### 63162 results for qubit oscillator frequency

Contributors: Chudzicki, Christopher, Strauch, Frederick W.

Date: 2010-08-10

**frequencies** of each node, the d -dimensional hypercube can be broken up... **qubit**-compatible schemes on the hypercube of dimension d (each with N...the qubit-compatible scheme. Entanglement transfer on the complete graph...**qubits** and **oscillators**. These theoretical models are inspired by recent...**qubit**-compatible scheme (QC), one entangled pair is sent on each subcube...**frequency**; dashed lines indicate couplings between **oscillators** with different...**qubit** experiments . For the hypercube schemes, the massively parallel ...**oscillator** with a tunable **frequency**. Each line (solid or dashed) indicates...**oscillator** networks. However, as long as only one sender-receiver pair...that qubit networks behave similarly. For this reason we call the parallel...**qubits** and **oscillators**, namely **qubits** do better on average, but do not...The **qubit** curves are, from top to bottom (for small η ), numerical simulations...**qubit**-compatible schemes on the hypercube of dimension d (each with N ...**oscillator** network with m = 1 ....**qubits** and oscillators. These theoretical models are inspired by recent...superconducting qubit experiments . For the hypercube schemes, the massively...between qubits and oscillators, namely qubits do better on average, but...**oscillator** **frequencies** for each channel from adjacent channels by an amount...**oscillator** modes. We further extend this to the distribution of entanglement...the “qubit-compatible” (QC) protocol. There are some notable differences...**Qubit**, entanglement, quantum computing, superconductivity, Josephson junction...**oscillators**. Solid lines indicate couplings between **oscillators** with the ... We study the routing of quantum information in parallel on multi-dimensional networks of tunable **qubits** and **oscillators**. These theoretical models are inspired by recent experiments in superconducting circuits using Josephson junctions and resonators. We show that perfect parallel state transfer is possible for certain networks of harmonic **oscillator** modes. We further extend this to the distribution of entanglement between every pair of nodes in the network, finding that the routing efficiency of hypercube networks is both optimal and robust in the presence of dissipation and finite bandwidth.

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Contributors: Shahriar, M. S., Pradhan, Prabhakar

Date: 2002-12-19

**oscillation** from the plot in (a). (c) The time-dependence of the Rabi **frequency**. Inset: BSO as a function of the absolute phase of the field...**qubit** operations due to the Bloch-Siegert Oscillation...**frequency** is comparable to the Bohr **frequency** so that the rotating wave...low-**frequency** transitions. We present a scheme for observing this effect...**oscillation**. (b) The BSO **oscillation** (amplified scale) by itself, produced...**oscillation** is present with the Rabi **oscillation**. We discuss how the sensitivity...**Oscillation** (BSO): (a) The population of state | 1 , as a function of ... We show that if the Rabi **frequency** is comparable to the Bohr **frequency** so that the rotating wave approximation is inappropriate, an extra **oscillation** is present with the Rabi **oscillation**. We discuss how the sensitivity of the degree of excitation to the phase of the field may pose severe constraints on precise rotations of quantum bits involving low-**frequency** transitions. We present a scheme for observing this effect in an atomic beam.

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Contributors: Hausinger, Johannes, Grifoni, Milena

