### 3137 results for qubit oscillator frequency

Contributors: Fedorov, Kirill

Date: 2013-01-01

This thesis presents experimental studies on developing of a novel fluxon readout for superconducting flux **qubits**. It is based on a scheme for detecting the microwave radiation of an **oscillating** fluxon in an annular Josephson junction (AJJ). The readout was implemented for a superconducting flux **qubit** coupled as a current dipole to the AJJ. An energy spectrum of the flux **qubit** was measured via detecting a **frequency** shift of the fluxon **oscillations** versus a flux bias through the **qubit**....**qubits** ... This thesis presents experimental studies on developing of a novel fluxon readout for superconducting flux **qubits**. It is based on a scheme for detecting the microwave radiation of an **oscillating** fluxon in an annular Josephson junction (AJJ). The readout was implemented for a superconducting flux **qubit** coupled as a current dipole to the AJJ. An energy spectrum of the flux **qubit** was measured via detecting a **frequency** shift of the fluxon **oscillations** versus a flux bias through the **qubit**.

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Contributors: Eugene Grichuk, Margarita Kuzmina, Eduard Manykin

Date: 2010-09-26

A network of coupled stochastic **oscillators** is
proposed for modeling of a cluster of entangled **qubits** that is
exploited as a computation resource in one-way quantum
computation schemes. A **qubit** model has been designed as a
stochastic **oscillator** formed by a pair of coupled limit cycle
**oscillators** with chaotically modulated limit cycle radii and
**frequencies**. The **qubit** simulates the behavior of electric field of
polarized light beam and adequately imitates the states of two-level
quantum system. A cluster of entangled **qubits** can be associated
with a beam of polarized light, light polarization degree being
directly related to cluster entanglement degree. Oscillatory network,
imitating **qubit** cluster, is designed, and system of equations for
network dynamics has been written. The constructions of one-**qubit**
gates are suggested. Changing of cluster entanglement degree caused
by measurements can be exactly calculated....network of stochastic **oscillators** ... A network of coupled stochastic **oscillators** is
proposed for modeling of a cluster of entangled **qubits** that is
exploited as a computation resource in one-way quantum
computation schemes. A **qubit** model has been designed as a
stochastic **oscillator** formed by a pair of coupled limit cycle
**oscillators** with chaotically modulated limit cycle radii and
**frequencies**. The **qubit** simulates the behavior of electric field of
polarized light beam and adequately imitates the states of two-level
quantum system. A cluster of entangled **qubits** can be associated
with a beam of polarized light, light polarization degree being
directly related to cluster entanglement degree. Oscillatory network,
imitating **qubit** cluster, is designed, and system of equations for
network dynamics has been written. The constructions of one-**qubit**
gates are suggested. Changing of cluster entanglement degree caused
by measurements can be exactly calculated.

Data types:

Contributors: Rastelli, Gianluca, Vanević, Mihajlo, Belzig, Wolfgang

Date: 2015-01-01

We analyze the coherent dynamics of a fluxonium device (Manucharyan et al 2009 Science 326 113) formed by a superconducting ring of Josephson junctions in which strong quantum phase fluctuations are localized exclusively on a single weak element. In such a system, quantum phase tunnelling by occurring at the weak element couples the states of the ring with supercurrents circulating in opposite directions, while the rest of the ring provides an intrinsic electromagnetic environment of the **qubit**. Taking into account the capacitive coupling between nearest neighbors and the capacitance to the ground, we show that the homogeneous part of the ring can sustain electrodynamic modes which couple to the two levels of the flux **qubit**. In particular, when the number of Josephson junctions is increased, several low-energy modes can have **frequencies** lower than the **qubit** **frequency**. This gives rise to a quasiperiodic dynamics, which manifests itself as a decay of **oscillations** between the two counterpropagating current states at short times, followed by **oscillation**-like revivals at later times. We analyze how the system approaches such a dynamics as the ring's length is increased and discuss possible experimental implications of this non-adiabatic regime. ... We analyze the coherent dynamics of a fluxonium device (Manucharyan et al 2009 Science 326 113) formed by a superconducting ring of Josephson junctions in which strong quantum phase fluctuations are localized exclusively on a single weak element. In such a system, quantum phase tunnelling by occurring at the weak element couples the states of the ring with supercurrents circulating in opposite directions, while the rest of the ring provides an intrinsic electromagnetic environment of the **qubit**. Taking into account the capacitive coupling between nearest neighbors and the capacitance to the ground, we show that the homogeneous part of the ring can sustain electrodynamic modes which couple to the two levels of the flux **qubit**. In particular, when the number of Josephson junctions is increased, several low-energy modes can have **frequencies** lower than the **qubit** **frequency**. This gives rise to a quasiperiodic dynamics, which manifests itself as a decay of **oscillations** between the two counterpropagating current states at short times, followed by **oscillation**-like revivals at later times. We analyze how the system approaches such a dynamics as the ring's length is increased and discuss possible experimental implications of this non-adiabatic regime.

