devices investigated in this work present potential building blocks for more extensive hybrid architectures for quantum information processing.
A revolution is underway in the construction of ‘artificial atoms’ out of superconducting electrical circuits. ‘Circuit QED’ permits strong-coupling non-linear optics at the single-photon level and gives an architecture for novel quantum information processing. The dispersive coupling between a qubit and a microwave cavity can be orders of magnitude larger than the line widths of both qubit and cavity. This yields a new ‘quantum toolbox’ which permits arbitrary control of the entangled quantum state of the system. For example one can flip the state of the qubit conditioned on there being exactly n photons in the cavity or one can displace the cavity oscillation amplitude conditioned on the state of the qubit. Using these tools it is now possible to create large ‘Schrödinger cat’ states containing more than 100 photons. An introduction to circuit QED and a review of recent experimental results will be presented.