Date: 2010-07-30

**oscillator** **frequency** approaches unity and goes beyond. In this regime ...**oscillator** **frequency** Ω , ε = l Ω . In this case we found that the levels...**qubit**-**oscillator** detuning. Furthermore, the dynamics is not governed anymore...**frequency** peaks coming from the two dressed **oscillation** **frequencies** Ω ...**Qubit**-oscillator system: An analytical treatment of the ultra-strong coupling...**qubit** for an **oscillator** at low temperature. We consider the coupling strength...**oscillations** **frequency** Ω j l . For l being not an integer those doublets...**qubit**-oscillator detuning. Furthermore, the dynamics is not governed anymore...**qubit** for an oscillator at low temperature. We consider the coupling strength...**qubit** ( ε / Ω = 0.5 ) at resonance with the oscillator Δ b = Ω in the ...**frequencies** through a variation of the coupling....**qubit** ( ε / Ω = 0.5 ) at resonance with the **oscillator** Δ b = Ω in the ...**frequency** range. The lowest **frequency** peaks originate from transitions...**qubit** tunneling matrix element $\Delta$ we are able to enlarge the regime...**oscillations**. With increasing time small differences between numerical...**oscillation** **frequency** Ω j 0 . Numerical calculations and VVP predict group...**oscillation** **frequencies** Ω j 1 and Ω j 2 influence the longtime dynamics...**qubit** ( ε / Ω = 0.5 ) being at resonance with the **oscillator** ( Δ b = Ω ... We examine a two-level system coupled to a quantum **oscillator**, typically representing experiments in cavity and circuit quantum electrodynamics. We show how such a system can be treated analytically in the ultrastrong coupling limit, where the ratio $g/\Omega$ between coupling strength and **oscillator** **frequency** approaches unity and goes beyond. In this regime the Jaynes-Cummings model is known to fail, because counter-rotating terms have to be taken into account. By using Van Vleck perturbation theory to higher orders in the **qubit** tunneling matrix element $\Delta$ we are able to enlarge the regime of applicability of existing analytical treatments, including in particular also the finite bias case. We present a detailed discussion on the energy spectrum of the system and on the dynamics of the **qubit** for an **oscillator** at low temperature. We consider the coupling strength $g$ to all orders, and the validity of our approach is even enhanced in the ultrastrong coupling regime. Looking at the Fourier spectrum of the population difference, we find that many **frequencies** are contributing to the dynamics. They are gathered into groups whose spacing depends on the **qubit**-**oscillator** detuning. Furthermore, the dynamics is not governed anymore by a vacuum Rabi splitting which scales linearly with $g$, but by a non-trivial dressing of the tunneling matrix element, which can be used to suppress specific **frequencies** through a variation of the coupling.

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Contributors: Du, Lingjie, Yu, Yang

Date: 2010-12-13

between a **qubit** and an electromagnetic system (such as the environment...**qubit** are identical **with **Fig. 4 (a)....**qubit** but also the systems with no crossover structure, e.g. phase **qubits**...of a flux **qubit**. The dotted curve represents the strong driving field ...**oscillation** induced interference. (a) describes the transition from state...**frequency** of the bath. In addition, we demonstrate the relaxation can ...**oscillation**, resulting respectively from the multi- or single-mode interaction...**qubit**. The dotted curve represents the strong driving field A cos ω t ...**qubit** and an electromagnetic system (such as the environment bath or a...**with **the **qubit**. (b). Quantum tunnel coupling exists between states | 0...**qubits**. The interaction between **qubits** and electromagnetic fields can ...**oscillation**, Rabi **oscillation** induced interference involves more complicated...**qubit**, with more controllable parameters including the strength and position...**qubit**. (b). Quantum tunnel coupling exists between states | 0 and | 1 ...final **qubit** population versus energy detuning and microwave amplitude....**qubit** states, leading to quantum interference in a microwave driven **qubit**...**qubit** are identical with Fig. 4 (a)....**qubits** and their environment. It also supplies a useful tool to characterize...**qubits** ... We study electromagnetically induced interference at superconducting **qubits**. The interaction between **qubits** and electromagnetic fields can provide additional coupling channels to **qubit** states, leading to quantum interference in a microwave driven **qubit**. In particular, the interwell relaxation or Rabi **oscillation**, resulting respectively from the multi- or single-mode interaction, can induce effective crossovers. The environment is modeled by a multi-mode thermal bath, generating the interwell relaxation. Relaxation induced interference, independent of the tunnel coupling, provides deeper understanding to the interaction between the **qubits** and their environment. It also supplies a useful tool to characterize the relaxation strength as well as the characteristic **frequency** of the bath. In addition, we demonstrate the relaxation can generate population inversion in a strongly driving two-level system. On the other hand, different from Rabi **oscillation**, Rabi **oscillation** induced interference involves more complicated and modulated photon exchange thus offers an alternative means to manipulate the **qubit**, with more controllable parameters including the strength and position of the tunnel coupling. It also provides a testing ground for exploring nonlinear quantum phenomena and quantum state manipulation, in not only the flux **qubit** but also the systems with no crossover structure, e.g. phase **qubits**.

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Contributors: Agarwal, S., Rafsanjani, S. M. Hashemi, Eberly, J. H.