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Contributors: Johnson, Kale Gifford

Date: 2016-01-01

Since the dawn of quantum information science, laser-cooled trapped atomic ions have been one of the most compelling systems for the physical realization of a quantum computer. By applying **qubit** state dependent forces to the ions, their collective motional modes can be used as a bus to realize entangling quantum gates. Ultrafast state-dependent kicks [1] can provide a universal set of quantum logic operations, in conjunction with ultrafast single **qubit** rotations [2], which uses only ultrafast laser pulses. This may present a clearer route to scaling a trapped ion processor [3]. In addition to the role that spin-dependent kicks (SDKs) play in quantum computation, their utility in fundamental quantum mechanics research is also apparent. In this thesis, we present a set of experiments which demonstrate some of the principle properties of SDKs including ion motion independence (we demonstrate single ion thermometry from the ground state to near room temperature and the largest Schrodinger cat state ever created in an **oscillator**), high speed operations (compared with conventional atom-laser interactions), and multi-**qubit** entanglement operations with speed that is not fundamentally limited by the trap **oscillation** **frequency**. We also present a method to provide higher stability in the radial mode ion **oscillation** **frequencies** of a linear radiofrequency (rf) Paul trap--a crucial factor when performing operations on the rf-sensitive modes. Finally, we present the highest atomic position sensitivity measurement of an isolated atom to date of ~0.5 nm Hz^(-1/2) with a minimum uncertainty of 1.7 nm using a 0.6 numerical aperature (NA) lens system, along with a method to correct aberrations and a direct position measurement of ion micromotion (the inherent **oscillations** of an ion trapped in an **oscillating** rf field). This development could be used to directly image atom motion in the quantum regime, along with sensing forces at the yoctonewton [10^(-24) N)] scale for gravity sensing, and 3D imaging of atoms from static to higher **frequency** motion. These ultrafast atomic **qubit** manipulation tools demonstrate inherent advantages over conventional techniques, offering a fundamentally distinct regime of control and speed not previously achievable. ... Since the dawn of quantum information science, laser-cooled trapped atomic ions have been one of the most compelling systems for the physical realization of a quantum computer. By applying **qubit** state dependent forces to the ions, their collective motional modes can be used as a bus to realize entangling quantum gates. Ultrafast state-dependent kicks [1] can provide a universal set of quantum logic operations, in conjunction with ultrafast single **qubit** rotations [2], which uses only ultrafast laser pulses. This may present a clearer route to scaling a trapped ion processor [3]. In addition to the role that spin-dependent kicks (SDKs) play in quantum computation, their utility in fundamental quantum mechanics research is also apparent. In this thesis, we present a set of experiments which demonstrate some of the principle properties of SDKs including ion motion independence (we demonstrate single ion thermometry from the ground state to near room temperature and the largest Schrodinger cat state ever created in an **oscillator**), high speed operations (compared with conventional atom-laser interactions), and multi-**qubit** entanglement operations with speed that is not fundamentally limited by the trap **oscillation** **frequency**. We also present a method to provide higher stability in the radial mode ion **oscillation** **frequencies** of a linear radiofrequency (rf) Paul trap--a crucial factor when performing operations on the rf-sensitive modes. Finally, we present the highest atomic position sensitivity measurement of an isolated atom to date of ~0.5 nm Hz^(-1/2) with a minimum uncertainty of 1.7 nm using a 0.6 numerical aperature (NA) lens system, along with a method to correct aberrations and a direct position measurement of ion micromotion (the inherent **oscillations** of an ion trapped in an **oscillating** rf field). This development could be used to directly image atom motion in the quantum regime, along with sensing forces at the yoctonewton [10^(-24) N)] scale for gravity sensing, and 3D imaging of atoms from static to higher **frequency** motion. These ultrafast atomic **qubit** manipulation tools demonstrate inherent advantages over conventional techniques, offering a fundamentally distinct regime of control and speed not previously achievable.