Date: 2012-01-13

**qubit** case....**qubit** system is extended to the multi-**qubit** case. For a two-**qubit** system...**qubits** are quasi-degenerate, i.e., with **frequencies** much smaller than ...**qubit**-**qubit** entanglement. Both number state and coherent state preparations...**qubits** are much smaller than the oscillator frequency and the coupling...**oscillator** **frequency**, ω 0 ≪ ω , while the coupling between the **qubits** ... a single qubit....two-qubit case. Qualitative differences between the single-qubit and the...**frequencies** of **oscillation**, 2 Ω N ω and 2 2 Ω N ω . Since three new basis...**oscillator** state with the lowest of the S x states. Note the breakup in... of two-qubit TC model derived within the RWA is valid. At resonance, ...**qubit** system as a consequence of having only one Rabi **frequency** in the...that the two-qubit analytic formula matches well to the corresponding ...**oscillator**. For an **oscillator** of mass M and **frequency** ω the zero point...one-**qubit** and (b.) two-**qubit** probability dynamics, and (c.) shows that... (a.) one-qubit and (b.) two-qubit probability dynamics, and (c.) shows... for the single qubit case....**frequencies** of the **qubits** are much smaller than the **oscillator** **frequency**...**qubit** interacting with a common **oscillator** mode is extended beyond the...single-**qubit** case where only one Rabi **frequency** determines the evolution...single qubit case....multi-qubit cases are highlighted. In particular, we study the collapse...to the two-qubit case. Qualitative differences between the single-qubit...**qubit** interacting with a common oscillator mode is extended beyond the...**qubits**...**qubit**....two-qubit case (Fig. f.collapse_revival_double). The RWA fails to describe...two-**qubit** dynamics that are different from the single **qubit** case, including ... The Tavis-Cummings model for more than one **qubit** interacting with a common **oscillator** mode is extended beyond the rotating wave approximation (RWA). We explore the parameter regime in which the **frequencies** of the **qubits** are much smaller than the **oscillator** **frequency** and the coupling strength is allowed to be ultra-strong. The application of the adiabatic approximation, introduced by Irish, et al. (Phys. Rev. B \textbf{72}, 195410 (2005)), for a single **qubit** system is extended to the multi-**qubit** case. For a two-**qubit** system, we identify three-state manifolds of close-lying dressed energy levels and obtain results for the dynamics of intra-manifold transitions that are incompatible with results from the familiar regime of the RWA. We exhibit features of two-**qubit** dynamics that are different from the single **qubit** case, including calculations of **qubit**-**qubit** entanglement. Both number state and coherent state preparations are considered, and we derive analytical formulas that simplify the interpretation of numerical calculations. Expressions for individual collapse and revival signals of both population and entanglement are derived.

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### Temperature square dependence of the low **frequency** 1/f charge noise in the Josephson junction **qubits**

Contributors: Astafiev, O., Pashkin, Yu. A., Nakamura, Y., Yamamoto, T., Tsai, J. S.

Date: 2006-04-04

**qubits**, we study temperature dependence of the 1/f noise and decay of ...of qubit dephasing during coherent oscillations. The coherent oscillations...**oscillations**. T^2 dependence of the 1/f noise is experimentally demonstrated...**oscillations** decay as exp - t 2 / 2 T 2 * 2 with...**frequency** 1/f noise and the quantum f noise recently measured in the Josephson...**qubits** off the electrostatic energy degeneracy point is consistently explained...**frequency** independent in the measured **frequency** range (and usually do ...**qubit** as an SET and measure the low **frequency** charge noise, which causes...**oscillations** measured at T = 50 mK and the dashed envelope exemplifies...**qubit** as an SET and measure the low frequency charge noise, which causes...**frequency** 1/f noise that is observed in the transport measurements....**oscillation** as a function of t away from the degeneracy point ( θ ≠ π ...**qubits**...**qubit** dephasing during coherent **oscillations**. The coherent **oscillations** ... To verify the hypothesis about the common origin of the low **frequency** 1/f noise and the quantum f noise recently measured in the Josephson charge **qubits**, we study temperature dependence of the 1/f noise and decay of coherent **oscillations**. T^2 dependence of the 1/f noise is experimentally demonstrated, which supports the hypothesis. We also show that dephasing in the Josephson charge **qubits** off the electrostatic energy degeneracy point is consistently explained by the same low **frequency** 1/f noise that is observed in the transport measurements.