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Contributors: Ying-Jie Chen, Hai-Tao Song, Jing-Lin Xiao

Date: 2017-10-14

Temperature effects on polaron in triangular quantum dot **qubit** subjected to an electromagnetic field are studied.
We derive the numerical results and formulate the derivative relationships of the ground and first
excited state energies, the electron probability density and the electron **oscillating** period in the superposition state of
the ground state and the first-excited state with the temperature, the cyclotron **frequency**, the electron-phonon coupling
constant, the electric field strength, the confinement strength and the Coulomb impurity potential, respectively....6-The electron **oscillating** period as functions of the temperature and the cyclotron **frequency** in triangular quantum dot **qubit** under an electric field.docx...7-The electron **oscillating** period as functions of the temperature and the electron-phonon coupling constant and etc. in triangular quantum dot **qubit** under an electric field.docx...2-The first excited state energy as functions of the temperature and the cyclotron **frequency** in triangular quantum dot **qubit** under an electric field.docx...3-The ground state energy as functions of the temperature and the electron-phonon coupling constant and etc. in triangular quantum dot **qubit** under an electric field.docx...1-The ground state energy as functions of the temperature and the cyclotron **frequency** in triangular quantum dot **qubit** under an electric field.docx ... Temperature effects on polaron in triangular quantum dot **qubit** subjected to an electromagnetic field are studied.
We derive the numerical results and formulate the derivative relationships of the ground and first
excited state energies, the electron probability density and the electron **oscillating** period in the superposition state of
the ground state and the first-excited state with the temperature, the cyclotron **frequency**, the electron-phonon coupling
constant, the electric field strength, the confinement strength and the Coulomb impurity potential, respectively.

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Contributors: Suri, Baladitya