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Contributors: Zueco, David, Reuther, Georg M., Kohler, Sigmund, Hänggi, Peter

Date: 2009-07-20

**Oscillator** **frequency** shift as function or the **qubit** splitting ϵ = ω + ...**qubit** splitting ϵ = ω + Δ for the spin state | ↓ obtained (a) within RWA...**qubit** state | ↓ ....**qubit**-**oscillator** coupling, we diagonalize the non-RWA Hamiltonian and ...**qubit** readout is possible. If several **qubits** are coupled to one resonator...**qubit**-**qubit** interaction of Ising type emerges, whereas RWA leads to isotropic...**qubits**....**Qubit**-oscillator dynamics in the dispersive regime: analytical theory ...**qubit**-oscillator coupling, we diagonalize the non-RWA Hamiltonian and ...**of** the **qubit** state | ↓ ....**qubit** state | ↓ , where σ z | ↓ = - | ↓ . The results are depicted in ... We generalize the dispersive theory of the Jaynes-Cummings model beyond the frequently employed rotating-wave approximation (RWA) in the coupling between the two-level system and the resonator. For a detuning sufficiently larger than the **qubit**-**oscillator** coupling, we diagonalize the non-RWA Hamiltonian and discuss the differences to the known RWA results. Our results extend the regime in which dispersive **qubit** readout is possible. If several **qubits** are coupled to one resonator, an effective **qubit**-**qubit** interaction of Ising type emerges, whereas RWA leads to isotropic interaction. This impacts on the entanglement characteristics of the **qubits**.

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Contributors: Kim, Mun Dae

Date: 2008-09-02

**oscillating** field it is shown that the high fidelity of the CNOT gate ... qubits. (b) Occupation probabilities of | ρ ρ ' states during Rabi-type...coupled-**qubit** states with the initial state, | ψ 0 = | 00 + | 10 / 2 for...**Qubits**...two-**qubit** **oscillation** deviates seriously from the Rabi **oscillation** and...**oscillations** of occupation probability of coupled-**qubit** states with the...**oscillating** field amplitude for any given values of **qubit** energy gap and...**oscillation**. Here, the unit of all numbers is GHz....**qubit** energy gap ω 0 . For small ω 0 and large J the **oscillations** are ... **qubit** energy gap ω 0 / 2 π =4GHz, and Rabi frequency Ω 0 / 2 π = 600 ...that the target qubit flips for a specific state of control qubit such...**oscillating** field with the resonant **frequency** ω = ω 0 < ω 1 ....values of qubit energy gap and coupling strength between qubits. While... qubits, where ρ , ρ ' ∈ 0 1 . E s s ' with s , s ' ∈ are shown as thin...coupled-**qubit** oscillation driven by an oscillating field. When the period...**qubit** energy gap ω 0 . For small ω 0 and large J the oscillations are ...**qubit** energy gap ω 0 / 2 π =4GHz, and Rabi **frequency** Ω 0 / 2 π = 600 MHz...coupled-**qubit** **oscillation** driven by an **oscillating** field. When the period...**qubit** energy gap in experiments....**oscillation** for strongly coupled **qubits**. While the P 00 ( P 01 ) is reversed...**oscillation**, we show that the controlled-NOT (CNOT) gate operation can...two-qubit oscillation deviates seriously from the Rabi oscillation and...**oscillations**, while for a sufficiently strong coupling it can be done ...**qubits**, where ρ , ρ ' ∈ 0 1 . E s s ' with s , s ' ∈ are shown as thin...to shift the qubits slightly away from the degeneracy point to detect ... We study the coupled-**qubit** **oscillation** driven by an **oscillating** field. When the period of the non-resonant mode is commensurate with that of the resonant mode of the Rabi **oscillation**, we show that the controlled-NOT (CNOT) gate operation can be demonstrated. For a weak coupling the CNOT gate operation is achievable by the commensurate **oscillations**, while for a sufficiently strong coupling it can be done for arbitrary parameter values. By finely tuning the amplitude of **oscillating** field it is shown that the high fidelity of the CNOT gate can be obtained for any fixed coupling strength and **qubit** energy gap in experiments.