Date: 2015-01-01

Superconducting **qubits**...I discuss the design, fabrication and measurement at millikelvin-temperatures of Al/AlO$_x$/Al Josephson junction-based transmon **qubits** coupled to superconducting thin-film lumped element microwave resonators made of aluminum on sapphire. The resonators had a center **frequency** of around $6\,$GHz, and a total quality factor ranging from 15,000 to 70,000 for the various devices. The area of the transmon junctions was about $150\, \mathrm{nm} \times 150\, \mathrm{nm}$ and with Josephson energy $E_J$ such that $10\,\text{GHz} \leq E_J / h \leq 30\,$GHz. The charging energy of the transmons arising mostly from the large interdigital shunt capacitance, was $E_c / h \approx 300\,$MHz.
I present microwave spectroscopy of the devices in the strongly dispersive regime of circuit quantum electrodynamics. In this limit the ac Stark shift due to a single photon in the resonator is greater than the linewidth of the **qubit** transition. When the resonator is driven coherently using a coupler tone, the transmon spectrum reveals individual ``photon number'' peaks, each corresponding to a single additional photon in the resonator. Using a weighted average of the peak heights in the **qubit** spectrum, I calculated the average number of photons $\bar{n}$ in the resonator. I also observed a nonlinear variation of $\bar{n}$ with the applied power of the coupler tone $P_{rf}$. I studied this nonlinearity using numerical simulations and found good qualitative agreement with data.
In the absence of a coherent drive on the resonator, a thermal population of $5.474\,$GHz photons in the resonator, at an effective temperature of $120\,$mK resulted in a weak $n=1$ thermal photon peak in the **qubit** spectrum. In the presence of independent coupler and probe tones, the $n=1$ thermal photon peak revealed an Autler-Townes splitting. The observed effect was explained accurately using the four lowest levels of the dispersively dressed Jaynes-Cummings transmon-resonator system, and numerical simulations of the steady-state master equation for the coupled system.
I also present time-domain measurements on transmons coupled to lumped-element resonators. From $T_1$ and Rabi **oscillation** measurements, I found that my early transmon devices (called design LEv5) had lifetimes ($T_1 \sim 1\,\mu$s) limited by strong coupling to the $50\,\Omega$ transmission line. This coupling was characterized by the the rate of change of the Rabi **oscillation** **frequency** with the change in the drive voltage ($\mathrm{d}f_{Rabi}\, / \mathrm{d}V$) -- also termed the Rabi coupling to the drive. I studied the design of the transmon-resonator system using circuit analysis and microwave simulations with the aim being to reduce the Rabi coupling to the drive. By increasing the resonance **frequency** of the resonator $\omega_r/2\pi$ from 5.4$\,$GHz to 7.2$\,$GHz, lowering the coupling of the resonator to the transmission line and thereby increasing the external quality factor $Q_e$ from 20,000 to 70,000, and reducing the transmon-resonator coupling $g/2\pi$ from 70$\,$MHz to 40$\,$MHz, I reduced the Rabi coupling to the drive by an order of magnitude ($\sim$ factor of 20). The $T_1 \sim 4\,\mu$s of devices in the new design (LEv6) was longer than that of the early devices, but still much shorter than the lifetimes predicted from Rabi coupling, suggesting the presence of alternative sources of noise causing **qubit** relaxation. Microwave simulations and circuit analysis in the presence of a dielectric loss tangent $\tan \delta \simeq 5\times10^{-6}$ agree reasonably well with the measured $T_1$ values, suggesting that surface dielectric loss may be causing relaxation of transmons in the new designs. ... I discuss the design, fabrication and measurement at millikelvin-temperatures of Al/AlO$_x$/Al Josephson junction-based transmon **qubits** coupled to superconducting thin-film lumped element microwave resonators made of aluminum on sapphire. The resonators had a center **frequency** of around $6\,$GHz, and a total quality factor ranging from 15,000 to 70,000 for the various devices. The area of the transmon junctions was about $150\, \mathrm{nm} \times 150\, \mathrm{nm}$ and with Josephson energy $E_J$ such that $10\,\text{GHz} \leq E_J / h \leq 30\,$GHz. The charging energy of the transmons arising mostly from the large interdigital shunt capacitance, was $E_c / h \approx 300\,$MHz.
I present microwave spectroscopy of the devices in the strongly dispersive regime of circuit quantum electrodynamics. In this limit the ac Stark shift due to a single photon in the resonator is greater than the linewidth of the **qubit** transition. When the resonator is driven coherently using a coupler tone, the transmon spectrum reveals individual ``photon number'' peaks, each corresponding to a single additional photon in the resonator. Using a weighted average of the peak heights in the **qubit** spectrum, I calculated the average number of photons $\bar{n}$ in the resonator. I also observed a nonlinear variation of $\bar{n}$ with the applied power of the coupler tone $P_{rf}$. I studied this nonlinearity using numerical simulations and found good qualitative agreement with data.
In the absence of a coherent drive on the resonator, a thermal population of $5.474\,$GHz photons in the resonator, at an effective temperature of $120\,$mK resulted in a weak $n=1$ thermal photon peak in the **qubit** spectrum. In the presence of independent coupler and probe tones, the $n=1$ thermal photon peak revealed an Autler-Townes splitting. The observed effect was explained accurately using the four lowest levels of the dispersively dressed Jaynes-Cummings transmon-resonator system, and numerical simulations of the steady-state master equation for the coupled system.
I also present time-domain measurements on transmons coupled to lumped-element resonators. From $T_1$ and Rabi **oscillation** measurements, I found that my early transmon devices (called design LEv5) had lifetimes ($T_1 \sim 1\,\mu$s) limited by strong coupling to the $50\,\Omega$ transmission line. This coupling was characterized by the the rate of change of the Rabi **oscillation** **frequency** with the change in the drive voltage ($\mathrm{d}f_{Rabi}\, / \mathrm{d}V$) -- also termed the Rabi coupling to the drive. I studied the design of the transmon-resonator system using circuit analysis and microwave simulations with the aim being to reduce the Rabi coupling to the drive. By increasing the resonance **frequency** of the resonator $\omega_r/2\pi$ from 5.4$\,$GHz to 7.2$\,$GHz, lowering the coupling of the resonator to the transmission line and thereby increasing the external quality factor $Q_e$ from 20,000 to 70,000, and reducing the transmon-resonator coupling $g/2\pi$ from 70$\,$MHz to 40$\,$MHz, I reduced the Rabi coupling to the drive by an order of magnitude ($\sim$ factor of 20). The $T_1 \sim 4\,\mu$s of devices in the new design (LEv6) was longer than that of the early devices, but still much shorter than the lifetimes predicted from Rabi coupling, suggesting the presence of alternative sources of noise causing **qubit** relaxation. Microwave simulations and circuit analysis in the presence of a dielectric loss tangent $\tan \delta \simeq 5\times10^{-6}$ agree reasonably well with the measured $T_1$ values, suggesting that surface dielectric loss may be causing relaxation of transmons in the new designs.