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Contributors: Huang, Ren-Shou, Dobrovitski, Viatcheslav, Harmon, Bruce

Date: 2005-04-18

one qubit coupled with 14 spins at T = 200 mK and T = 10 mK. The left ...**qubit** decohered by many spins undergoing Rabi **oscillation** by a coherent...where the qubit is coupled to a spurious resonator, and the dotted line...result **of a **qubit dephased by 14 spins with and without a spurious resonator...**frequency** ω = 2 α . At high **frequency** the Fourier spectrum is dominated...result produced by a qubit under the direct influence** of** 1/f noise. In...**oscillations** of a **qubit** dephased and relaxed by a many-spin system. The...**qubits** have suggested the existence in the tunnel barrier of bistable ... of the qubit transition frequency. Here this situation is numerically...**qubit** transition **frequency**. Here this situation is numerically simulated...is the qubit and the resonator peak is barely visible. When the qubit ...**oscillation** of one **qubit** coupled with 14 spins at T = 200 mK and T = 10...spectroscopic data** of** the qubit transition frequency. Here this situation...**qubit** and the resonator peak is barely visible. When the **qubit** energy ...**oscillations** of the **qubit** exhibit multiple stages of decay. New approaches...**qubit** exhibit multiple stages of decay. New approaches are established...**qubit** coupled to a spurious resonator is also studied, where we proposed...**qubit** dephased by 14 spins with and without a spurious resonator, which...oscillations **of a **qubit dephased and relaxed by a many-spin system. The...**oscillation** of a **qubit** coupled to a spurious resonator is also studied...**oscillation**....of the qubit decohered by many spins undergoing Rabi oscillation by a ... a qubit dephased and relaxed by a many-spin system. The parameters are...**qubit** under the direct influence of 1/f noise. In the graph of the Fourier...**Qubit** Rabi Oscillation Decohered by Many Two-Level Systems ... Recent experiments on Josephson junction **qubits** have suggested the existence in the tunnel barrier of bistable two level fluctuators that are responsible for decoherence and 1/f critical current noise. In this article we treat these two-level systems as fictitious spins and investigate their influence quantum mechanically with both analytical and numerical means. We find that the Rabi **oscillations** of the **qubit** exhibit multiple stages of decay. New approaches are established to characterize different decoherence times and to allow for easier feature extraction from experimental data. The Rabi **oscillation** of a **qubit** coupled to a spurious resonator is also studied, where we proposed an idea to explain the serious deterioration of the Rabi osillation amplitude.

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Contributors: Zorin, A. B.

Date: 2003-12-09

**qubit** state with the rf oscillation span ± π / 2 is preferable in either...**frequency** ω r f ≈ ω 0 , the resonant **frequency** of the uncoupled tank circuit...**frequency** ω 0 = 2 π × 100 MHz, L T / C T 1 / 2 = 100 Ω , k 2 Q β L = ...lines). The **qubit** parameters are the same as in Fig. 2....**qubit** state with the rf **oscillation** span ± π / 2 is preferable in either...radio-**frequency** readout of the **qubit**. (a) The resonance curves of the ...**qubit** based on a superconducting single charge transistor inserted in ...states of the **qubit**....**given** **qubit** parameters (see caption of Fig. 2)....**qubit** whose value, as well as the produced **frequency** shift δ ω 0 , is ...The **qubit** is controlled by charge Q 0 generated by the gate and flux Φ...charge-flux **qubit** are characterized by self-capacitances C 1 and C 2 and...**oscillations** induced in the **qubit**. Recently, we proposed a transistor ...**frequency** of these **oscillations** is sufficiently low, ω r f ≪ Ω , they ...**qubit** whose value, as well as the produced frequency shift δ ω 0 , is ...**e for** the **given** **qubit** parameters (see caption of Fig. 2)....**qubit** dephasing and relaxation due to electric and magnetic control lines...**qubit** states by measuring the effective Josephson inductance of the transistor...**qubit** dephasing is of minor importance, while the requirement of a sufficiently...**qubit** in magic points producing minimum decoherence are given....**qubit** parameters are the same as in Fig. 2....radio-**frequency** driven tank circuit enabling the readout of the **qubit** ...**qubit** calculated for the mean Josephson coupling E J 0 ≡ 1 2 E J 1 + E...**frequency** Ω . Increase in amplitude of steady **oscillations** up to φ a ≈...**oscillations** and has a small effect on the rise time of the response signal...**qubit** with radio frequency readout: coupling and decoherence ... The charge-phase Josephson **qubit** based on a superconducting single charge transistor inserted in a low-inductance superconducting loop is considered. The loop is inductively coupled to a radio-**frequency** driven tank circuit enabling the readout of the **qubit** states by measuring the effective Josephson inductance of the transistor. The effect of **qubit** dephasing and relaxation due to electric and magnetic control lines as well as the measuring system is evaluated. Recommendations for operation of the **qubit** in magic points producing minimum decoherence are given.

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