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Contributors: Preskill, John

Date: 2011-01-01

We explain how continuous-variable quantum error-correcting codes can be invoked to protect quantum gates in superconducting circuits against thermal and Hamiltonian noise. The gates are executed by turning on and off a tunable Josephson coupling between an LC **oscillator** and a **qubit** or pair of quits; assuming perfect **qubits**, we show that the gate errors are exponentially small when the **oscillator**'s impedance is large in natural units. The protected gates are not computationally universal by themselves, but a scheme for universal fault-tolerant quantum computation can be constructed by combining them with unprotected noisy operations. ... We explain how continuous-variable quantum error-correcting codes can be invoked to protect quantum gates in superconducting circuits against thermal and Hamiltonian noise. The gates are executed by turning on and off a tunable Josephson coupling between an LC **oscillator** and a **qubit** or pair of quits; assuming perfect **qubits**, we show that the gate errors are exponentially small when the **oscillator**'s impedance is large in natural units. The protected gates are not computationally universal by themselves, but a scheme for universal fault-tolerant quantum computation can be constructed by combining them with unprotected noisy operations.

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Contributors: Wigger, Daniel, Schneider, Christian, Gerhardt, Stefan, Kamp, Martin, Höfling, Sven, Kuhn, Tilmann, Kasprzak, Jacek

Date: 2018-01-01

While the advanced coherent control of **qubits** is now routinely carried out in low **frequency** (GHz) systems like single spins, it is far more challenging to achieve for two-level systems in the optical domain. This is because the latter evolve typically in the THz range, calling for tools of ultrafast, coherent, nonlinear optics. Using four-wave mixing micro-spectroscopy, we here measure the optically driven Bloch vector dynamics of a single exciton confined in a semiconductor quantum dot. In a combined experimental and theoretical approach, we reveal the intrinsic Rabi **oscillation** dynamics by monitoring both central exciton quantities, i.e., its occupation and the microscopic coherence, as resolved by the four-wave mixing technique. In the **frequency** domain this **oscillation** generates the Autler-Townes splitting of the light-exciton dressed states, directly seen in the four-wave mixing spectra. We further demonstrate that the coupling to acoustic phonons strongly influences the FWM dynamics on the picosecond timescale, because it leads to transitions between the dressed states. ... While the advanced coherent control of **qubits** is now routinely carried out in low **frequency** (GHz) systems like single spins, it is far more challenging to achieve for two-level systems in the optical domain. This is because the latter evolve typically in the THz range, calling for tools of ultrafast, coherent, nonlinear optics. Using four-wave mixing micro-spectroscopy, we here measure the optically driven Bloch vector dynamics of a single exciton confined in a semiconductor quantum dot. In a combined experimental and theoretical approach, we reveal the intrinsic Rabi **oscillation** dynamics by monitoring both central exciton quantities, i.e., its occupation and the microscopic coherence, as resolved by the four-wave mixing technique. In the **frequency** domain this **oscillation** generates the Autler-Townes splitting of the light-exciton dressed states, directly seen in the four-wave mixing spectra. We further demonstrate that the coupling to acoustic phonons strongly influences the FWM dynamics on the picosecond timescale, because it leads to transitions between the dressed states.

Data types:

Contributors: Wigger, Daniel, Schneider, Christian, Gerhardt, Stefan, Kamp, Martin, Höfling, Sven, Kuhn, Tilmann, Kasprzak, Jacek

Date: 2018-01-01

While the advanced coherent control of **qubits** is now routinely carried out in low **frequency** (GHz) systems like single spins, it is far more challenging to achieve for two-level systems in the optical domain. This is because the latter evolve typically in the THz range, calling for tools of ultrafast, coherent, nonlinear optics. Using four-wave mixing micro-spectroscopy, we here measure the optically driven Bloch vector dynamics of a single exciton confined in a semiconductor quantum dot. In a combined experimental and theoretical approach, we reveal the intrinsic Rabi **oscillation** dynamics by monitoring both central exciton quantities, i.e., its occupation and the microscopic coherence, as resolved by the four-wave mixing technique. In the **frequency** domain this **oscillation** generates the Autler-Townes splitting of the light-exciton dressed states, directly seen in the four-wave mixing spectra. We further demonstrate that the coupling to acoustic phonons strongly influences the FWM dynamics on the picosecond timescale, because it leads to transitions between the dressed states. ... While the advanced coherent control of **qubits** is now routinely carried out in low **frequency** (GHz) systems like single spins, it is far more challenging to achieve for two-level systems in the optical domain. This is because the latter evolve typically in the THz range, calling for tools of ultrafast, coherent, nonlinear optics. Using four-wave mixing micro-spectroscopy, we here measure the optically driven Bloch vector dynamics of a single exciton confined in a semiconductor quantum dot. In a combined experimental and theoretical approach, we reveal the intrinsic Rabi **oscillation** dynamics by monitoring both central exciton quantities, i.e., its occupation and the microscopic coherence, as resolved by the four-wave mixing technique. In the **frequency** domain this **oscillation** generates the Autler-Townes splitting of the light-exciton dressed states, directly seen in the four-wave mixing spectra. We further demonstrate that the coupling to acoustic phonons strongly influences the FWM dynamics on the picosecond timescale, because it leads to transitions between the dressed states.

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Contributors: Suter, Dieter, Klieber, Robert, Rippe, Lars, Nilsson, Mattias, Kröll, Stefan

Date: 2005-01-01

In optically controlled quantum computers it may be favorable to address different **qubits** using light with different **frequencies**, since the optical diffraction does not then limit the distance between **qubits**. Using **qubits** that are close to each other enables **qubit**-**qubit** interactions and gate operations that are strong and fast in comparison to **qubit**-environment interactions and decoherence rates. However, as **qubits** are addressed in **frequency** space, great care has to be taken when designing the laser pulses, so that they perform the desired operation on one **qubit**, without affecting other **qubits**. Complex hyperbolic secant pulses have theoretically been shown to be excellent for such **frequency**-addressed quantum computing [I. Roos and K. Molmer, Phys. Rev. A 69, 022321 (2004)]—e.g., for use in quantum computers based on optical interactions in rare-earth-metal-ion-doped crystals. The optical transition lines of the rare-earth-metal-ions are inhomogeneously broadened and therefore the **frequency** of the excitation pulses can be used to selectively address **qubit** ions that are spatially separated by a distance much less than a wavelength. Here, **frequency**-selective transfer of **qubit** ions between **qubit** states using complex hyperbolic secant pulses is experimentally demonstrated. Transfer efficiencies better than 90% were obtained. Using the complex hyperbolic secant pulses it was also possible to create two groups of ions, absorbing at specific **frequencies**, where 85% of the ions at one of the **frequencies** was shifted out of resonance with the field when ions in the other **frequency** group were excited. This procedure of selecting interacting ions, called **qubit** distillation, was carried out in preparation for two-**qubit** gate operations in the rare-earth-metal-ion-doped crystals. The techniques for **frequency**-selective state-to-state transfer developed here may be also useful also for other quantum optics and quantum information experiments in these long-coherence-time solid-state systems. ... In optically controlled quantum computers it may be favorable to address different **qubits** using light with different **frequencies**, since the optical diffraction does not then limit the distance between **qubits**. Using **qubits** that are close to each other enables **qubit**-**qubit** interactions and gate operations that are strong and fast in comparison to **qubit**-environment interactions and decoherence rates. However, as **qubits** are addressed in **frequency** space, great care has to be taken when designing the laser pulses, so that they perform the desired operation on one **qubit**, without affecting other **qubits**. Complex hyperbolic secant pulses have theoretically been shown to be excellent for such **frequency**-addressed quantum computing [I. Roos and K. Molmer, Phys. Rev. A 69, 022321 (2004)]—e.g., for use in quantum computers based on optical interactions in rare-earth-metal-ion-doped crystals. The optical transition lines of the rare-earth-metal-ions are inhomogeneously broadened and therefore the **frequency** of the excitation pulses can be used to selectively address **qubit** ions that are spatially separated by a distance much less than a wavelength. Here, **frequency**-selective transfer of **qubit** ions between **qubit** states using complex hyperbolic secant pulses is experimentally demonstrated. Transfer efficiencies better than 90% were obtained. Using the complex hyperbolic secant pulses it was also possible to create two groups of ions, absorbing at specific **frequencies**, where 85% of the ions at one of the **frequencies** was shifted out of resonance with the field when ions in the other **frequency** group were excited. This procedure of selecting interacting ions, called **qubit** distillation, was carried out in preparation for two-**qubit** gate operations in the rare-earth-metal-ion-doped crystals. The techniques for **frequency**-selective state-to-state transfer developed here may be also useful also for other quantum optics and quantum information experiments in these long-coherence-time solid-state systems.

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